distribution and a combination of normal distributions

Вычисление расстояния по Вассерштейну между распределениями вероятностей на прямой. С. С. Валландер, 824. О точном выражении уровня значимости усеченного ...
[CITATION] Вычисление расстояния по Вассерштейну между распределениями вероятностей на прямой

СС Валландер - Теория вероятностей и ее применения, 1973 - mathnet.ru

1. ВЛ Левин,“Формула для оптимального значения задачи Монжа–Канторовича с

гладкой функцией стоимости и характеризация циклически монотонных отображений”,

Матем. сб., 181: 12 (1990), 1694–1709 mathnet mathscinet zmath adsnasa; VL Levin,“A …

Leonid Vaserstein Interview

[Russian Computation of Vaserstein distance between between probability distributions on line]

1980

L Vaserstein - 1980 - ecommons.library.cornell.edu

... Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/15168. Title: Leonid

Vaserstein Interview. Authors: Vaserstein, Leonid. Issue Date: Aug-1980. URI: http://hdl.handle.

net/1813/15168. Appears in Collections: Vaserstein, Leonid N. Files in This Item: ...

by Vaserstein, Leonid

08/1980

.... Vaserstein in August 1980. The interview is in two parts.

Web ResourceCitation Online

1980 zzz zzzz

[CITATION] Leonid Vaserstein Interview

L Vaserstein - 1980 - ecommons.cornell.edu

… Account. Search Search. Browse: Communities & Collections; Issue Date;

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Help; Login. eCommons Open scholarship at Cornell. View Item: Home; Cornell University Library; …

1982

Economics and mathematical methods

- Volume 18 - Page 723 1982 -

Found inside - Page 723

Валандер С. С. Вычислеппе расстояния по Вассерштейну между распределениями вероятностей на прямой.— Теория вероятностей и ее прпменения, 1973, т. XVIII, No 4. 14. Золотарев В. М. О близости распределений двух сумм ...

<—5

1987

MR0882802 van der Kallen, Wilberd Vaserstein's pre-stabilization theorem over commutative rings. Comm. Algebra 15 (1987), no. 3, 657–663. (Reviewer: Roger C. Alperin) 18F25 (16A54 19B10)

2 Citations

Vaserstein's pre-stabilization theorem over commutative rings

by WV Der Kallen - ‎1987 - ‎Cited by 6 - ‎Related articles

51 Summary. We give a new proof of Vaserstein's Pre-stabilization theorem. This theorem ... only for commutative rings (or ideals in such rings) but it does not ...

1988

Normal subgroups of gauge groups L.N. VASERSTEIN Max ...

https://archive.mpim-bonn.mpg.de › eprint › prep...

PDF

by LN Vaserstein · 1988 · Cited by 3 — Introduction. Lie groups G have been used in mathematical physics for a long time. Recently, infinite-dimensional groups staned to appear there too'(as ...

1988

of Symplectic Groups Over Rings LN VASERSTEIN Max ...https://archive.mpim-bonn.mpg.de › preprint_198...PDFby O

Rings · Cited by 39 — Abstract. We consider a module with an alternating fonn over a commutative ring. Undcr cenain

condilions, which hold. for example, when the fonn is ...

<— 8 till 1989

1991

MR1209844 Simonot, François Analyse de la stabilité de systèmes de stockage par la métrique de Wasserstein. (French) [Analysis of the stability of storage systems using the Vaserstein metric] Statist. Anal. Données 16 (1991), no. 3, 183–201. 60K30

[PDF] Analyse de la stabilité de systèmes de stockage par la métrique de Wasserstein

F Simonot - Statistique et analyse des données, 1991 - numdam.org

Résumé Nous présentons une méthode de construction de majorants de la distance

séparant les suites stationnaires (Xn) and (Xn) engendrées par les relations Xn+j= max (X „-

Bm0)+ An et X'„+ y= max (X'n-B'n, 0)+ A'n en fonction de la distance entre les séquences de

contrôle fAft B „) et (A'n, B'n). Les distances sont évaluées en utilisant différentes métriques,

en particulier celle de Wasserstein and Lévy-Prohorov. Une attention particulière est

accordée au cas des séquences de contrôle constituées de va Li. d.

1991

MR1113961 Hinson, Edward K. On Vaserstein's power operation on elementary orbits. Comm. Algebra 19 (1991), no. 6, 1851–1854. (Reviewer: Charles Weibel) 19B99 (20H25)

On vaserstein's power operation on elementary orbits

EK Hinson - Communications in Algebra, 1991 - Taylor & Francis

Clearly I (cY) is always nonempty (as it contains 0) and I (a)= I (P) when [a]=[P) It follows by the associativity of+ that if I (Q) contains k it also contains any integer multiple of k. By Suslin's result, a sufficient condition for I (a) to contain nonzero integers is that So (n, R)= SL (n, R) or equivalently, Umc (n, R)= Moreover, $ k ([ff])=[&I] if and only if $-k ([~])=[EI] by Lemma 13.1 of [5].

Commun. Algebra 19, No. 6, 1851-1854 (1991).

<—10

1991

Hinson, Edward K.

On Vaserstein’s power operation on elementary orbits. (English) Zbl 0766.20014

Reviewer: L.N.Vaserstein and E.R.Wheland (University Park)

MSC: 20H25 20F05 05C25 20G35

On vaserstein's power operation on elementary orbits

Full Text: DOI

<—11 till 1991

1992

MR1155684 Hinson, Edward K. On Vaserstein's power operation on elementary orbits. Comm. Algebra 20 (1992), no. 1, 303–307. (Reviewer: Charles Weibel) 19B99 (20H25)

1 Citation

EK Hinson - Communications in Algebra, 1991 - Taylor & Francis

Clearly I (cY) is always nonempty (as it contains 0) and I (a)= I (P) when [a]=[P) It follows by

the associativity of+ that if I (Q) contains k it also contains any integer multiple of k. By

Suslin's result, a sufficient condition for I (a) to contain nonzero integers is that So (n, R)= SL

(n, R) or equivalently, Umc (n, R)= Moreover, $ k ([ff])=[&I] if and only if $-k ([~])=[EI] by

Lemma 13.1 of [5].

Commun. Algebra 20, No. 1, 303-307 (1992).

1992

Hinson, Edward K.

On Vaserstein’s power operation on elementary orbits. (English) Zbl 0795.20034

Reviewer: L.N.Vaserstein and E.R.Wheland (University Park)

MSC: 20H25 20F05 05C25 20G35

n vaserstein's power operation on elementary orbits

Full Text: DOI

1992

EK Hinson - Communications in algebra, 1992 - Taylor & Francis

Clearly I (a) is always nonempty (as it contains 0) and I (a)= I (@) when [a]=[PI. It follows by the associativity of $ that if I (a) contains k it also contains any integer multiple of k. By Suslin's result, a sufficient condition for I (a) to contain nonzero integers is that So (n, R)= SL (n, R) or equivalently, Umc (n, R)= Moreover, & ([a])=[cl] if and only if $-k ([or])=[cl] by Lemma 13.1 of [5].

1992
On vaserstein's power operation on elementary orbits

EK Hinson - Communications in algebra, 20:1 1992 - Taylor & Francis

Clearly I (a) is always nonempty (as it contains 0) and I (a)= I (@) when [a]=[PI. It follows by

the associativity of $ that if I (a) contains k it also contains any integer multiple of k. By

Suslin's result, a sufficient condition for I (a) to contain nonzero integers is that So (n, R)= SL

(n, R) or equivalently, Umc (n, R)= Moreover, & ([a])=[cl] if and only if $-k ([or])=[cl] by Lemma

13.1 of [5].

关于一个 Vaserstein 问题

[CITATION] ON VASERSTEIN POWER OPERATION ON ELEMENTARY ORBITS

EK HINSON - COMMUNICATIONS IN ALGEBRA, 1991 - MARCEL DEKKER INC 270 …

<—15 till 1992

1994

MR1352866 Zhang, Zhao Ji On a problem of Vaserstein. (Chinese) Zhejiang Daxue Xuebao Ziran Kexue Ban 28 (1994), no. 5, 608–611. (Reviewer: Qi Sun) 11C20 (11A05)

Vaserstein asked whether, for any given integer p and any matrix A in Mn(Z), there are x, y in Mn(Z) such that (1) x+y=A and det(x)=det(y)=p, where Mn(Z) denotes the ring of n×n integral matrices.

In this paper, the author proves that if n is even, then (1) holds and if n is odd, then (1) holds iff 2p is divisible by the gcd of all elements of A. Hence Vaserstein's problem is solved.

The reviewer asks whether, for any given integers p, q and any matrix A in Mn(Z), there are x, y in Mn(Z) such that x+y=A and det(x)=p, det(y)=q.

Reviewed by Qi Sun

Zbl 0838.11022

1994

关于一个 Vaserstein 问题 [Chonese About a Vaserstein question]

张兆基 - 浙江大学学报: 自然科学版, 1994 - cqvip.com

张兆基 - 浙江大学学报: 自然科学版, 1994 - cqvip.com

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> 《中文科技期刊数据库》 > 自然科学 > 数学 > 代数/数论/组合理论 > 摘要关于一个Vaserstein …

About a Vaserstein question [About a Vaserstein question]

Zhang Zhaoji - Journal of Zhejiang University: Natural Science Edition, 1994 - cqvip.com

About a Vaserstein problem

Zhang Zhaoji - Journal of Zhejiang University: Natural Science Edition, 1994 - cqvip.com

1994

关于一个 Vaserstein 问题

张兆基 - 浙江大学学报 (工学版), 1994 - cnki.com.cn

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Commun. Algebra 15, 657-663 (1987).

[Chinese Regarding a Vaserstein problem]

1995

[CITATION] … ONE RINGS Pere MENAL Department of Mathematics, Universitat Autònoma, Barcelona, Spain Leonid N. VASERSTEIN Department of Mathematics …

LN VASERSTEIN - Collected Works, 1995 - Birkhäuser

1998

van der Kallen, Wilberd

Vaserstein’s pre-stabilization theorem over commutative rings. (English) Zbl 0614.16019

Reviewer: M.Golasiński

MSC: 16E20 13D15 20G35 18F25

Approximation of L1-Wasserstein distance

<—20

1999

MR1701386 Abdellaoui, Taoufiq Approximation de la

L1-distance de Wasserstein. (French) [Approximation of

L1-Vaserstein distance] C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1203–1206. 60E05

T Abdellaoui - Comptes Rendus de l'Academie des Sciences Series I …, 1999 - infona.pl

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of R n space, can be obtained via the resolution of nonlinear equation g (.)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

Approximation de la L1-distance de Wasserstein

T Abdellaoui - Comptes Rendus de l'Académie des Sciences-Series I …, 1999 - Elsevier

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of ℝ n space, can be obtained via the resolution of nonlinear equation g (·)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

Вычисление расстояния по Вассерштейну между ...

1973

MR0328982 (48 #7324) Vallander, S. S. Calculations of the Vasseršteĭn distance between probability distributions on the line. (Russian) Teor. Verojatnost. i Primenen. 18 (1973), 824--827. (Reviewer: I. Csiszar) 60B05. English translation: Theory Probab. Appl., 18(4), 784–786. (3 pages)

Abstract: We prove that the Wasserstein distance between probability distributions on thVasershtein in title from Math. Reviews 1 item

itations (104) *

- Translate this page

by СС Валландер - ‎1973 - ‎Cited by 9 - ‎Related articles

Настоящая заметка посвящена вычислению расстояния Вассерштейна в случае^ когда X = R1 с обычной евклидовой метрикой. Теорема. оо. R(P,Q) = С \F ...

CALCULATION OF WASSERSTEIN DISTANCE BETWEEN PROBABILITY DISTRIBUTIONS ON LINE

By: VALLANDE.SS

TEORIYA VEROYATNOSTEI I YEYE PRIMENIYA Volume: ‏ 18 Issue: ‏ 4 Pages: ‏ 824-827 Published: ‏ 1973

1980

MR0583946 (82e:62057) Papantoni-Kazakos, P. The Vasershtein distance as the stability criterion in robust estimation.

IEEE Trans. Inform. Theory 26 (1980), no. 5, 620--625. 62F35

In the models used by Hampel as well as by Gray and the author for the qualitative analysis of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein distance is proposed here as an alternative stability measure. This measure, in contrast to the Prohorov criterion, implies performance stability of the estimators and leads to a constructive analysis for exponentially fast convergence.

The Vasershtein distance as the stability criterion in robust estimation (Corresp.)

P Papantoni-Kazakos - IEEE Transactions on Information …, 1980 - ieeexplore.ieee.org

In the models used by Hampel as well as by Gray and the author for the qualitative analysis

of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein

distance is proposed here as an alternative stability measure. This measure, in contrast to …

Zbl 0445.62049 Papantoni-Kazakos, P.

The Vasershtein distance as the stability criterion in robust estimation. (English)

IEEE Trans. Inf. Theory 26, 620-625 (1980).

Show Scanned Page

The Vasershtein distance as the stability criterion in robust estimation (Corresp.)

P Papantoni-Kazakos - IEEE Transactions on Information …, 1980 - ieeexplore.ieee.org

In the models used by Hampel as well as by Gray and the author for the qualitative analysis

of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein

distance is proposed here as an alternative stability measure. This measure, in contrast to …

Vasserstein distances in two-state systems

1989

MR1015898 (90k:82006) Kirillov, A. B.; Rădulescu, D. C.; Styer, D. F. Vasserstein distances in two-state systems. J. Statist. Phys. 56 (1989), no. 5-6, 931--937. (Reviewer: Milos Zahradnik) 82A05 (82A68)

Abstract We present formulas for the Vasserstein distance between two statistical

mechanical states of a two-state system. For example, in a ferromagnetic spin-1/2 Ising

model the Vasserstein distance is half the difference in the magnetizations.

AB Kirillov, DC Radulescu, DF Styer - Journal of Statistical Physics, 1989 - Springer

We present formulas for the Vasserstein distance between two statistical mechanical states of

a two-state system. For example, in a ferromagnetic spin-l/2 Ising model the Vasserstein distance

is half the difference in the magnetizations … KEY WORDS: Rigorous statistical mechanics; …

We present formulas for the Vasserstein distance between two statistical mechanical states of a two-state system. For example, in a ferromagnetic spin-l/2 Ising model the Vasserstein distance is half the difference in the magnetizations … KEY WORDS: Rigorous statistical mechanics; …

Vasserstein distances in two-state systems

1989 [PDF] researchgate.net

Vasserstein distances in two-state systems

AB Kirillov, DC Radulescu, DF Styer - Journal of Statistical Physics, 1989 - Springer

… We present formulas for the Vasserstein distance between two statistical mechanical

states of a two-state system. For example, in a ferromagnetic spin-l/2 Ising model the … (5) …

<—Vaserstein Васерштейн—— 25 titles end 1972-1999 Vaserstein

including 2 titles with Vasserstein,

1 title with Vasershtein

Starting 2000, , all titles with my name are listed together, by year.

Wasserstein start 1972-1982

1972

epubs.siam.org › doi › abs

Calculation of the Wasserstein Distance Between Probability Distributions on the Line. Article Data. History. Submitted: 05 April 1972. Published 2006

[CITATION] CALCULATION OF WASSERSTEIN DISTANCE BETWEEN PROBABILITY DISTRIBUTIONS ON LINE

VALLANDE. SS - TEORIYA VEROYATNOSTEI I …, 1973 - MATH INST. OF THE ACAD OF SCI …

Calculation of the Wasserstein distance between probability ...

1 till 1972

1973 see 1974

by SS Vallander - ‎1973 - ‎Cited by 29 - ‎Related articles

Abstract: We prove that the Wasserstein distance between probability distributions on the line coincides with the $L^1$-distance between their distribution function.

1973 [PDF] mathnet.ru

[C] Вычисление расстояния по Вассерштейну между распределениями вероятностей на прямой

СС Валландер - Теория вероятностей и ее применения, 1973 - mathnet.ru

… З а м е ч а н и е 1. Теорема^ мгновенно обобщается на случай X = Rn с /^мет рикой. З а м е ч а н и е 2. Из доказанной теоремы легко выводятся явные формула для расстояния Вассерштейна между мерами на любом конечном метрическом про странстве …

Vallander, S. S.

Calculation of the Wasserstein distance between probability distributions on the line. (English. Russian original) Zbl 0351.60009

Theory Probab. Appl. 18(1973), 784-786 (1974); translation from Teor. Veroyatn. Primen. 18, 824-827 (1973).

MSC: 60B99 60A05

[CITATION] Calculation of the Wasserstein distance between probability distributions on the line

SS Vallander - Teoriya Veroyatnostei i ee Primeneniya, 1973 - mathnet.ru

… i Primenen., 1973, Volume 18, Issue 4, Pages 824–827 (Mi tvp4387), This article is cited in 1

scientific paper (total in 1 paper) Short Communications Calculation of the Wasserstein distance

between probability distributions on the line SS Vallander Abstract: We prove that the Wasserstein …

SS Vallander, “Calculation of the Wasserstein distance ...

see 2

Zbl 0351.60009

1973

http://www.mathnet.ru › eng › tvp4387

by SS Vallander · 1973 · Cited by 34 — Abstract: We prove that the Wasserstein distance between probability distributions on the line coincides with the $L^1$-distance between their distribution ...

[CITATION] Calculation of the Wasserstein distance between probability distributions on the line

SS Vallander - Teoriya Veroyatnostei i ee Primeneniya, 1973 - mathnet.ru

… i Primenen., 1973, Volume 18, Issue 4, Pages 824–827 (Mi tvp4387), This article is cited in 2 scientific papers (total in 2 papers) Short Communications Calculation of the Wasserstein distance between probability distributions on the line SS Vallander Abstract: We prove that the Wasserstein …

Cited by 31 Related articles

[CITATION] Calculation of the Wasserstein distance between probability distributions on the line

SS Vallander - Teoriya Veroyatnostei i ee Primeneniya, 1973 - mathnet.ru

… i Primenen., 1973, Volume 18, Issue 4, Pages 824–827 (Mi tvp4387), This article is cited in 2

scientific papers (total in 2 papers) Short Communications Calculation of the Wasserstein distance

between probability distributions on the line SS Vallander Abstract: We prove that the Wasserstein …

[CITATION] CALCULATION OF WASSERSTEIN DISTANCE BETWEEN PROBABILITY DISTRIBUTIONS ON LINE

VALLANDE. SS - TEORIYA VEROYATNOSTEI I …, 1973 - MATH INST. OF THE ACAD OF SCI …

[CITATION] Calculation of the Wasserstein distance between probability distributions on the line

SS Vallander - Teoriya Veroyatnostei i ee Primeneniya, 1973 - mathnet.ru

… i Primenen., 1973, Volume 18, Issue 4, Pages 824–827 (Mi tvp4387), This article is cited in 2

scientific papers (total in 2 papers) Short Communications Calculation of the Wasserstein distance

between probability distributions on the line SS Vallander Abstract: We prove that the Wasserstein …

[CITATION] CALCULATION OF WASSERSTEIN DISTANCE BETWEEN PROBABILITY DISTRIBUTIONS ON LINE

VALLANDE. SS - TEORIYA VEROYATNOSTEI I …, 1973 - MATH INST. OF THE ACAD OF SCI …

Calculation of the Wasserstein Distance Between Probability ...

1973 see 1974

https://epubs.siam.org › doi › pdf

by SS Vallender · 1974 · Cited by 299 — February 16, 1973 ... PROBABILITY DISTRIBUTIONS ON THE LINE ... Wasserstein distance R(P, Q) between the probability measures P and Q on (x, ) ...

[CITATION] Calculation of the Wasserstein distance between probability distributions on the line

SS Vallander - Teoriya Veroyatnostei i ee Primeneniya, 1973 - mathnet.ru

… i Primenen., 1973, Volume 18, Issue 4, Pages 824–827 (Mi tvp4387), This article is cited in 2

scientific papers (total in 2 papers) Short Communications Calculation of the Wasserstein distance

between probability distributions on the line SS Vallander Abstract: We prove that the Wasserstein …

[CITATION] CALCULATION OF WASSERSTEIN DISTANCE BETWEEN PROBABILITY DISTRIBUTIONS ON LINE

VALLANDE. SS - TEORIYA VEROYATNOSTEI I …, 1973 - MATH INST. OF THE ACAD OF SCI …

Вычисление расстояния по Вассерштейну между ...

1973

http://www.mathnet.ru › php › getFT

by СС Валландер · 1973 · Cited by 10 — ВЫЧИСЛЕНИЕ РАССТОЯНИЯ ПО ВАССЕРШТЕЙНУ МЕЖДУ. РАСПРЕДЕЛЕНИЯМИ ВЕРОЯТНОСТЕЙ НА ПРЯМОЙ. С. С. ВАЛЛАНДЕР. В работах Вассерштейна [1] и Добрушина [2] была ...

С. С. Валландер, Вычисление расстояния по Вассерштейну между распределениями вероятностей на прямой, Теория вероятн. и ее примен., 1973, том 18, выпуск 4, 824–827

[PDF] mathnet.ru

[CITATION] Вычисление расстояния по Вассерштейну между распределениями вероятностей на прямой

СС Валландер - Теория вероятностей и ее применения, 1973 - mathnet.ru

… Из доказанной теоремы легко выводятся явные формула для расстояния Вассерштейна

между мерами на любом конечном метрическом про странстве. К сожалению, эти …

Calculation of the Wasserstein distance between probability distributions on the line

<—1972-1973 —6 1+5

1 till 1972

+ 5 on 1973

= 6 till 1972

1974

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two

probability measures was introduced. It was called by Dobrushin the Wasserstein distance.

Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The …

1974

Calculation of the Wasserstein distance between probability distributions on the line

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two

probability measures was introduced. It was called by Dobrushin the Wasserstein distance.

Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The …

1974

Calculation of the Wasserstein distance between probability distributions on the line

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two

probability measures was introduced. It was called by Dobrushin the Wasserstein distance.

Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The …

1974

Calculation of the Wasserstein Distance Between Probability ...

https://epubs.siam.org › doi › pdf

by SS Vallender · 1974 · Cited by 352 — The present note isdevoted to calculating the Wasserstein distance in the case X R with the usual Euclidean metric. Theorem. formula (1), we ...

1974

Calculation of the Wasserstein distance between probability distributions on the line

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two probability measures was introduced. It was called by Dobrushin the Wasserstein distance. Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The …

1974
Calculation of the Wasserstein distance between probability distributions on the line

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two probability measures was introduced. It was called by Dobrushin the Wasserstein distance. Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The Wasserstein distance R (P, Q) between the probability measures P and Q on (x,) is defined in the following way:

Cited by 239 Related articles

[CITATION] Calculation of the Wasserstein distance between probability distribution on the line

RS Valander - Theory Probab Appl, 1973

Calculation of the Wasserstein distance between probability distributions on the line

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two

probability measures was introduced. It was called by Dobrushin the Wasserstein distance.

Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The …

Calculation of the Wasserstein Distance Between Probability Distributions on the Line

by SS Vallender - ‎1974 - ‎Cited by 217 - ‎Related articles

Peer-reviewed
Calculation of the Wasserstein Distance Between Probability Distributions on the Line

Author:S. S. Vallender

Downloadable Article
Publication:Theory of Probability & Its Applications, 18, 197409, 784

1974

Calculation of the Wasserstein distance between probability distributions on the line

SS Vallender - Theory of Probability & Its Applications, 1974 - SIAM

In the articles of Wasserstein 1] and Dobrushin 2], a characteristicof proximity of two

probability measures was introduced. It was called by Dobrushin the Wasserstein distance.

Let X be a metric space with metric p, and let B be the a-algebra of Borel subsets of X. The …

[CITATION] Calculation of the Wasserstein distance between probability distributions on the line

SS Vallander - Teoriya Veroyatnostei i ee Primeneniya, 1973 - mathnet.ru

… i Primenen., 1973, Volume 18, Issue 4, Pages 824–827 (Mi tvp4387), This article is cited in 2

scientific papers (total in 2 papers) Short Communications Calculation of the Wasserstein distance

between probability distributions on the line SS Vallander Abstract: We prove that the Wasserstein …

Cited by 26 Related articles

<—1973-4——13 1+5+7

6till 1972

+7 in 1974

= 13 till 1974

1978

MR0536824 (81e:60003) Szulga, Alicja On the Wasserstein metric. Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. B, pp. 267--273, Reidel, Dordrecht-Boston, Mass., 1978. (Reviewer: V. J. Paulauskas) 60B05 (90A05)

[CITATION] On the Wasserstein metric

A Szulga - Transactions of the 8th Prague Conference on …, 1978

Transactions of the Eighth Prague Conference: on Information Theory, Statistical Decision Functions, Random Processes held at Prague, from August 28 to September 1, 1978 Volume B - Transactions of the Prague Conferences on Information Theory 8B (Hardback) Jaroslav Kozesnik (volume editor)

Zbl 0411.60016

1978

MR0536797 (80d:62004b) Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Vol. B. Held in Prague, August 28–September 1, 1978. D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1978. 402 pp. ISBN: 90-277-0913-0 62-06 (60-06 90-06 93Exx 94Axx)

1978

Szulga, Alicja … On minimal Wasserstein metric

O metrryce minimalnej Wassersteina [Polish]

О минимальной метрике Вассерштейна [Russian]

1978, No 141, 63—81 ( польск., рез. англ.)

Реферативный журнал: Математика 1979 - Page 2

Szulga, Alicja On the Wasserstein metric. (English) Zbl 0411.60016

Information theory, statistical decision functions, random processes; Trans. 8th Prague Conf., Vol. B, Prague 1978, 267-273 (1978).

MSC: 60B99 60K35

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[CITATION] On the Wasserstein metric

A Szulga - Transactions of the 8th Prague Conference on …, 1978

Cited by 24 Related articles

[CITATION] On the Wasserstein metric

A Szulga - Transactions of the 8th Prague Conference on …, 1978

Cited by 26 Related articles

[CITATION] On the Wasserstein metric

A Szulga - Transactions of the 8th Prague Conference on …, 1978

Cited by 24 Related articles

<—1973-4,8——16 1+5+7+3

13 till 1974

+ 3 in 1978

= 16 till 1978

1979 see 1978 zzz 1

[CITATION] ON THE WASSERSTEIN METRIC

A it cj a Szulga - Transactions of the Eighth Prague Conference on …, 1979 - Not Avail

Notes on the Wasserstein metric in Hilbert spaces

1989 [PDF] projecteuclid.org

JA Cuesta, C Matrán - The Annals of Probability, 1989 - projecteuclid.org

Abstract Let $(X, Y) $ be a pair of Hilbert-valued random variables for which the Wasserstein distance between the marginal distributions is reached. We prove that the mapping $\omega\rightarrow (X (\omega), Y (\omega)) $ is increasing in a certain sense. Moreover, if …

[PDF] res earchgate.net

[PDF] NOTES ON THE WASSERSTEIN METRIC IN HILBERT SPACES1

J ANTONIO - The AnnaLs of Probability, 1989 - researchgate.net

Let (X, Y) be a pair of Hilbert-valued random variables for which the Wasserstein distance between the marginal distributions is reached. We prove that the mapping to—+(X (w), Y (w)) is increasing in a certain sense. More-over, if Y satisﬁes a nondegeneration condition …

1984

A class of Wasserstein metrics for probability distributions.

https://projecteuclid.org › euclid.mmj

A class of Wasserstein metrics for probability distributions. 1984 A class of Wasserstein metrics for probability distributions. There is no online version at ...

[CITATION] A class of Wasserstein metrics for probability distributions.

CR Givens, RM Shortt - The Michigan Mathematical Journal, 1984 - projecteuclid.org

0. Introduction. There are several natural metrics that one can place on spaces of probability

distributions (or" laws"). These include total variation, Prohorov's p metric, dual norms

induced by spaces of Lipschitz functions, and the so-called Wasserstein distance. A …

Cited by 387 Related articles

1984

A class of Wasserstein metrics for probability distributions.

projecteuclid.org › euclid.mmj

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[CITATION] A class of Wasserstein metrics for probability distributions.

CR Givens, RM Shortt - The Michigan Mathematical Journal, 1984 - projecteuclid.org

0. Introduction. There are several natural metrics that one can place on spaces of probability

distributions (or" laws"). These include total variation, Prohorov's p metric, dual norms

induced by spaces of Lipschitz functions, and the so-called Wasserstein distance. A …

1987 zzz 2

[CITATION] Eigenschaften von Wasserstein-Metriken zwischen Maßen: Quantitative Konvergenzaussagen bei diskreten Approximationen von Maßen

M Gelbrich - 1987

1984

A class of Wasserstein metrics for probability distributions. - Project Euclid

https://projecteuclid.org › euclid.mmj

by CR Givens · 1984 · Cited by 393 — This website uses cookies to provide you with a variety of services and to improve the usability of our website. By using the website, you agree to the use of ...

Cited by 393 Related articles

[CITATION] A class of Wasserstein metrics for probability distributions.

CR Givens, RM Shortt - The Michigan Mathematical Journal, 1984 - projecteuclid.org

0. Introduction. There are several natural metrics that one can place on spaces of probability

distributions (or" laws"). These include total variation, Prohorov's p metric, dual norms

induced by spaces of Lipschitz functions, and the so-called Wasserstein distance. A …

January 1984

A class of Wasserstein metrics for probability distributions.

Clark R. Givens, Rae Michael Shortt

Michigan Mathematical Journal Vol. 31, Issue 2 (Jan 1984), pg(s) 231-240

A class of Wasserstein metrics for probability distributions.

https://explore.openaire.eu › search › publication

A class of Wasserstein metrics for probability distributions. Rae Michael Shortt; Clark R. Givens;. Open Access English. Published: 31 Dec 1983; Publisher: ..
A class of Wasserstein metrics for probability distributions.

[CITATION] A class of Wasserstein metrics for probability distributions.

Cited by 398 Related articles

A class of Wasserstein metrics for probability distributions

1985

The Wasserstein distance and approximation theorems

L Rüschendorf - Probability Theory and Related Fields, 1985 - Springer

By an extension of the idea of the multivariate quantile transform we obtain an explicit

formula for the Wasserstein distance between multivariate distributions in certain cases. For

the general case we use a modification of the definition of the Wasserstein distance and …

1985

The Wasserstein distance and approximation theorems

L Rüschendorf - Probability Theory and Related Fields, 1985 - Springer

By an extension of the idea of the multivariate quantile transform we obtain an explicit

formula for the Wasserstein distance between multivariate distributions in certain cases. For

the general case we use a modification of the definition of the Wasserstein distance and …

[CITATION] The Wasserstein distance and approximation theorems, Prob. Theory Rel., 70, 117–129

L Rüschendorf - 1985

Notes on the Wasserstein metric in Hilbert spaces

1989 [PDF] projecteuclid.org

JA Cuesta, C Matrán - The Annals of Probability, 1989 - projecteuclid.org

Abstract Let $(X, Y) $ be a pair of Hilbert-valued random variables for which the Wasserstein

distance between the marginal distributions is reached. We prove that the mapping

$\omega\rightarrow (X (\omega), Y (\omega)) $ is increasing in a certain sense. Moreover, if …

http://personal.psu.edu › lxv1 › VinTitleBook

[PDF] NOTES ON THE WASSERSTEIN METRIC IN HILBERT SPACES1

J ANTONIO - The AnnaLs of Probability, 1989 - researchgate.net

Let (X, Y) be a pair of Hilbert-valued random variables for which the Wasserstein distance

between the marginal distributions is reached. We prove that the mapping to—+(X (w), Y

(w)) is increasing in a certain sense. More-over, if Y satisﬁes a nondegeneration condition …

1989 see 1985 thesis Untitled

1989. Lp-Wasserstein-Metriken [Lp-Wasserstein-Metriken] und Approximationen stochastischer Differentialgleichungen. Matthias Gelbrich, 1989 154 pages.

[CITATION] (1989). LP-Wasserstein-Metriken und Approximation stochastischer Differentialgleichungen. Ph. D. thesis, Dissert. A, Humboldt-Universitat Berlin.

1989

Notes on the Wasserstein metric in Hilbert spaces

JA Cuesta, C Matrán - The Annals of Probability, 1989 - projecteuclid.org

Abstract Let $(X, Y) $ be a pair of Hilbert-valued random variables for which the Wasserstein

distance between the marginal distributions is reached. We prove that the mapping

$\omega\rightarrow (X (\omega), Y (\omega)) $ is increasing in a certain sense. Moreover, if …

The Wasserstein distance and approximation theorems

[PDF] NOTES ON THE WASSERSTEIN METRIC IN HILBERT SPACES1

J ANTONIO - The AnnaLs of Probability, 1989 - researchgate.net

Let (X, Y) be a pair of Hilbert-valued random variables for which the Wasserstein distance

between the marginal distributions is reached. We prove that the mapping to—+(X (w), Y

(w)) is increasing in a certain sense. More-over, if Y satisﬁes a nondegeneration condition …

M Gelbrich - 1989

1985 [PDF] researchgate.net

L Rüschendorf - Probability Theory and Related Fields, 1985 - Springer

By an extension of the idea of the multivariate quantile transform we obtain an explicit

formula for the Wasserstein distance between multivariate distributions in certain cases. For

the general case we use a modification of the definition of the Wasserstein distance and …

[CITATION] The Wasserstein distance and approximation theorems, Prob. Theory Rel., 70, 117–129

L Rüschendorf - 1985

The Wasserstein distance and approximation theorems

1985 [PDF] researchgate.net

L Rüschendorf - Probability Theory and Related Fields, 1985 - Springer

By an extension of the idea of the multivariate quantile transform we obtain an explicit

formula for the Wasserstein distance between multivariate distributions in certain cases. For …

1988 book
On a formula for the $L 2$ Wasserstein metric between measures on Euclidean and Hilbert spaces

Author:M. Gelbrich
Print Book, 1988
English
Publisher:Humboldt-Universität zu Berlin. Sektion Mathematik, Berlin, 1988
On a formula for the L2 Wasserstein metric between measures on Euclidean and Hilbert spaces

Author:Matthias Gelbrich
Print Book, 1988
English
Publisher:Sekt. Mathematik der Humboldt-Univ., Berlin, 1988

1989 thesis
L_1hnp-Wasserstein-Metriken [Lp-Wasserstein-Metriken] und Approximationen stochastischer Differentialgleichungen

Author:Matthias Gelbrich (

Author)
Thesis, Dissertation, 1989
German
Publisher:1989

1987 thesis
Eigenschaften von Wasserstein-Metriken zwischen Maßen : Quantitative Konvergenzaussagen bei diskreten Approximationen von Maßen

Author:Matthias Gelbrich
Thesis, Dissertation, 1987
German
Publisher:1987

1989
L-Wasserstein-Metriken und Approximationen stochastischer Differentialgleichungen

Author:Matthias Gelbrich
Thesis, Dissertation, 1989
German
Publisher:1989
<——1983-1989——— 30——— end 1983-1989 Wasserstein

Wasserstein start 1990-1991

1990 1

MR1127323 (93a:62081) Gelbrich, Matthias On a formula for the $L^2$ Wasserstein metric between measures on Euclidean and Hilbert spaces. Math. Nachr. 147 (1990), 185--203. (Reviewer: Juan A. Cuesta-Albertos) 62H05 (60B11 62E10)

On a formula for the L2 Wasserstein metric between measures on Euclidean and Hilbert spaces

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library Vol 147 Issue 1

Abstract. For a separable metric space (X, d ) LP WASSERSTEIN metrics between probability

mea-sures p and v on X arc defined by ... The LP WASSERSTEIN metrics form a special family

among the great variety of distances between probability measures. They may be ...

Cited by 94 Related articles
Zbl 0711.60003

1990 2 Zbl 0718.60057 Gelbrich, Matthias

L${}\sp p$-Wasserstein-Metriken und Approximationen stochastischer Differentialgleichungen. $(L\sp p$ Wasserstein metrics and approximations

of stochastic differential equations). (German)

Berlin: Humboldt-Universität Berlin, Mathematisch- Naturwissenschaftliche Fakultät, Diss. 77 S. (1990). MSC2000: *60H10 60B10, Reviewer: M.Gelbrich

Lp-Wasserstein-Metriken und Approximationen stochastischer Differentialgleichungen

M Gelbrich - 1990

Wasserstein-Metriken und Approximationen stochastischer Differentialgleichungen

thesis

1990 3

MR1074632 (92d:60007) Rachev, S. T.; Shortt, R. M. Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals. Dissertationes Math. (Rozprawy Mat.) 299 (1990), 35 pp. (Reviewer: Donald L. Cohn) 60B10 (60F05 60F17)

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

S.T. Rachev and R.M. Shortt. google books

Warszawa : Państwowe Wydawn. Naukowe, 1990. 39 pp 8301099704 9788301099701

Zbl 0716.60005 Rachev, S.T.; Shortt, R.M. Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals. (English)

[J] Diss. Math. 299, 35 p. (1990). ISSN 0012-3862

Duality Theorems for Kantorovich-Rubinstein and Wasserstein Functionals

Svetlozar Todorov Rachev, ‎Rae Michael Shortt - 1990 book
Rachev, S. T.; Shortt, R. M.

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals. (English) Zbl 0716.60005

Diss. Math. 299, 35 p. (1990).

Reviewer: J.Szulga

MSC: 60B05 54E70 90C05 28A35

1990 4

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

ST Rachev - 1990 - eudml.org

Abstract top CONTENTS § 0. Introduction............................................................................................

....................................... 5 § 1. Notation and terminology......................................................................

........................................ 6 § 2. A generalization of the Kantorovich-Rubinstein …

[CITATION] Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals.(1990)

ST Rachev - 1990

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

book

1990 5

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

ST Rachev - 1990 - eudml.org

Abstract top CONTENTS § 0. Introduction............................................................................................

....................................... 5 § 1. Notation and terminology......................................................................

........................................ 6 § 2. A generalization of the Kantorovich-Rubinstein …

[CITATION] Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals.(1990)

ST Rachev - 1990

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

1990 6

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 94 Related articles

1990 7

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over

all probability measures η on X× X with marginal distributions μ and v, respectively. After

mentioning some basic properties of these metrics as well as explicit formulae for X= R a

formula for the L2 Wasserstein metric with X= Rn will be cited from 5, 9, and 21 and proved …

Cited by 94 Related articles

[CITATION] On a formula for the Lp Wasserstein metric between measures on Euclidean and Hilbert spaces. Preprint 179, 1988. Sektion Mathematik der Humboldt …

M Gelbrich - Lp-Wasserstein-Metriken und Approximationen … see 1990

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

1990 8

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 95 Related articles

1990 9

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 95 Related articles

1990 10

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

ST Rachev - 1990 - eudml.org

Abstract top CONTENTS § 0. Introduction............................................................................................

....................................... 5 § 1. Notation and terminology......................................................................

........................................ 6 § 2. A generalization of the Kantorovich-Rubinstein …

1990 11

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^ p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 96 Related articles

1990 12

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

ST Rachev - 1990 - eudml.org

Abstract top CONTENTS § 0. Introduction................................................................................................................................... 5 § 1. Notation and terminology.............................................................................................................. 6 § 2. A generalization of the Kantorovich-Rubinstein …

[CITATION] Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals.(1990)

ST Rachev - 1990

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

1990 13

ST Rachev - 1990 - eudml.org

Abstract top CONTENTS § 0. Introduction............................................................................................

....................................... 5 § 1. Notation and terminology......................................................................

........................................ 6 § 2. A generalization of the Kantorovich-Rubinstein …

[CITATION] Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals.(1990)

ST Rachev - 1990

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

1990 14

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 97 Related articles

1990 15

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 99 Related articles

1990 16

On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

M Gelbrich - Mathematische Nachrichten, 1990 - Wiley Online Library

For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ

and v on X are defined by article empty W_p\left (μ, ν\right):=\inf\left {\left (\mathop fx * xd^

p\left (x, y\right) d η\right)^ 1/p\right\}, p\; ε\;\left (1, ∞\right), where the infimum is taken over …

Cited by 105 Related articles

1990 17 Peer-reviewed
On a Formula for the L² Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

Author:Matthias Gelbrich
Summary:For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ and v on X are defined by \documentclass{article}\pagestyle{empty}\begin{document}$$ W_p \left({\mu,\nu } \right): = \inf \left\{ {\left({\mathop f\limits_{x \times x} d^p \left({x,y} \right)d\eta } \right)^{1/p} } \right\},p\;\varepsilon \;\left({1,\infty } \right),$$\end{document} where the infimum is taken over all probability measures η on X × X with marginal distributions μ and v, respectively. After mentioning some basic properties of these metrics as well as explicit formulae for X = R a formula for the L² Wasserstein metric with X = Rn will be cited from [5], [9], and [21] and proved for any two probability measures of a family of elliptically contoured distributions.Finally this result will be generalized for Gaussian measures to the case of a separable Hilbert spaceShow more
Article, 1990
Publication:Mathematische Nachrichten, 147, 1990, 185
Publisher:1990

1991 18

Skorohod Representation Theorem and Wasserstein Metrics

J. A. Cuesta Albertos, ‎Carlos Matrán Bea - 1991 - ‎No preview

Universidad de Cantabria, Servicio …

[CITATION] Skorohod representation theorem and Wasserstein metrics

JA Cuesta-Albertos, CM Bea - 1991 - Universidad de Cantabria

Skorohod representation theorem and wasserstein metrics

1991 19

Authors:Juan A. Cuesta-Albertos, Carlos Matrán Bea

Print Book, 1991

English

Publisher:Universidad de Cantabria, Santander, 1991

1991 20

Aplicaciones crecientes. Relaciones con las métricas Wasserstein ...

by MAT Díaz - ‎1991

Información de la tesis doctoral Aplicaciones crecientes. Relaciones con las métricas Wasserstein.

[Spanish Growing applications Relations with Wasserstein metrics]

All 2 versions
[CITATION] Aplicaciones crecientes. Relaciones con las métricas de Wasserstein

A Tuero - 1991 - Univ. de Cantabria Santander

Aplicaciones crecientes. Relaciones con las métricas Wasserstein

year 1991 21

MAT Díaz - 1991 - dialnet.unirioja.es

Resumen DEMOSTRACIONES DE LA MEDIBILIDAD Y CONTINUIDAD DE LAS

APLICACIONES CRECIENTES EN ESPACIOS DE HILBERT, SI PN CONVERGEN

DEBILMENTE HACIA PY (X, HN (X)) SON EMPAREJAMIENTOS OPTIMOS (EO) ENTRE PN …

PDF] Analyse de la stabilité de systèmes de stockage par la métrique de Wasserstein

1991 22

F Simonot - Statistique et analyse des données, 1991 - numdam.org

de la revue « Statistique et analyse des données » im- plique l'accord avec les conditions générales

d'utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression …

1991 23

Aplicaciones crecientes. Relaciones con las métricas Wasserstein

MA Tuero Díaz - 1991 - dialnet.unirioja.es

Resumen: DEMOSTRACIONES DE LA MEDIBILIDAD Y CONTINUIDAD DE LAS

APLICACIONES CRECIENTES EN ESPACIOS DE HILBERT, SI PN CONVERGEN

DEBILMENTE HACIA PY (X, HN (X)) SON EMPAREJAMIENTOS OPTIMOS (EO) ENTRE ...

1991 24

[PDF] Analyse de la stabilité de systèmes de stockage par la métrique de Wasserstein

F Simonot - Statistique et analyse des données, 1991 - numdam.org

de la revue « Statistique et analyse des données » im- plique l'accord avec les conditions générales

d'utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression …

1991 25

Aplicaciones crecientes. Relaciones con las métricas Wasserstein

MAT Díaz - 1991 - dialnet.unirioja.es

Resumen DEMOSTRACIONES DE LA MEDIBILIDAD Y CONTINUIDAD DE LAS

APLICACIONES CRECIENTES EN ESPACIOS DE HILBERT, SI PN CONVERGEN

DEBILMENTE HACIA PY (X, HN (X)) SON EMPAREJAMIENTOS OPTIMOS (EO) ENTRE PN …

Aplicaciones crecientes. Relaciones con las métricas ... - Dialnet

https://dialnet.unirioja.es › tesis

by MAT Díaz · 1991 — Aplicaciones crecientes. Relaciones con las métricas Wasserstein. Autores: M. Araceli Tuero Díaz; Directores de la Tesis: Juan Antonio Cuesta Albertos ( dir. tes ...

[CITATION] Aplicaciones crecientes. Relaciones con las métricas de Wasserstein

A Tuero - 1991 - Dissertation. Universidad de …

[PDF] Analyse de la stabilité de systèmes de stockage par la métrique de Wasserstein

1991 26

F Simonot - Statistique et analyse des données, 1991 - numdam.org

de la revue « Statistique et analyse des données » im- plique l'accord avec les conditions générales

d'utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression …

1991 27 see 18 19 zzz 6

[CITATION] Skorohod representation theorem and Wasserstein metrics

JA CUEsTA, C MATRAN - Preprint, 1991

[CITATION] Skorohod representation theorem and Wasserstein metrics

JA Cuesta-Albertos, CM Bea - 1991 - Universidad de Cantabria

Skorhod representation theorem and Wasserstein metrics

199128

JA Cuesta Albertos - 1991 - opensigle.inist.fr 19 pp

Volume 6, Issue 1991 of Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria

... Please use this identifier to cite or link to this item: http://hdl.handle.net/10068/294976.

Authors: Cuesta Albertos, Juan

A. Matran Bea, Carlos Cantabria Univ., Santander (Spain). Dept. ...

Cached - All 2 versions

Santander: Universidad de …

[CITATION] Skorhod representation theorem and Wasserstein metrics

Univ. de Cantabria, Santander (Spain). Dept. de … - 1991 - opengrey.eu

… Search. XML. To cite or link to this reference: http://hdl.handle.net/10068/295133. Title :

Skorhod representation theorem and Wasserstein metrics. Authors : Cuesta Albertos, Juan

A. ; Matran Bea, Carlos ; Corporate author : Univ. de Cantabria, Santander (Spain). Dept …

[CITATION] Skorohod representation theorem and Wasserstein metrics. Preprint, 1991. JA Cuesta-Albertos and C. Matrán. A review on strong convergence of …

JA Cuesta-Albertos - Journal of Stat. Planning Infer, 1992

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

[CITATION] Skorhod representation theorem and Wasserstein metrics

Univ. de Cantabria, Santander (Spain). Dept. de … - 1991 - opengrey.eu

… Search. XML. To cite or link to this reference: http://hdl.handle.net/10068/295133. Title :

Skorhod representation theorem and Wasserstein metrics. Authors : Cuesta Albertos, Juan

A. ; Matran Bea, Carlos ; Corporate author : Univ. de Cantabria, Santander (Spain). Dept …

[CITATION] Skorohod Representation Theorem and Wasserstein Metrics

JAC Albertos, CM Bea - 1991 - Universidad de Cantabria …

<—-1990-1991———28— end 1990-1991

Wasserstein start 1992-1993

1992 1

MR1165653 (93h:60010) Cuesta, Juan A.; Matrán, Carlos A review on strong convergence of weighted sums of random elements based on Wasserstein metrics. J. Statist. Plann. Inference 30 (1992), no. 3, 359——370. (Reviewer: A. Bozorgnia) 60B12 (60B11)

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost

sure convergence for weighted sums of real random variables to the case of Banach-valued

random elements. The method arises from the extension of Skorohod's Representation …

[CITATION] … metrics. Preprint, 1991. JA Cuesta-Albertos and C. Matrán. A review on strong convergence of weighted sums of random elements based on Wasserstein …

JA Cuesta-Albertos - Journal of Stat. Planning Infer, 1992

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

1992 2

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost sure convergence for weighted sums of real random variables to the case of Banach-valued random elements. The method arises from the extension of Skorohod's Representation …

[CITATION] … metrics. Preprint, 1991. JA Cuesta-Albertos and C. Matrán. A review on strong convergence of weighted sums of random elements based on Wasserstein …

JA Cuesta-Albertos - Journal of Stat. Planning Infer, 1992

A REVIEW ON STRONG-CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENTS BASED ON WASSERSTEIN METRICS

1992 3

By: CUESTA, JA; MATRAN, C

JOURNAL OF STATISTICAL PLANNING AND INFERENCE Volume: ‏ 30 Issue: ‏ 3 Pages: ‏ 359-370 Published: ‏ MAR

1992 4

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost

sure convergence for weighted sums of real random variables to the case of Banach-valued

random elements. The method arises from the extension of Skorohod's Representation …

1992 5 see 1991 12009 zzz 7

[CITATION] Skorohod representation theorem and Wasserstein metrics. Preprint, 1991. JA Cuesta-Albertos and C. Matrán. A review on strong convergence of …

JA Cuesta-Albertos - Journal of Stat. Planning Infer, 1992

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

1992 6

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

[CITATION] … metrics. Preprint, 1991. JA Cuesta-Albertos and C. Matrán. A review on strong convergence of weighted sums of random elements based on Wasserstein …

JA Cuesta-Albertos - Journal of Stat. Planning Infer, 1992

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

1992 7

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost

sure convergence for weighted sums of real random variables to the case of Banach-valued

random elements. The method arises from the extension of Skorohod's Representation …

1992 8

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost

sure convergence for weighted sums of real random variables to the case of Banach-valued

random elements. The method arises from the extension of Skorohod's Representation …

1992 9

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost

sure convergence for weighted sums of real random variables to the case of Banach-valued

random elements. The method arises from the extension of Skorohod's Representation …

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

JA Cuesta, C Matrán - Journal of statistical planning and inference, 1992 - Elsevier

In a previous paper the authors proposed a simple method to extend results about almost

sure convergence for weighted sums of real random variables to the case of Banach-valued

random elements. The method arises from the extension of Skorohod's Representation …

1993 1

On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

J. A. Cuesta-Albertos, ‎Carlos Matrán Bea, ‎Universidad de Cantabria. Servicio de Publicaciones - 1993 - Volume 7 ‎19 pages

[CITATION] On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

JAC Albertos, CM Bea, A Tuero-Díaz - 1993 - Universidad de Cantabria … see 1996

[CITATION] On Lower Bounds for the L [elevado A] 2-Wasserstein Metric in a Hilbert Space

JA Cuesta-Albertos - 1993 - Universidad de Cantabria, Servicio …

1993 2

Relations between the iyo processes based on the wasserstein function

W Choi - 1993 - mathnet.or.kr

Communications of the Korean Mathematical Society ( Vol.8 NO.4 / 1993 ). Title, Relations

between the iyo processes based on the wasserstein function(eng). Author, Won Choi. MSC,

Publication, Page, 793-797 Page. Abstract, Own Status, Keyword, Note, Summary, Attach,

[CITATION] Relations between the iyo processes based on the wasserstein function

1993 3

MR1207216 (94a:60019) Tuero, Araceli On the stochastic convergence of representations based on Wasserstein metrics. Ann. Probab. 21 (1993), no. 1, 72--85. (Reviewer: Ludger Rüschendorf) 60E05 (60B10)

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

Suppose that P and Pn, n∈ N, are probabilities on a real, separable Hilbert space, V. It is

known that if P satisfies some regularity conditions and X is such that PX= P, then there exist

mappings Hn: V→ V, such that PHn (X)= Pn and the Wasserstein distance between Pn and …

1993 4

RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

W Choi - Communications of the Korean Mathematical Society, 1993 - koreascience.or.kr

제 2 조 (용어의 정의) ① "이용자"라 함은 당 사이트에 접속하여 이 약관에 따라 당 사이트가 제공하는

서비스를 받는 회원 및 비회원을 말합니다. ② "회원"이라 함은 서비스를 이용하기 위하여 당 사이트에

개인정보를 제공하여 아이디(ID)와 비밀번호를 부여 받은 자를 말합니다. ③ "회원 아이디(ID)"라 …

On the stochastic convergence of representations based on Wasserstein metrics

1993 5

[CITATION] On Lower Bounds for the L [elevado A] 2-Wasserstein Metric in a Hilbert Space

JA Cuesta-Albertos - 1993 - Universidad de Cantabria, Servicio …

[CITATION] On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

JAC Albertos, CM Bea, A Tuero-Díaz - 1993 - U

1993 6

A Tuero - The Annals of Probability, 1993 - JSTOR

… [7] FERNIQUE, X. (1988). Un modele presque sure pour la convergence in loi. CR Acad. Sci … [18] SCHIEF, A. (1989). Almost surely convergent random variables with given laws. Probab … [19] SKOROHOD, AV (1956). Limit theorems for stochastic processes. Theory Probab …

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

Suppose that P and Pn, n∈ N, are probabilities on a real, separable Hilbert space, V. It is

known that if P satisfies some regularity conditions and X is such that PX= P, then there exist

mappings Hn: V→ V, such that PHn (X)= Pn and the Wasserstein distance between Pn and …

1993 7

On lower bounds for the L2-Wasserstein metric in a Hilbert ...

personales.unican.es › BoundWassersteinDistances

by JA Cuesta-Albertos · Cited by 41 — We provide two families of lower bounds for the L2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus ... Then there exist real random variables {Zi;i ∈ L} such that. ∑ j∈L. 1≤j≤k.

Missing: [elevado ‎| Must include: [elevado

[CITATION] On Lower Bounds for the L [elevado A] 2-Wasserstein Metric in a Hilbert Space

JA Cuesta-Albertos - 1993 - Universidad de Cantabria, Servicio …

[CITATION] On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

JAC Albertos, CM Bea, A Tuero-Díaz - 1993 - Universidad de Cantabria …

1993 8

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

Suppose that P and Pn, n∈ N, are probabilities on a real, separable Hilbert space, V. It is known that if P satisfies some regularity conditions and X is such that PX= P, then there exist mappings Hn: V→ V, such that PHn (X)= Pn and the Wasserstein distance between Pn and …

1993 9

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

1993 10

[CITATION] On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

JAC Albertos, CM Bea, A Tuero-Díaz - 1993 - Universidad de Cantabria …

[CITATION] On Lower Bounds for the L [elevado A] 2-Wasserstein Metric in a Hilbert Space

JA Cuesta-Albertos - 1993 - Universidad de Cantabria, Servicio …

1993 11 [PDF] koreascience.or.kr

RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

W Choi - Communications of the Korean Mathematical Society, 1993 - koreascience.or.kr

Suppose that (S, d) is a Polish space and is a fixed but arbitrarily chosen point in S. For each p with 1: S p< 00, define M p= Mp (S) to be the collection of all probability measures P on the Borel sets of S for which l dP (X, O) dP (X) is finite. Let PI and P2 be members of M p for 1:::; …

1993 12

ON THE STOCHASTIC CONVERGENCE OF REPRESENTATIONS BASED ON WASSERSTEIN METRICS

By: TUERO, A

ANNALS OF PROBABILITY Volume: ‏ 21 Issue: ‏ 1 Pages: ‏ 72-85 Published: ‏ JAN 1993

On the Stochastic Convergence of Representations Based on Wasserstein Metrics

Times Cited: 10

1 January 1993

Araceli Tuero

The Annals of Probability Vol. 21, Issue 1 (Jan 1993), pg(s) 72-85

KEYWORDS: ‎Hilbert spaces, increasing functions, Skorohod's representation theorem, stochastic convergence of representations, Wasserstein distance, weak convergence

On lower bounds for the L2-Wasserstein metric in a Hilbert space

1993 13 modified 2017 see 1996

personales.unican.es › BoundWassersteinDistances

by JA Cuesta-Albertos · Cited by 41 — We provide two families of lower bounds for the L2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus ... Then there exist real random variables {Zi;i ∈ L} such that. ∑ j∈L. 1≤j≤k.

On lower bounds for the L2-Wasserstein metric in a Hilbert space

personales.unican.es › BoundWassersteinDistances

PDF updated 2017

We provide two families of lower bounds for the L2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. ... j∈L jE(Y 2 j ) < ∞. To prove the convergence of the series ∑ i∈L Z2 i we will see that. ∑.

by JA Cuesta-Albertos · ‎Cited by 41 · ‎Related articles

Missing: [elevado ‎| Must include: [elevado

[CITATION] On Lower Bounds for the L [elevado A] 2-Wasserstein Metric in a Hilbert Space

JA Cuesta-Albertos - 1993 - Universidad de Cantabria, Servicio …

1993 14

RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

W Choi - Communications of the Korean Mathematical Society, 1993 - koreascience.or.kr

Suppose that (S, d) is a Polish space and is a fixed but arbitrarily chosen point in S. For each

p with 1: S p< 00, define M p= Mp (S) to be the collection of all probability measures P on the

Borel sets of S for which l dP (X, O) dP (X) is finite. Let PI and P2 be members of M p for 1:::; …

On the Stochastic Convergence of Representations ... baser on Wasserstein metrics - jstor

https://www.jstor.org › stable

1993 15

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

Suppose that P and Pn, n∈ N, are probabilities on a real, separable Hilbert space, V. It is

known that if P satisfies some regularity conditions and X is such that PX= P, then there exist

mappings Hn: V→ V, such that PHn (X)= Pn and the Wasserstein distance between Pn and …

1993 16

The Hope for Compassion: Wasserstein, Petru evskaja and Fischerová

V Ambros - Zeitschrift für Slawistik, 1993 - search.proquest.com

Z. Slaw. 38 (1993) 2, 236-243 Veronika A mbros The Hope for Compassion: Wasserstein,

Petrusevskaja and Fischerova'As a rule the gender of an author does not serve as a base for

a literary analysis. Yet, it has not been until just recently, that is in the last two decades, that …

1993 17

RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

W Choi - Communications of the Korean Mathematical Society, 1993 - koreascience.or.kr

Suppose that (S, d) is a Polish space and is a fixed but arbitrarily chosen point in S. For each

p with 1: S p< 00, define M p= Mp (S) to be the collection of all probability measures P on the

Borel sets of S for which l dP (X, O) dP (X) is finite. Let PI and P2 be members of M p for 1:::; …

1993 18 [PDF] koreascience.or.kr

RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

W Choi - Communications of the Korean Mathematical Society, 1993 - koreascience.or.kr

Suppose that (S, d) is a Polish space and is a fixed but arbitrarily chosen point in S. For each

p with 1: S p< 00, define M p= Mp (S) to be the collection of all probability measures P on the

Borel sets of S for which l dP (X, O) dP (X) is finite. Let PI and P2 be members of M p for 1:::; …

1993 19

RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

W Choi - Communications of the Korean Mathematical Society, 1993 - koreascience.or.kr

Suppose that (S, d) is a Polish space and is a fixed but arbitrarily chosen point in S. For each

p with 1: S p< 00, define M p= Mp (S) to be the collection of all probability measures P on the

Borel sets of S for which l dP (X, O) dP (X) is finite. Let PI and P2 be members of M p for 1:::; …

1993 20 [PDF] projecteuclid.org

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

1993 21 [PDF] projecteuclid.org

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

… P, then there exist mappings H n : V → V, such that P H n (X) = P n and the Wasserstein

distance between P n and P coincides with (∫|x - H n (x)| 2 dP) 1/2 , n ∈ N. In this paper we

prove that the weak convergence of {P n } to P is enough to ensure that {H n (X)} converges to X …

<——1992-1993 ——— 30 —

1993 book
On lower bounds for the $ L ^2 $-Wasserstein metric in a Hilbert space

Authors:J. A. Cuesta-Albertos, C. Matrán-Bea, A. Tuero-Diaz
Print Book, 1993
English
Publisher:Universidad de Cantabria. Departamento de Matematicas, Estadistica y Computacion, Santander, 1993

1993
On lower bounds for the L[elevado a]2-Wasserstein metric in a Hilbert space

Authors:J. A. Cuesta-Albertos, Universidad de Cantabria
Print Book, 1993
English
Publisher:Universidad de Cantabria, Servicio de publicaciones, Santander, 1993
View AllFormats & Editions

1993
RELATIONS BETWEEN THE ITÔ PROCESSES BASED ON THE WASSERSTEIN FUNCTION

Author:WON CHOI
Downloadable Article, 1993
Publication:Communications of the Korean Mathematical Society = 대한수학회논문집, 8, 1993년, 793
Publisher:1993

<——1992-1993 ———— 33 — end 1992-1993

Wasserstein start 1994-1995

1994

MEAN RATES OF CONVERGENCE OF EMPIRICAL MEASURES IN THE WASSERSTEIN METRIC

By: HOROWITZ, J; KARANDIKAR, RJ

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏ 55 Issue: ‏ 3 Pages: ‏ 261-273 Published: ‏ NOV 30 1994

Times Cited: 19

1994

MR1297788 (95i:60026) Cuesta-Albertos, Juan A.; Matrán-Bea, Carlos Stochastic convergence through Skorohod representation theorems and Wasserstein distances. First International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures (Palermo, 1993). Rend. Circ. Mat. Palermo (2) Suppl. No. 35 (1994), 89--113. (Reviewer: Mindaugas Bloznelis) 60F15 (60B11 60B12 60F25)

[CITATION] Stochastic convergence through Skorohod representation theorems and Wasserstein metrics

JA Cuesta - Suppl. Rendic. Circolo Matem. Palermo II, 1994 - ci.nii.ac.jp

… 検索. すべて. 本文あり. すべて. 本文あり. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN.

巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

利用者のみなさまにご不便をおかけしておりますことをお詫び申し上げます。NII-ELS …

[CITATION] Stochastic convergence through Skorohod representation theorems and Wasserstein metrics

JA Cuesta - Suppl. Rendic. Circolo Matem. Palermo II, 1994 - ci.nii.ac.jp

1994

MR1329874 (96d:60020) Horowitz, Joseph; Karandikar, Rajeeva L. Mean rates of convergence of empirical measures in the Wasserstein metric. J. Comput. Appl. Math. 55 (1994), no. 3, 261--273. (Reviewer: Joseph E. Yukich) 60D05 (60C05)

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical

measure of a sequence of iid random vectors and the common probability law of the

sequence. The same result holds for an infinite exchangeable sequence and its directing …

Mean rates of convergence of empirical measures in the Wasserstein metric

1994

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical

measure of a sequence of iid random vectors and the common probability law of the

sequence. The same result holds for an infinite exchangeable sequence and its directing …

<—5

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical measure of a sequence of iid random vectors and the common probability law of the sequence. The same result holds for an infinite exchangeable sequence and its directing …

1994

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical

measure of a sequence of iid random vectors and the common probability law of the

sequence. The same result holds for an infinite exchangeable sequence and its directing …

1994

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical measure of a sequence of iid random vectors and the common probability law of the sequence. The same result holds for an infinite exchangeable sequence and its directing …

`1994

On the stochastic convergence of representations based on Wasserstein metrics

A Tuero - The Annals of Probability, 1993 - JSTOR

Suppose that P and Pn, n∈ N, are probabilities on a real, separable Hilbert space, V. It is

known that if P satisfies some regularity conditions and X is such that PX= P, then there exist

mappings Hn: V→ V, such that PHn (X)= Pn and the Wasserstein distance between Pn and …

1994

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical

measure of a sequence of iid random vectors and the common probability law of the

sequence. The same result holds for an infinite exchangeable sequence and its directing …

Cited by Cited by 76 Related articles All 4 versions

<—10

1994

Mean rates of convergence of empirical measures in the Wasserstein metric

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical

measure of a sequence of iid random vectors and the common probability law of the

sequence. The same result holds for an infinite exchangeable sequence and its directing …

1994 zzz 8

[CITATION] Stochastic convergence through Skorohod representation theorems and Wasserstein metrics

JA Cuesta - Suppl. Rendic. Circolo Matem. Palermo II, 1994 - ci.nii.ac.jp

… 検索. すべて. 本文あり. すべて. 本文あり. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN.

巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. [機関認証]

利用継続手続きのご案内. Stochastic convergence through Skorohod representation …

1996
On lower bounds for the L 2-Wasserstein metric in a Hilbert space

1994 zzz 7b

[CITATION] Stochastic convergence through Skorohod representation theorems and Wasserstein metrics

JA Cuesta - Suppl. Rendic. Circolo Matem. Palermo II, 1994 - ci.nii.ac.jp

… 検索. すべて. 本文あり. すべて. 本文あり. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. [機関認証] 利用継続手続きのご案内. Stochastic convergence through Skorohod representation …

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<——1994-1995———1994-1995——- 12— end 1994-1995

Wasserstein start 1996-1997

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

On lower bounds for the L 2-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be …

1996

On lower bounds for theL²-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

Cuesta-Albertos, J. A.; Matrán-Bea, C.; Tuero-Diaz, A.

On lower bounds for the L2

-Wasserstein metric in a Hilbert space. (English) Zbl 0870.60005

J. Theor. Probab. 9, No. 2, 263-283 (1996).

1996

On lower bounds for theL²-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

1996

Discretization for Stochastic Differential Equations, L^p Wasserstein Metrics, and Econometrical Models

M Gelbrich, ST Rachev - Lecture Notes-Monograph Series, 1996 - JSTOR

The paper deals with weak approximations of stochastic differential equations of Itô type,

where convergence rates of the approximate solutions are obtained using. The rates can

also be interpreted as rates for the Lp Wasserstein metrics, p∊[1,∞), between the …

1996

MR1385397 (97d:60025) Cuesta-Albertos, J. A.; Matrán-Bea, C.; Tuero-Diaz, A. On lower bounds for the $L^2$-Wasserstein metric in a Hilbert space. J. Theoret. Probab. 9 (1996), no. 2, 263--283. (Reviewer: Ludger Rüschendorf) 60E15

On lower bounds for theL ²-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

<-5

1996

[PDF] Optimal maps for the-Wasserstein distance

JA Cuesta-Albertos, C Matrán, A Tuero-Díaz - preprint, 1996 - personales.unican.es

In this paper we analize properties of the maps that give optimal transportation plans for the

L-2-Wasserstein distance. The main topics treated include existence, measurability,

continuity, uniqueness and convergence with respect to the weak convergence of probability …

[CITATION] Discretization for stochastic differential equations, L^ p-Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related …

1996

M GELBRICH - IMS Lecture Notes Monogr. Ser., 1996 - ci.nii.ac.jp

… Discretization for stochastic differential equations, L^p-Wasserstein metrics, and econometrical

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Discretization for Stochastic Differential Equations, L^p Wasserstein Metrics, and Econometrical Models

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The paper deals with weak approximations of stochastic differential equations of Itô type,

where convergence rates of the approximate solutions are obtained using. The rates can

also be interpreted as rates for the Lp Wasserstein metrics, p∊[1,∞), between the …

<——1996-1997———————1996-1997——- 10 —

1996

On lower bounds for theL²-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

1996

On lower bounds for the L2-Wasserstein metric in a Hilbert Spac

[PDF] Optimal maps for the L2-Wasserstein distance

JA Cuesta-Albertos, C Matrán, A Tuero-Dıaz - preprint, 1996 - pdfs.semanticscholar.org

In this paper we analize properties of the maps that give optimal transportation plans for the

L-2-Wasserstein distance. The main topics treated include existence, measurability,

continuity, uniqueness and convergence with respect to the weak convergence of probability …

1996

Journal of Theoretical Probability volume 9, pages 263–283 (1996)

by JA Cuesta-Albertos - ‎1996 - ‎Cited by 33 - ‎Related articles

We provide two families of lower bounds for the L2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we ...

<-10

1996

Independence of prime factors: total variation and Wasserstein metrics, insertions and deletions, and the Poisson-Dirichlet process

R Arratia - preprint, 1996 available from rarratia@math.usc.edu (1996)

Cited by 10 - Related articles . cited in in Microsurveys in Discrete Probability: Dimacs Workshop, June 2-6, 1997 By D. David J. Aldous, James Propp and Contemporary Combinatorics edited by Bela Bollobas

Series: Bolyai Society Mathematical Studies, Vol. 10 2002, II, 300 p.

[CITATION] Independence of prime factors: total variation and Wasserstein metrics, insertions and deletions, and the Poisson-Dirichlet process

R Arratia - preprint, 1996

On lower bounds for the L 2-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be …

1996

Discretization for Stochastic Differential Equations, L^p Wasserstein Metrics, and Econometrical Models

M Gelbrich, ST Rachev - Lecture Notes-Monograph Series, 1996 - JSTOR

The paper deals with weak approximations of stochastic differential equations of Itô type, where convergence rates of the approximate solutions are obtained using. The rates can also be interpreted as rates for the Lp Wasserstein metrics, p∊[1,∞), between the …

[CITATION] Discretization for stochastic differential equations, L^ p-Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related …

M GELBRICH - IMS Lecture Notes Monogr. Ser., 1996 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. CiNii窓口業務の再開について. Discretization for stochastic differential equations …

[CITATION] … for stochastic differential equations, L^ p-Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related topics

M GELBRICH - IMS Lecture Notes Monogr. Ser., 1996 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属.

刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Discretization for stochastic differential equations …

1996

On lower bounds for the L 2-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

<—15

1996

On lower bounds for the L 2 -Wasserstein metric in a Hilbert ...

link.springer.com/article/10.1007/BF02214649

We provide two families of lower bounds for theL 2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we f In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.

Author: J. A. Cuesta-Albertos, C. Matrán-Bea, A. Tuero-Diaz

Cited by: 17

Publish Year: 1996

1996

On lower bounds for the <Emphasis Type="Italic">L ...

link.springer.com › content › pdf

by JA Cuesta-Albertos · 1996 · Cited by 41 — KEY WORDS: L2-Wasserstein metric; Lower bound; Gaussian distributions;. Hilbert spaces. 1. INTRODUCTION. Although the L2-Wasserstein distance can be ...
CITATION] On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

JAC Albertos, CM Bea, A Tuero-Díaz - 1993 - Universidad de Cantabria …

1996 zzz 9

[CITATION] Independence of small prime factors: total variation and Wasserstein metrics, insertions and deletions, and the Poisson–Dirichlet process

R Arratia - Draft, available from rarratia@ math. usc. edu, 1996

[CITATION] Independence of small prime factors: total variation and Wasserstein metrics, insertions and deletions, and the Poisson–Dirichlet process

R Arratia - Draft, available from rarratia@ math. usc. edu, 1996

[CITATION] Independence of small prime factors: total variation and Wasserstein metrics, insertions and deletions, and the Poisson–Dirichlet process

R Arratia - Draft, available from rarratia@ math. usc. edu, 1996

[CITATION] Independence of small prime factors of a uniformly distributed integer: total variation and Wasserstein metrics

R Arratia - 1996 - Manuscrit

1996

On lower bounds for the L 2-Wasserstein metric in a Hilbert space

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

1996

[PDF] Optimal maps for the L2-Wasserstein distance

JA Cuesta-Albertos, C Matrán, A Tuero-Dıaz - preprint, 1996 - personales.unican.es

In this paper we analize properties of the maps that give optimal transportation plans for the

L-2-Wasserstein distance. The main topics treated include existence, measurability,

continuity, uniqueness and convergence with respect to the weak convergence of probability …

On lower bounds for the L 2-Wasserstein metric in a Hilbert space

<-20

1996

JA Cuesta-Albertos, C Matrán-Bea… - Journal of Theoretical …, 1996 - Springer

We provide two families of lower bounds for the L 2-Wasserstein metric in separable Hilbert

spaces which depend on the basis chosen for the space. Then we focus on one of these

families and we provide a necessary and sufficient condition for the supremum in it to be …

1996

[PDF] Optimal maps for the L2-Wasserstein distance

JA Cuesta-Albertos, C Matrán, A Tuero-Dıaz - preprint, 1996 - personales.unican.es

In this paper we analize properties of the maps that give optimal transportation plans for the

L-2-Wasserstein distance. The main topics treated include existence, measurability,

continuity, uniqueness and convergence with respect to the weak convergence of probability …

Discretization for stochastic differential equations,

1996 January 1996 see 1998

L^p- Wasserstein metrics, and econometrical models

Matthias Gelbrich, Svetlozar T. Rachev

From Book: Distributions with fixed marginals and related topics

DOWNLOAD PDF

1996

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

1996 JOURNAL OF THEORETICAL PROBABILITY

J. A. Cuesta-Albertos ¹,C. Matrán-Bea ²,A. Tuero-Diaz ¹

¹ University of Cantabria ,² University of Valladolid

Discretization for stochastic differential equations, $L\sp p$ Wasserstein metrics, and econometrical models

Hilbert manifold

View More (8+)

We provide two families of lower bounds for theL2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional... View Full Abstract

1996

Matthias Gelbrich ,Svetlozar T. Rachev

1996

Stochastic partial differential equation

Stochastic differential equation

View More (3+)

[CITATION] Discretization for stochastic differential equations, L^ p-Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related …

M GELBRICH - IMS Lecture Notes Monogr. Ser., 1996 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属.

刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Discretization for stochastic differential equations …

Discretization for stochastic differential equations, $L\sp p$ Wasserstein metrics, and econometrical models
Discretization for Stochastic Differential Equations, L p Wasserstein Metrics, and Econometrical Models

<-25

1996 [PDF] projecteuclid.org

Discretization for Stochastic Differential Equations, L^p Wasserstein Metrics, and Econometrical Models

M Gelbrich, ST Rachev - Lecture Notes-Monograph Series, 1996 - JSTOR

The paper deals with weak approximations of stochastic differential equations of Itô type, where convergence rates of the approximate solutions are obtained using. The rates can also be interpreted as rates for the Lp Wasserstein metrics, p∊[1,∞), between the …

[CITATION] Discretization for stochastic differential equations, L^ p-Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related …

M GELBRICH - IMS Lecture Notes Monogr. Ser., 1996 - ci.nii.ac.jp

CiNii 論文 - Discretization for stochastic differential equations, L^p-Wasserstein metrics, and econometrical models. Distributions with fixed marginals and related topics … Discretization for stochastic differential equations, L^p-Wasserstein metrics, and econometrical models …

<-26 `1996

1997

Aplicaciones de las métricas de Wasserstein al análisis de datos

JMR Rodríguez - 1997 - dialnet.unirioja.es

Resumen SE DAN APLICACIONES DE LAS METRICAS DE WASSERSTEIN A LA

ESTADISTICA Y AL ANALISIS DE DATOS, LAS APLICACIONES SE BASAN EN LA

COMPARACION DE UNA DISTRIBUCION CON UNA FAMILIA DE DISTRIBUCIONES DE …

1997

Aplicaciones de las métricas de Wasserstein al análisis de datos

JM Rodríguez Rodríguez - 1997 - dialnet.unirioja.es

Resumen: SE DAN APLICACIONES DE LAS METRICAS DE WASSERSTEIN A LA

ESTADISTICA Y AL ANALISIS DE DATOS, LAS APLICACIONES SE BASAN EN LA

COMPARACION DE UNA DISTRIBUCION CON UNA FAMILIA DE DISTRIBUCIONES DE ...

Cached - All 2 versions

1997

Aplicaciones de las métricas de Wasserstein al análisis de datos

JMR Rodríguez - 1997 - dialnet.unirioja.es

Resumen SE DAN APLICACIONES DE LAS METRICAS DE WASSERSTEIN A LA

ESTADISTICA Y AL ANALISIS DE DATOS, LAS APLICACIONES SE BASAN EN LA

COMPARACION DE UNA DISTRIBUCION CON UNA FAMILIA DE DISTRIBUCIONES DE …

<——1996-1997———1996-1997———- 29 ——— end 1996-1997—

Wasserstein start 1998-1999

1999

MR1740113 (2001a:60024) del Barrio, Eustasio; Cuesta-Albertos, Juan A.; Matrán, Carlos; Rodríguez-Rodríguez, Jesús M. Tests of goodness of fit based on the $L_2$-Wasserstein distance. Ann. Statist. 27 (1999), no. 4, 1230--1239. (Reviewer: Lajos Horváth) 60F05 (60F25 62E20) }

Tests of goodness of fit based on

[PDF] TESTS OF GOODNESS OF FIT BASED ON THE L2-WASSERSTEIN DISTANCE

JA Cuesta-Albertos, E Del Barrio, C Matrán - 1999 - Citeseer

The Annals of Statistics 1999, Vol. 27, No. 4, 1230–1239

Abstract Given P1 and P2 in the set of probabilities on the line with nite second order

moment, P2 (<); the L2-Wasserstein distance between P1 and P2, is de ned as the lowest L2-

distance between random variables with these distribution laws. When P 2 P2 (<); has ...

Published 1999

Tests of Goodness of Fit Based on the L₂-Wasserstein Distance

E del Barrio, JA Cuesta-Albertos, C Matrán… - Annals of Statistics, 1999 - JSTOR

We consider the Wasserstein distance between a sample distribution and the set of normal

distributions as a measure of nonnormality. By considering the standardized version of this

distance we obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of …

Tests of goodness of fit based on the $L_2$-Wasserstein distance

1999

[PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

Alison L Gibbs - 1999 - Citeseer

Abstract This paper gives precise bounds on the convergence time of the Gibbs sampler

used in the Bayesian restoration of a degraded image. Convergence to stationarity is

assessed using the Wasserstein metric, rather than the usual choice of total variation ...

Shape recognition via Wasserstein distance

published 2004

1999

W Gangbo, RJ McCann - 1999 - mis.mpg.de

Quarterly of applied mathematics, 58 (2000) 4, p. 705-737

Abstract: The Kantorovich-Rubinstein-Wasserstein metric defines the distance between two

probability measures f and g on R d+ 1 by computing the cheapest way to transport the mass

of f onto g, where the cost per unit mass transported is a given function c (x, y) on R 2d+ 2. ...

Shape recognition via Wasserstein distance

1999

MR1698999 (2000g:60034) del Barrio, Eustasio; Giné, Evarist; Matrán, Carlos Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Ann. Probab. 27 (1999), no. 2, 1009--1071. (Reviewer: Lajos Horváth) 60F05 (60B12 62E20). Zentralblatt MATH: 0958.60012. Cited by 45

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

MR1726488 (2000k:65173) Kinderlehrer, David; Walkington, Noel J. Approximation of parabolic equations using the Wasserstein metric. M2AN Math. Model. Numer. Anal. 33 (1999), no. 4, 837--852. (Reviewer: Wilfrid Gangbo) 65M60 (35A35)

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling and …, 1999 - cambridge.org

We illustrate how some interesting new variational principles can be used for the numerical

approximation of solutions to certain (possibly degenerate) parabolic partial differential

equations. One remarkable feature of the algorithms presented here is that derivatives do …

Approximation of Parabolic Equations Using the Wasserstein Metric

1999 [PDF] hokudai.ac.jp

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

1999

Tests of goodness of fit based on the L-2-Wasserstein distance

[PDF] Tests of goodness of fit based on the L 2-Wasserstein distance

JA Cuesta-Albertos, C Matrán… - The Annals of …, 1999 - pdfs.semanticscholar.org

Given P1 and P2 in the set of probabilities on the line with nite second order moment, P2 (<);

the L2-Wasserstein distance between P1 and P2, is de ned as the lowest L2-distance

between random variables with these distribution laws. When P 2 P2 (<); has variance 2 0; …

1999

By: Del Barrio, E; Cuesta-Albertos, JA; Matran, C; et al.

ANNALS OF STATISTICS Volume: ‏ 27 Issue: ‏ 4 Pages: ‏ 1230-1239 Published: ‏ AUG 1999

Times Cited: 57

1999

Approximation of parabolic equations using the Wasserstein metric

By: Kinderlehrer, D; Walkington, NJ

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE Volume: ‏ 33 Issue: ‏ 4 Pages: ‏ 837-852 Published: ‏ JUL-AUG 1999

Approximation of L-1-Wasserstein distance

Times Cited: 33

1999

By: Abdellaoui, T

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE Volume: ‏ 328 Issue: ‏ 12 Pages: ‏ 1203-1206 Published: ‏ JUN 15 1999

<——1998-1999————1998-1999——-—- 10—-

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

By: Del Barrio, E; Gine, E; Matran, C

ANNALS OF PROBABILITY Volume: ‏ 27 Issue: ‏ 2 Pages: ‏ 1009-1071 Published: ‏ APR 1999

Central Limit Theorems for the Wasserstein Distance Between the Empirical and the True Distributions

Times Cited: 64

1999

[PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

AL Gibbs - 1999 - Citeseer

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the

Bayesian restoration of a degraded image. Convergence to stationarity is assessed using

the Wasserstein metric, rather than the usual choice of total variation distance. The …

PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

1999

AL Gibbs - 1999 - Citeseer

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the

Bayesian restoration of a degraded image. Convergence to stationarity is assessed using

the Wasserstein metric, rather than the usual choice of total variation distance. The

Wasserstein metric may be more easily applied in some applications, particularly those on

continuous state spaces. Bounds on convergence time are established by considering the

number of iterations required to approximately couple two realisations of the Markov chain to …

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

1999

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we

study the asymptotic behavior of the dynamical systems which describe their approximation

of the Fokker-Planck equation and characterize the limit as a solution to a class of variational

problems. We also give a simple approach in a one-dimensional case.

[CITATION] Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric, Series 464 (1999)T Mikami

Cited by 3 Related articles see 2000

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

rojecteuclid.org › download › pdf_1 › euclid.aos

by E del Barrio · 1999 · Cited by 135 — 1. Introduction. Goodness-of-fit tests are often based on some distances between probability laws (p.l.'s). In this work we follow this approach by using the L2-Wasserstein distance between a fixed distribution and a location scale family of probability distributions on R.

The Annals of Statistics

Vol. 27, No. 4 (Aug., 1999), pp. 1230-1239 (10 pages)

[CITATION] Rodriguezrodriguez Jes US M. Tests of goodness of fit based on the 12-wasserstein distance

BE Del, JA Cuestaalbertos, M Carlos - Annals of Statistics, 1999

1999

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling …, 1999 - esaim-m2an.org

We illustrate how some interesting new variational principles can be used for the numerical

approximation of solutions to certain (possibly degenerate) parabolic partial differential

equations. One remarkable feature of the algorithms presented here is that derivatives do …

[CITATION] Approximation of parabolic equations using the Wasserstein metric

DKN Walkington - Rairo-mathematical modelling and numerical …, 1999

1999

[PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

AL Gibbs - 1999 - Citeseer

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the

Bayesian restoration of a degraded image. Convergence to stationarity is assessed using

the Wasserstein metric, rather than the usual choice of total variation distance. The …

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

1999

[PDF] hokudai.ac.jp

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

1999

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling …, 1999 - esaim-m2an.org

We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do …

[CITATION] Approximation of parabolic equations using the Wasserstein metric

DKN Walkington - Rairo-mathematical modelling and numerical …, 1999

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

1999

[PDF] hokudai.ac.jp

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

[PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

AL Gibbs - 1999 - Citeseer

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the Bayesian restoration of a degraded image. Convergence to stationarity is assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The …

Tests of Goodness of Fit Based on the L₂-Wasserstein Distance

E Del Barrio, JA Cuesta-Albertos, C Matrán… - Annals of Statistics, 1999 - JSTOR

We consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality. By considering the standardized version of this distance we obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of …

1999

[PDF] Tests of goodness of fit based on the L 2-Wasserstein distance

JA Cuesta-Albertos, C Matrán… - … Annals of Statistics, 1999 - Citeseer

Given P1 and P2 in the set of probabilities on the line with nite second order moment, P2 (<); the L2-Wasserstein distance between P1 and P2, is de ned as the lowest L2-distance between random variables with these distribution laws. When P 2 P2 (<); has variance 2 0; …

1999

Tests of Goodness of Fit Based on the L₂-Wasserstein Distance

E Del Barrio, JA Cuesta-Albertos, C Matrán… - Annals of Statistics, 1999 - JSTOR

1999

[PDF] Tests of goodness of fit based on the L 2-Wasserstein distance

JA Cuesta-Albertos, C Matrán… - The Annals of …, 1999 - Citeseer

1999

Approximation de la L1-distance de Wasserstein

T Abdellaoui - Comptes Rendus de l'Académie des Sciences-Series I …, 1999 - Elsevier

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case of ℝ n space, can be obtained via the resolution of nonlinear equation g (·)= α, where g is a cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

<——1998-1999———————1998-1999——- 30—

1999

Approximation de la L1-distance de Wasserstein

T Abdellaoui - Comptes Rendus de l'Académie des Sciences-Series I …, 1999 - Elsevier

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of ℝ n space, can be obtained via the resolution of nonlinear equation g (·)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling …, 1999 - esaim-m2an.org

We illustrate how some interesting new variational principles can be used for the numerical

approximation of solutions to certain (possibly degenerate) parabolic partial differential

equations. One remarkable feature of the algorithms presented here is that derivatives do …

[CITATION] Approximation of parabolic equations using the Wasserstein metric

DKN Walkington - Rairo-mathematical modelling and numerical …, 1999

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling …, 1999 - esaim-m2an.org

We illustrate how some interesting new variational principles can be used for the numerical

approximation of solutions to certain (possibly degenerate) parabolic partial differential

equations. One remarkable feature of the algorithms presented here is that derivatives do …

[CITATION] Approximation of parabolic equations using the Wasserstein metric

DKN Walkington - Rairo-mathematical modelling and numerical …, 1999

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

Tests of Goodness of Fit Based on the L₂-Wasserstein Distance

E Del Barrio, JA Cuesta-Albertos, C Matrán… - Annals of Statistics, 1999 - JSTOR

We consider the Wasserstein distance between a sample distribution and the set of normal

distributions as a measure of nonnormality. By considering the standardized version of this

distance we obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of …

<-5->

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

[PDF] Tests of goodness of fit based on the L 2-Wasserstein distance

JA Cuesta-Albertos, C Matrán… - The Annals of …, 1999 - Citeseer

Given P1 and P2 in the set of probabilities on the line with nite second order moment, P2 (<);

the L2-Wasserstein distance between P1 and P2, is de ned as the lowest L2-distance

between random variables with these distribution laws. When P 2 P2 (<); has variance 2 0; …

1999

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

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Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

Tests of Goodness of Fit Based on the L₂-Wasserstein Distance

E Del Barrio, JA Cuesta-Albertos, C Matrán… - Annals of Statistics, 1999 - JSTOR

We consider the Wasserstein distance between a sample distribution and the set of normal

distributions as a measure of nonnormality. By considering the standardized version of this

distance we obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of …

PDF] psu.edu

[PDF] Tests of goodness of fit based on the L 2-Wasserstein distance

JA Cuesta-Albertos, C Matrán… - The Annals of …, 1999 - Citeseer

Given P1 and P2 in the set of probabilities on the line with nite second order moment, P2 (<);

the L2-Wasserstein distance between P1 and P2, is de ned as the lowest L2-distance

between random variables with these distribution laws. When P 2 P2 (<); has variance 2 0; …

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling …, 1999 - esaim-m2an.org

We illustrate how some interesting new variational principles can be used for the numerical

approximation of solutions to certain (possibly degenerate) parabolic partial differential

equations. One remarkable feature of the algorithms presented here is that derivatives do …

[<——1998-1999———————1998-1999——- 40—

[PDF] hokudai.ac.jp

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

Approximation of L1-Wasserstein distance

T Abdellaoui - Comptes Rendus de l'Academie des Sciences Series I …, 1999 - infona.pl

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of R n space, can be obtained via the resolution of nonlinear equation g (.)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

[PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

AL Gibbs - 1999 - Citeseer

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the

Bayesian restoration of a degraded image. Convergence to stationarity is assessed using

the Wasserstein metric, rather than the usual choice of total variation distance. The …

[PDF] Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications in Image Processing

<-5->

1999

AL Gibbs - 1999 - Citeseer

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the

Bayesian restoration of a degraded image. Convergence to stationarity is assessed using

the Wasserstein metric, rather than the usual choice of total variation distance. The …

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

1999

[PDF] hokudai.ac.jp

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

Approximation de la L1-distance de Wasserstein

1999

T Abdellaoui - Comptes Rendus de l'Académie des Sciences-Series I …, 1999 - Elsevier

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of ℝ n space, can be obtained via the resolution of nonlinear equation g (·)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

Mean rates of convergence of empirical measures in the Wasserstein metric

1999

J Horowitz, RL Karandikar - Journal of Computational and Applied …, 1994 - Elsevier

An upper bound is given for the mean square Wasserstein distance between the empirical

measure of a sequence of iid random vectors and the common probability law of the

sequence. The same result holds for an infinite exchangeable sequence and its directing …

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

<——1998-1999———————1998-1999——- 50—

1999

Approximation of parabolic equations using the Wasserstein metric

D Kinderlehrer, NJ Walkington - ESAIM: Mathematical Modelling …, 1999 - esaim-m2an.org

We illustrate how some interesting new variational principles can be used for the numerical

approximation of solutions to certain (possibly degenerate) parabolic partial differential

equations. One remarkable feature of the algorithms presented here is that derivatives do …

[CITATION] Approximation of parabolic equations using the Wasserstein metric

DKN Walkington - Rairo-mathematical modelling and numerical …, 1999

Approximation de la L1-distance de Wasserstein

1999

T Abdellaoui - Comptes Rendus de l'Académie des Sciences-Series I …, 1999 - Elsevier

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of ℝ n space, can be obtained via the resolution of nonlinear equation g (·)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

Approximation of L1-Wasserstein distance

1999

T Abdellaoui - Comptes Rendus de l'Academie des Sciences Series I …, 1999 - infona.pl

In this Note, we show that an optimal coupling for the L 1-Wasserstein distance, in the case

of R n space, can be obtained via the resolution of nonlinear equation g (.)= α, where g is a

cyclically monotone application. Hence, to get an approximation to the optimal coupling, it …

1999

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t)-

F (t)| dt of the centered empirical process, tends to zero as The object of this article is to …

1999

Tests of Goodness of Fit Based on the L₂-Wasserstein Distance

E Del Barrio, JA Cuesta-Albertos, C Matrán… - Annals of Statistics, 1999 - JSTOR

We consider the Wasserstein distance between a sample distribution and the set of normal

distributions as a measure of nonnormality. By considering the standardized version of this

distance we obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of …

Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metric

[PDF] Tests of goodness of fit based on the L 2-Wasserstein distance

JA Cuesta-Albertos, C Matrán… - The Annals of …, 1999 - Citeseer

Given P1 and P2 in the set of probabilities on the line with nite second order moment, P2 (<);

the L2-Wasserstein distance between P1 and P2, is de ned as the lowest L2-distance

between random variables with these distribution laws. When P 2 P2 (<); has variance 2 0; …

1999

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the

Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein …

Plank equation by the Wasserstein metric

T Mikami - Hokkaido University Preprint Series in …, 1999 - eprints.lib.hokudai.ac.jp

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional and the Gibbs-Boltzmann entropy functional. In this paper we …

Tests of goodness of fit based on the -Wasserstein distance

1999 [PDF] projecteuclid.org

JA Cuesta-Albertos, C Matrán… - The Annals of …, 1999 - projecteuclid.org

… We consider the Wasserstein distance between a sample … of this distance we obtain a version

of Shapiro–Wilk’s test of normality. … by using the L2-Wasserstein distance between a fixed …

1999 [PDF] projecteuclid.org

Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E Del Barrio, E Giné, C Matrán - Annals of Probability, 1999 - JSTOR

If X is integrable, F is its cdf and Fn is the empirical cdf based on an iid sample from F, then

the Wasserstein distance between Fn and F, which coincides with the L1 norm∫∞-∞| Fn (t) …

1999
Tests of Goodness of Fit Based on the L 2 -Wasserstein Distance

Authors:Eustasio del Barrio, Juan A. Cuesta-Albertos, Carlos Matran, Jesus M. Rodriguez-Rodriguez
Summary:We consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality. By considering the standardized version of this distance we obtain a version of Shapiro-Wilk's test of normality. The asymptotic behavior of the statistic is studied using approximations of the quantile process by Brownian bridges. This method differs from the "ad hoc" method of de Wet and Venter and permits a similar analysis for testing other location scale familiesShow
Article, 1999
Publication:The Annals of Statistics, 27, 19990801, 1230
Publisher:1999

<——1998-1999———————1998-1999——- 60—

1999
Approximations of parabolic equations based upon Wasserstein's variational principle

Authors:David Kinderlehrer, Noel Walkington
Summary:Abstract: "We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into the variational formulations."Show more
Print Book, [1999]
English
Publisher:Carnegie Mellon University, Dept. of Mathematical Sciences, Center for Nonlinear Analysis, Pittsburgh, Pa., [1999]

1999 Peer-reviewed
Approximation de la L 1-distance de WassersteinAuthor:Taoufiq Abdellaoui
Summary:Dans cette Note, nous montrons qu'un couple optimal de la L 1 -distance de Wasserstein, dans le cas ℝ n
Article
Publication:Comptes Rendus de l'Academie des Sciences Series I Mathematics, 328, 1999, 120

Tests of goodness of fit based on the L2~-Wasserstein distance

Authors:E. del Barrio, J. A. Cuesta-Albertos, C. Matran, J. M. Rodriguez-Rodriguez
Article, 1999
Publication:ANNALS OF STATISTICS, 27, 1999, 1230
Publisher:1999

1999 Peer-reviewed
Approximation de la L1^-distance de Wasserstein

Author:T. Abdellaoui
Article, 1999
Publication:COMPTES RENDUS- ACADEMIE DES SCIENCES PARIS SERIE 1, 328, 1999, 1203
Publisher:1999
View AllFormats & Editions

1999
Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric Toshio MikamiAuthor:Toshio Mikami
Print Book, 1999
English
Publisher:Dept. of Mathematics, Hokkaido Univ., Sapporo, 1999

<5>

v1999

Tests of Goodness of Fit Based on the L₂

JSTOR

https://www.jstor.org › stable

by E del Barrio · 1999 · Cited by 172 — Goodness-of-fit tests are often based on some distances between probability laws (p.l.'s). In this work we follow this approach by using the L2-Wasserstein ...

1998

TESTS OF GOODNESS OF FIT BASED ON THE L2- ...

unican.es

https://personales.unican.es › cuestaj › L2Based...

by E del Barrio · Cited by 172 — Abstract. We consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of non-normality.

9 pages

[CITATION] Descriptive statistics and tests of goodness of fit based on the L2-Wasserstein distance

E del Barrio, C Matrán, J Rodrıguez-Rodrıguez… - 1998 - Technical report, Univ. Valladolid

Distances de Wasserstein et de Zolotarev

<——1998-1999———————1998-1999——- 67— end 1998-1999

Wasserstein start 2000

MR1769953 (2001b:60008) Belili, Nacereddine; Heinich, Henri Distances de Wasserstein et de Zolotarev. (French) [Wasserstein and Zolotarev distances] C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 9, 811--814. 60B10 (60E05)

N Belili, H Heinich - Comptes Rendus de l'Académie des Sciences-Series I …, 2000 - Elsevier

Résumé. Dans cette Note nous comparons la distance minimale (de Wasserstein) et celle de

Zolotarev pour des probabilités sur Rd. Dans le cas d = 1, nous donnons une nouvelle preuve

SAS … Abstract. In this Note we compare Wasserstein and Zolotarev distances between probability

des sciences/Éditions scientifiques et médicales Elsevier SAS … Pour simplifier, toutes les variables …

MR1784174 (2002b:60055) Mikami, T. Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric. Appl. Math. Optim. 42 (2000), no. 2, 203--227. (Reviewer: Shuenn Jyi Sheu) 60F15 (60H30 82C35)

Dynamical Systems in the Variational Formulation of the Fokker—Planck Equation by the Wasserstein Metric

T Mikami - Applied Mathematics and Optimization, 2000 - Springer

R. Jordan, D. Kinderlehrer, and F. Otto proposed the discrete-time approximation of the

Fokker—Planck equation by the variational formulation. It is determined by the Wasserstein

metric, an energy functional, and the Gibbs—Boltzmann entropy functional. In this paper we …

2000 see 1999

MR1788425 (2002k:94006) Gangbo, Wilfrid; McCann, Robert J.

Shape recognition via Wasserstein distance. Quart. Appl. Math. 58 (2000), no. 4, 705--737. 94A08 (28A35 49Q20). Zbl 1039.49038
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Times Cited: 37

2000

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APPLIED MATHEMATICS AND OPTIMIZATION Volume: ‏ 42 Issue: ‏ 2 Pages: ‏ 203-227 Published: ‏ SEP-OCT 2000

Times Cited: 8

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<——2000—————2000——— -10—

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2000

[PDF] hokudai.ac.jp

Dynamical Systems in the Variational Formulation of the Fokker—Planck Equation by the Wasserstein Metric

T Mikami - Applied Mathematics and Optimization, 2000 - Springer

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Dynamical Systems in the Variational Formulation ... - HUSCAP

eprints.lib.hokudai.ac.jp › dspace › bitstream › AMO42-2

PDF 2000

Key words: Fokker-Planck equation, Wasserstein metric, energy functional, Gibbs-. Boltzmann entropy functional, dynamical systems, variational problem.
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A time dependent minimization problem for the computation of a mixed L2/Wasserstein

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<——2000———2000——— -20—

omment: Testing for Weibull scale families as a test case for ...

www.researchgate.net › publication › 292298461_Comm...

Download Citation | On Jun 1, 2000, W Stute published Comment: Testing for Weibull scale families as a test case for Wasserstein correlation tests | Find, read ...

2000 zzzz 13

[CITATION] Comment: Testing for Weibull scale families as a test case for Wasserstein correlation tests

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2000 Research article
Distances de Wasserstein et de Zolotarev
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2000 PDF see 2001

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citeseerx.ist.psu.edu › viewdoc › download

PDF

by JD Benamou · 2000 · Cited by 51 — A time dependent minimization problem for the computation of a mixed L2/Wasserstein distance between two prescribed density functions is ...

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Abstract A time dependent minimization problem for the computation of a

mixedL2/Wasserstein distance between two prescribed density functions is introduced (in

the spirit of 1] for the\ classical" Wasserstein distance). The optimum of the cost function ...

2000

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S Csorgo - 2000 - … 104, 2 IZDA, 28004 MADRID, SPAIN

CITATION] Testing for Weibull scale families as a test case for Wasserstein correlation tests (Discussion of [7])

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2000 zzz 10

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N Belili, H Heinich - COMPTES RENDUS DE L …, 2000 - … MEDICALES ELSEVIER 23 RUE …

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<——2000———2000——— -30—

Shape recognition via Wasserstein distance

W Gangbo, RJ McCann - Quarterly of Applied Mathematics, 2000 - JSTOR

The Kantorovich-Rubinstein-Wasserstein metric defines the distance between two

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Comment: Testing for Weibull scale families ... - ResearchGate

https://www.researchgate.net › ... › Weibull Distribution

We formulate a general theorem concerning the asymptotic null distribution of weighted correlation test statistics for scale families, and demonstrate that the ...

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Comment: Testing for Weibull scale families ... - ResearchGatehttps://www.researchgate.net › ... › Weibull Distributionhttps:
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We formulate a general theorem concerning the asymptotic null distribution of weighted correlation test statistics for scale
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[PDF] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E Giné, C Matrán, E del Barrio - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

<——2000———2000——— -36— end 2000

Wasserstein start 2001

2001

MR1865668 (2002h:49069) Benamou, J. D.; Brenier, Y. Mixed $L^2$-Wasserstein optimal mapping between prescribed density functions. J. Optim. Theory Appl. 111 (2001), no. 2, 255--271. 49Q20 (49M30 65K10)

Mixed L²-Wasserstein Optimal Mapping Between Prescribed Density Functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

MR1878316 (2003d:46087) Biane, P.; Voiculescu, D.

A free probability analogue of the Wasserstein metric on the trace-state space. Geom. Funct. Anal. 11 (2001), no. 6, 1125--1138. (Reviewer: Dimitri Y. Shlyakhtenko) 46L54

Cited by 70 Related articles

A Free Probability Analogue of the Wasserstein Metric on the ...

by P Biane - ‎2000 - ‎Cited by 70 - ‎Related articles

Jun 6, 2000 - ... Analogue of the Wasserstein Metric on the Trace-State Space ... distance to the semi-circle distribution is majorized by a modified free ...

Missing: TA

2001

Wasserstein-metric - Abteilung für Mathematische …

Wasserstein-metric The ‘Wasserstein-metric’ has a colourful history with several quite diﬀerent ﬁelds of appli-cations. It also has various historical sources. Bernulli 11(1) 2005, 131-189
[CITATION] Wasserstein-metric

L. Rüschendorf, “Wasserstein metric”, in Hazewinkel Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers,

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2001

Asymptotics for Wasserstein distances pdf

E del Barrio - unavarra.es

Wp is a metric on the space of probability measures with finite p-th moment that metrices weak

convergence plus convergence of p-th moments. These metrics have interesting applications

in Probability and Statistics, remarkably in the problem of testing goodness of fit. Here we ...

[CITATION] Asymptotics for empirical Wasserstein distances

Eustasio del Barrio Department of Statistics and Operations Research, University of Valladolid, Prado de la Magdalena S/N, 47005, Valladolid, Spain [tasio@eio.uva.es]

Feb 23, 2001 –

2001

Mixed L-2-Wasserstein optimal mapping between prescribed density functions

By: Benamou, JD; Brenier, Y

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS Volume: ‏ 111 Issue: ‏ 2 Pages: ‏ 255-271 Published: ‏ NOV 2001

Times Cited: 23

2001

A free probability analogue of the Wasserstein metric on the trace-state space

By: Biane, P; Voiculescu, D

GEOMETRIC AND FUNCTIONAL ANALYSIS Volume: ‏ 11 Issue: ‏ 6 Pages: ‏ 1125-1138 Published: ‏ 2001

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical

one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle

distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

Encyclopaedia of Mathematics - Springer

https://www.springer.com › book

No information is available for this page.

Learn why

[CITATION] Wasserstein metric

L Rüschendorf - Hazewinkel, Michiel, Encyclopaedia of Mathematics …, 2001

Cited by 82 Related articles

Times Cited: 36

Mixed L²-Wasserstein Optimal Mapping Between Prescribed Density Functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

Cited by 49 Related articles All 15 versions
<——2001——2001—— -10—

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical

one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle

distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical

one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle

distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

Mixed L 2-Wasserstein optimal mapping between prescribed density functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

Mixed L 2-Wasserstein optimal mapping between prescribed density functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

Mixed L 2-Wasserstein optimal mapping between prescribed density functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

[

[CITATION] Wasserstein metric

L Rüschendorf - Encyclopedia of Mathematics (ed. M. Hazewinkel) …, 2001

Cited by 82 Related articles

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical

one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle

distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

2001

Mixed L 2-Wasserstein optimal mapping between prescribed density functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical

one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle

distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

<——2001——— -20—

2001

CITATION] Wasserstein (Vasershtein) metric

L Rueshendorff - Encyclopaedia of Mathematics, 2001 - Springer

Wasserstein metric - Encyclopedia of Mathematics

encyclopediaofmath.org › wiki › Wasserstein_metric

Jul 1, 2020 - Vasershtein metric. The "Wasserstein metric" has a colourful history with several quite different fields of applications. It also has various ...

Mixed L 2-Wasserstein optimal mapping between prescribed density functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of the cost function corresponds to an optimal …

Mixed L 2-Wasserstein optimal mapping between prescribed density functions

JD Benamou, Y Brenier - Journal of Optimization Theory and Applications, 2001 - Springer

A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein

distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the

classical Wasserstein distance. The optimum of t

2001 [PDF] arxiv.org

A free probability analogue of the Wasserstein metric on the trace-state space

P Biane, D Voiculescu - Geometric & Functional Analysis GAFA, 2001 - Springer

Abstract We define a free probability analogue of the Wasserstein metric, which extends the classical

one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle

distribution is majorized by a modified free entropy quantity … The Wasserstein distance between …

he cost function corresponds to an optimal …

Mixed L-2-Wasserstein optimal mapping between prescribed density functions

Benamou, JD and Brenier, Y

Nov 2001 | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 111 (2) , pp.255-271

A time-dependent minimization problem for the computation of a mixed L-2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed initial and final densities. We enforce the final density conditions through a penalization term a

Mixed L 2-Wasserstein Optimal Mapping ... - Springer Link

25 Citations 7 References Related records

2021

2001

https://link.springer.com › article

by JD Benamou · 2001 · Cited by 54 — A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein distance between two prescribed density functions is introduced in the.

2001

Mixed L 2 -Wasserstein Optimal Mapping Between Prescribed ...

https://www.researchgate.net › ... › Geoscience › Mapping

Jul 5, 2022 — A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein distance between two prescribed density functions is ...

Peer-reviewed
Mixed L2-Wasserstein Optimal Mapping Between Prescribed Density FunctionsAuthors:J. D. Benamou, Y. Brenier
Summary:A time-dependent minimization problem for the computation of a mixed L2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed initial and final densities. We enforce the final density conditions through a penalization term added to our cost function. A conjugate gradient method is used to solve this relaxed problem. We obtain an algorithm which computes an interpolated L2-Wasserstein distance between two densities and the corresponding optimal mappingShow more
Article, 2001
Publication:Journal of Optimization Theory and Applications, 111, 200111, 255
Publisher:2001
MIXED L2-WASSERSTEIN OPTIMAL MAPPING BETWEEN PRESCRIBED DENSITY FUNCTIONSAuthors:J.D. BENAMOU, Y. BRENIER
Article, 2001
Undefined
Publication:Journal of optimization theory and applications
Publisher:2001

<——2001——— 28—emd 2001 titles with Wasserstein (Vasershtein)

Wasserstein start 2002

2002

MR1915779 (2003d:62061) de Wet, T. Goodness-of-fit tests for location and scale families based on a weighted $L_2$-Wasserstein distance measure. Test 11 (2002), no. 1, 89--107. 62F05 (60G15 62E20). Zentralblatt MATH: 1037.62007

link.springer.com › article

by T de Wet - ‎2002 - ‎Cited by 35 - ‎Related articles

(2000) consider a new class of goodness-of-fit statistics based on theL ₂-Wasserstein distance. ... These weight functions are such that the corresponding minimum distance estimators for the location parameter and the scale parameter are asymptotically efficient. Examples are discussed for both location and scale families.

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class

of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting

distribution of these statistics and show that the normal distribution is the only location-scale …

MR1936827 (2003h:28006) Belili, Nacereddine; Heinich, Henri Approximation pour la distance de Wasserstein. (French) [Approximation for the Wasserstein distance] C. R. Math. Acad. Sci. Paris 335 (2002), no. 6, 537--540. (Reviewer: Klaus D. Schmidt) 28A33 (60A10)

Approximation pour la distance de Wasserstein - ScienceDirect

by N Belili - ‎2002 - ‎Cited by 1 - ‎Related articles

Sep 15, 2002 - ... où l est le carré de la distance de Wasserstein. Pour citer cet article : N. Belili, H. Heinich, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 537–540.

MR2058979 (2005k:62030) Cuesta-Albertos, Juan A.; Matrán Bea, Carlos; Rodríguez Rodríguez, Jesús M. Shape of a distribution through the $L_2$-Wasserstein distance. Distributions with given marginals and statistical modelling, 51--61, Kluwer Acad. Publ., Dordrecht, 2002. 62E10 (62E17 62H05)

Shape of a Distribution Through the L₂-Wasserstein Distance

JA Cuesta-Albertos, CM Bea… - Distributions with Given …, 2002 - Springer

Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures

on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest

law to Q in ℑ, through the L 2-Wasserstein distance, as a descriptive measure associated to …

2002 see 2005 zzz 12

[CITATION] Asymptotics for L 2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances

Eustasio Del Barrio, Evarist Giné, and Frederic Utzet … - Preprint, 2002 published Bernoulli Volume 11, Number 1 (2005), 131-189.

ABSTRACT Weighted L₂ functionals of the empirical quantile process appear as a component of many test statistics, in particular in tests of fit to location-scale families of distributions based on weighted Wasserstein distances. An essentially complete set of distributional limit theorems for the squared empirical quantile process integrated with respect to general weights is presented. The results rely on limit theorems for quadratic forms in exponential random variables, and the proofs use only simple asymptotic theory for probability distributions in Rⁿ. The limit theorems are then applied to determine the asymptotic distribution of the test statistics on which weighted Wasserstein tests are based. In particular, this paper contains an elementary derivation of the limit distribution of the Shapiro-Wilk test statistic under normality.

Asymptotics for L2 functionals of the empirical quantile process, with ...

by E Del Barrio - ‎2005 - ‎Cited by 40 - ‎Related articles

Cited by 64 Related articles

Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

E Del Barrio, E Giné, F Utzet - Bernoulli, 2005 - projecteuclid.org

… This is the main component in statistics used, for example, in tests of fit based on the correlation

coefficient (see Lockhart and Stephens 1998; and references therein), and in the related tests

of fit based on Wasserstein distances (del Barrio et al. 1999a) …

Cited by 78 Related articles All 7 versions
[CITATION] Asymptotics for L 2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances

E del Barrio, E Gine - Preprint, 2002

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

2002

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting distribution of these statistics and show that the normal distribution is the only location-scale …

2002

Approximation for the Wasserstein distance

By: Belili, N; Heinich, H

COMPTES RENDUS MATHEMATIQUE Volume: ‏ 335 Issue: ‏ 6 Pages: ‏ 537-540 Article Number: PII S1631-073X(02)02522-0/FLA Published: ‏ SEP 15 2002

Approximation pour la distance de Wasserstein

N Belili, H Heinich - Comptes Rendus Mathematique, 2002 - Elsevier

Let C be a set of probability-measures and P a probability on R d. Under some conditions,

we show that we have a solution to the approximation problem of P by C. There exists a

probability Q 0∈ C, such that l (P, Q 0)⩽ l (P, Q),∀ Q∈ C where l is the square of the …

Wasserstein at Lazard:'One Firm'

Distributional Sliced-Wasserstein and Applications to Generative Modeling

K Nguyen, N Ho, T Pham, H Bui - arXiv preprint arXiv:2002.07367, 2020 - arxiv.org

Sliced-Wasserstein distance (SWD) and its variation, Max Sliced-Wasserstein distance (Max-

SWD), have been widely used in the recent years due to their fast computation and

scalability when the probability measures lie in very high dimension. However, these …

Times Cited: 14

(from Web of Scie

Shape of a Distribution Through the L₂-Wasserstein Distance

JA Cuesta-Albertos, CM Bea… - Distributions with Given …, 2002 - Springer

Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures

on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest

law to Q in ℑ, through the L 2-Wasserstein distance, as a descriptive measure associated to …

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class

of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting

distribution of these statistics and show that the normal distribution is the only location-scale …

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class

of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting

distribution of these statistics and show that the normal distribution is the only location-scale …

[

2002 PDF

Approximate Bayesian computation with the Wasserstein ...

espenbernton.github.io › files › wabc_arxiv

recently developed approximations of the Wasserstein distance allow the method ... models is approximate Bayesian computation (ABC, Beaumont et al., 2002; ...

[CITATION] Approximation for the Wasserstein distance

N Belili, H Heinich - COMPTES RENDUS …, 2002 - ELSEVIER FRANCE-EDITIONS …

Shape of a Distribution Through the L₂-Wasserstein Distance

JA Cuesta-Albertos, CM Bea… - Distributions with Given …, 2002 - Springer

Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures

on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest

law to Q in ℑ, through the L 2-Wasserstein distance, as a descriptive measure associated to …

Asynptotics for L2 functionals of the empirical quantile ...

www.semanticscholar.org › paper › Asymptotics-for-L2-f...

... extracted view of "Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances" by ...

[CITATION] Asymptotics for L 2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances

E del Barrio, E Gine - Preprint, 2002

Cited by 2 Related articles See 2005

2002

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

Shape of a Distribution Through the L₂-Wasserstein Distance

JA Cuesta-Albertos, CM Bea… - Distributions with Given …, 2002 - Springer

Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest law to Q in ℑ, through the L 2-Wasserstein distance, as a descriptive measure associated to …

The Monge–Kantorovitch mass transfer and its computational fluid mechanics formulation

JD Benamou, Y Brenier, K Guittet - International Journal for …, 2002 - Wiley Online Library

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2002; 40:21–30 (DOI: 10.1002/ d.264) … The Monge–Kantorovitch mass transfer and its computational uid mechanics formulation … J.-D. Benamou1;2;∗ , Y. Brenier1;2 and K. Guittet1;2 …

Approximation pour la distance de Wasserstein

N Belili, H Heinich - Comptes Rendus Mathematique, 2002 - Elsevier

Let C be a set of probability-measures and P a probability on R d. Under some conditions, we show that we have a solution to the approximation problem of P by C. There exists a probability Q 0∈ C, such that l (P, Q 0)⩽ l (P, Q),∀ Q∈ C where l is the square of the …

2002

Approximation pour la distance de Wasserstein

N Belili, H Heinich - Comptes Rendus Mathematique, 2002 - Elsevier

Let C be a set of probability-measures and P a probability on R d. Under some conditions,

we show that we have a solution to the approximation problem of P by C. There exists a

probability Q 0∈ C, such that l (P, Q 0)⩽ l (P, Q),∀ Q∈ C where l is the square of the …

<——2002————-2002———20—

2002

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class

of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting

distribution of these statistics and show that the normal distribution is the only location-scale …

2002 see 2005 zzz 13

[CITATION] Asymptotics for L 2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances

E del Barrio, E Gine - Preprint, 2002

Shape of a Distribution Through the L₂-Wasserstein Distance

JA Cuesta-Albertos, CM Bea… - Distributions with Given …, 2002 - Springer

Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures

on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest

law to Q in ℑ, through the L 2-Wasserstein distance, as a descriptive measure associated to …

[CITATION] Asymptotics for L 2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances

E del Barrio, E Gine - Preprint, 2002

Approximate Bayesian computation with the Wasserstein ...

2002 PDF

[CITATION] Approximation for the Wasserstein distance

N Belili, H Heinich - COMPTES RENDUS …, 2002 - ELSEVIER FRANCE-EDITIONS …

https://espenbernton.github.io › files › wabc_arxiv

recently developed approximations of the Wasserstein distance allow the method ... models is approximate Bayesian computation (ABC, Beaumont et al., 2002; ...

2002 [PDF] unican.es

Shape of a Distribution Through the L₂-Wasserstein Distance

JA Cuesta-Albertos, CM Bea… - Distributions with Given …, 2002 - Springer

Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures

on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest

law to Q in ℑ, through the L 2-Wasserstein distance, as a descriptive measure associated to …

2002

Approximation pour la distance de Wasserstein

N Belili, H Heinich - Comptes Rendus Mathematique, 2002 - Elsevier

Let C be a set of probability-measures and P a probability on R d. Under some conditions,

we show that we have a solution to the approximation problem of P by C. There exists a

probability Q 0∈ C, such that l (P, Q 0)⩽ l (P, Q),∀ Q∈ C where l is the square of the …

2002 [PDF] sciencedirect.com

Approximation pour la distance de Wasserstein

N Belili, H Heinich - Comptes Rendus Mathematique, 2002 - Elsevier

Let C be a set of probability-measures and P a probability on R d. Under some conditions,

we show that we have a solution to the approximation problem of P by C. There exists a

probability Q 0∈ C, such that l (P, Q 0)⩽ l (P, Q),∀ Q∈ C where l is the square of the …

Approximation pour la distance de Wasserstein

N Belili, H Heinich - Comptes Rendus Mathematique, 2002 - Elsevier

Let C be a set of probability-measures and P a probability on R d. Under some conditions,

we show that we have a solution to the approximation problem of P by C. There exists a

probability Q 0∈ C, such that l (P, Q 0)⩽ l (P, Q),∀ Q∈ C where l is the square of the …

Goodnes-of-fit tests for location and scale families based on a weighted L₂-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class

of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting

distribution of these statistics and show that the normal distribution is the only location-scale …

Goodnes-of-fit tests for location and scale families based on a weighted L 2-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

In two recent papers del Barrio et al.(1999) and del Barrio et al.(2000) consider a new class

of goodness-of-fit statistics based on the L 2-Wasserstein distance. They derive the limiting

distribution of these statistics and show that the normal distribution is the only location-scale …

<——2002————-2002——— -30—

2002 see 2001

Asymptotics for Wasserstein distances

http://www.unavarra.es › abstracts › Barrio

http://www.unavarra.es › abstracts › BarrioPDF

(2002). Asymptotics for L2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances. Preprint. [ ...

1 page

Goodnes-of-fit tests for location and scale families based on a weighted L2-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

… -of-fit statistics based on theL 2 -Wasserstein distance. They derive the limiting distribution of

… In this paper a weightedL 2 -Wasserstein distance is considered and it is proven that these …

Goodnes-of-fit tests for location and scale families based on a weighted L2-Wasserstein distance measure

Approximation for the Wasserstein distance

Belili, N and Heinich, H

Sep 15 2002 | COMPTES RENDUS MATHEMATIQUE 335 (6) , pp.537-540

Let C be a set of probability-measures and P a probability on R-d. Under some conditions, we show that we have a solution to the approximation problem of P by C. There exists a probability Q(0) is an element of C, such that l(P, Q(0)) less than or equal to l(P, Q), For AllQ is an element of C where l is the square of the Wasserstein distance. (C) 2002 Academie des sciences/Editions scientifique

4th Meeting on Distributions with Given Marginals and Statistical Modelling

3eferences

Cuesta-Albertos, JA; Bea, CM and Rodriguez, JMR

2002 | DISTRIBUTIONS WITH GIVEN MARGINALS AND STATISTICAL MODELLING , pp.51-61

Let Q be a probability measure on R-d and let J be a family of probability measures on Rd which will be considered as a pattern. For suitable patterns we consider the closest law to Q in J, through the L-2-Wasserstein distance, as a descriptive measure associated to Q. The distance between Q and J is a natural measure of the fit of Q to the pattern.

We analyze this approach via the consid

Goodness-of-fit tests for location and scale families based on a weighted L-2-Wasserstein distance measure

5 Citations 9 References Related records

de Wet, T

Jun 2002 | TEST 11 (1) , pp.89-107

In two recent papers del Barrio et at. (1999) and del Barrio et al. (2000) consider a new class of goodness-of-fit statistics based on the L-2-Wasserstein distance. They derive the limiting distribution of these statistics and show that the normal distribution is the only location-scale family for which this limiting distribution has the "loss of degrees of freedom" property, due to the estimat

MR1983782 (2004c:49027) Carlen, E. A.; Gangbo, W.

<—2002———2002——— -35— end 2002

Wasserstein start 2003

2003

MR1964961 (2004b:60060) del Barrio, Eustasio; Giné, Evarist; Matrán, Carlos Correction: ``Central limit theorems for the Wasserstein distance between the empirical and the true distributions'' [Ann. Probab. 27 (1999), no. 2, 1009--1071; MR1698999 (2000g:60034)]. Ann. Probab. 31 (2003), no. 2, 1142--1143. 60F05 (60B12 62E20)

Constrained steepest descent in the 2-Wasserstein metric. Ann. of Math. (2) 157 (2003), no. 3, 807--846. (Reviewer: Luigi De Pascale) 49J45 (35Q99 49J10 60H15 82C35)

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In particular, Jordan, Kinderlehrer and Otto, have shown in [12] that the heat equation is gradient flow for the entropy func- tional in the 2-Wasserstein metric. We can arrive most rapidly to the point of departure for our own problem, which concerns constrained gradient flow, by reviewing this result.

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MR2073437 (2005f:60056) Haeusler, Erich; Mason, David M. Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function. Stochastic inequalities and applications, 279--298, Progr. Probab., 56, Birkhäuser, Basel, 2003. (Reviewer: Lajos Horváth) 60F05 (62G30)

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T Schreiber - Colloquium Mathematicum, 2003 - pdfs.semanticscholar.org

1. Introduction and main results. The pioneering paper of Sanov (1957) on large deviations

for empirical measures generated by independent random elements gave rise to an

important number of refinements and applications both in probability theory (see eg Dembo

and Zeitouni (1993), Deuschel and Stroock (1989), Dupuis and Ellis (1997), Groeneboom,

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Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

By: Haeusler, E; Mason, DM

Conference: Conference on Stochastic Inequalities and Applications Location: ‏ BARCELONA, SPAIN Date: ‏ JUN 18-22, 2002

Sponsor(s): ‏Ctr Recerca Matemat

STOCHASTIC INEQUALITIES AND APPLICATIONS Book Series: ‏ PROGRESS IN PROBABILITY Volume: ‏ 56 Pages: ‏ 279-298 Published: ‏ 2003

Times Cited: 1

Constrained steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a

probability density F0 on Rd and a time-step h> 0, we seek to minimize over all of the …

Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

[CITATION] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

Asymptotics for Wasserstein distances

[CITATION] Correction-Central limit theorems for the Wasserstein distance between the empirical and the true distributions

ED Barrio, E Gine, C Matran - Annals of …, 2003 - Hayward, Calif.[etc.] Institute of …

E del Barrio - unavarra.es

Wp is a metric on the space of probability measures with finite p-th moment that metrices weak

convergence plus convergence of p-th moments. These metrics have interesting applications

in Probability and Statistics, remarkably in the problem of testing goodness of fit. Here we will …

2003 see 2004

Gradient flows with metric and differentiable structures ... - cvgmt

Dec 18, 2003 — In this paper we summarize some of the main results of a forthcoming book on this topic, where we examine in detail the theory of curves of ...

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

CORRECTION CENTRAL LIMIT THEOREMS FOR THE ...https://projecteuclid.org › volume-31 › issue-2 › aophttps://projecteuclid.org › volume-31 › issue-2 › aopby E Giné · 2003 — CORRECTION. CENTRAL LIMIT THEOREMS FOR. THE WASSERSTEIN DISTANCE BETWEEN. THE EMPIRICAL AND THE TRUE DISTRIBUTIONS. BY EUSTASIO DEL BARRIO, EVARIST GINÉ AND ...

[CITATION] Correction-Central limit theorems for the Wasserstein distance between the empirical and the true distributions

ED Barrio, E Gine, C Matran - Annals of …, 2003 - Hayward, Calif.[etc.] Institute of …

2003

arXiv:math/0312063 [pdf, ps, other] math.CA math.MG
Constrained deepest descent in the 2-Wasserstein metric
Authors: E. A. Carlen, W. Gangbo
Abstract: We study several constrained variational problem in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density F
…over all of the probability densities F
that have the same mean and variance as F
…, where S(F) is th… ▽ More
Submitted 2 December, 2003; originally announced December 2003.
Comments: 40 pages published version
Journal ref: Ann. of Math. (2), Vol. 157 (2003), no. 3, 807--846

Constrained steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a

probability density F0 on Rd and a time-step h> 0, we seek to minimize over all of the …

Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

2003

Asymptotics for Wasserstein distances

E del Barrio - unavarra.es

Wp is a metric on the space of probability measures with finite p-th moment that metrices weak

convergence plus convergence of p-th moments. These metrics have interesting applications

in Probability and Statistics, remarkably in the problem of testing goodness of fit. Here we will …

mpirical Wasserstein distances

E del Barrio

2003 [PDF] projecteuclid.org

Correction: Central limit theorems for the Wasserstein distance ...https://projecteuclid.org › volume-31 › issue-2 › aop
by E Giné · 2003 — April 2003 Correction: Central limit theorems for the Wasserstein distance between the empirical and
the true distributions. Evarist Giné, Carlos Matrán, ...

[CITATION] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

Gradient flows with metric and differentiable structures ... - cvgmt

2003 see 2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space. created on 18 Dec 2003. [BibTeX]. Accepted Paper Inserted: ...

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

Gradient flows with metric and differentiable structures ... - cvgmt

2003 see 2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space. created on 18 Dec 2003. [BibTeX]. Accepted Paper Inserted: ...

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

Gradient flows with metric and differentiable structures ... - cvgmt

2003 see 2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space. created on 18 Dec 2003. [BibTeX]. Accepted Paper Inserted: ...

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

Asymptotic distributions of trimmed Wasserstein distances between

the true and the empirical distribution function

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

<——2003—————-2003——— -20—

Gradient flows with metric and differentiable structures ... - cvgmt

https://cvgmt.sns.it › paper

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space. created on 18 Dec 2003. [BibTeX]. Accepted Paper

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

2003

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

2003 [PDF] projecteuclid.org

[PDF] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E Giné, C Matrán, E del Barrio - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

[CITATION] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

[PDF] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

2003 [PDF] projecteuclid.org

E Giné, C Matrán, E del Barrio - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

[PDF] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E Giné, C Matrán, E del Barrio - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

[CITATION] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

2003

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

2003 [PDF] projecteuclid.org

[PDF] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E Giné, C Matrán, E del Barrio - The Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

[CITATION] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

[PDF] bdim.eu

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

2003

Gradient flows with metric and differentiable structures ... - cvgmt

https://cvgmt.sns.it › paper

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space. created on 18 Dec 2003. [BibTeX]. Accepted Paper

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

Constrained steepest descent in the 2-Wasserstein metric

2003 [PDF] arxiv.org

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a

probability density F0 on Rd and a time-step h> 0, we seek to minimize over all of the …

<——2003—————-2003——— -30—

2003 see 2004

[CITATION] Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

LANGG Savare - Notes, 2003

Constrained steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a

probability density F0 on Rd and a time-step h> 0, we seek to minimize over all of the …

2003 zzz 14

CITATION] The Kantorovich-Rubinshtein-Vassershtein norm for measures on the circle

A Horsley, AJ Wrobel - a manuscript, 2003

Asymptotics for Wasserstein distances

2003

E del Barrio - unavarra.es

Wp is a metric on the space of probability measures with finite p-th moment that metrices weak

convergence plus convergence of p-th moments. These metrics have interesting applications

in Probability and Statistics, remarkably in the problem of testing goodness of fit. Here we will …

[CITATION] Asymptotics for empirical Wasserstein distances

E del Barrio

Constrained steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a

probability density F0 on Rd and a time-step h> 0, we seek to minimize over all of the …

2003

Constrained steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a

probability density F0 on Rd and a time-step h> 0, we seek to minimize over all of the …

Asymptotic distributions of trimmed Wasserstein distances between the true and the empirical distribution function

E Haeusler, DM Mason - Stochastic Inequalities and Applications, 2003 - Springer

If the distribution function F has a finite mean, then the Wasserstein distance d (F _ n,

F)=\smallint _-∞^ ∞| F _ n (x)-F (x)| dx between F and the corresponding empirical

distribution function F n, based on a sample of size n converges almost surely to zero as …

1 April 2003

Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

Evarist Giné, Carlos Matrán, Eustasio del Barrio

The Annals of Probability Vol. 31, Issue 2 (Apr 2003), pg(s) 1142-1143

Constrained steepest descent in the 2-Wasserstein metric

86 citations*

2003 ANNALS OF MATHEMATICS

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Georgia Institute of Technology

Constrained deepest descent in the 2-Wasserstein metric

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We study several constrained variational problems in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density F0 on d and a time-step h> 0, we seek to minimize I(F )= hS(F )+W 2 2 (F0 ,F ) over all of the pr... View Full Abstract

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We study several constrained variational problem in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density $F_0$ on $\R^d$ and a time-step $h>0$, we seek to minimize $I(F) = hS(F) + W_2^2(F_0,F)$ over all ... View Full Abstract

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Gradient flows with metric and differentiable structures, and

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https://www.stat.cmu.edu › ~larry › Opt

by S Kolouri — The Wasserstein distance — which arises from the idea of optimal transport — is being used more and more in Statistics and Machine Learning.

13 pages

2003. [PDF] arxiv.org

Constrained steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Annals of mathematics, 2003 - JSTOR

We study several constrained variational problems in the 2-Wasserstein metric for which the

set of probability densities satisfying the constraint is not closed. For example, given a …

<——2003—————-2003——— -44— end 2003
including 1 title with Vassershtein

Wasserstein start 2004

Contractivity of Wasserstein-type distances:

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File Format: PDF/Adobe Acrobat

José A. Carrillo. Instituci`o Catalana de. Recerca i ...

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Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

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2004 see 2005 2015 book

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2005 by L Ambrosio, N Gigli, G

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MR2094049 (2005k:60231) Gibbs, Alison L.

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration. Stoch. Models 20 (2004), no. 4, 473--492. (Reviewer: John P. Lehoczky) 60J20 (62M40)

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dx.doi.org › doi:10.1081 › STM-200033117

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L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

… Matematica e Applicazioni}, keywords = {Gradient flows; Wasserstein metric; Optimal transport},

language = {eng}, month = {12}, number = {3-4}, pages = {327-343}, publisher = {Accademia

Nazionale dei Lincei}, title = {Gradient flows with metric and differentiable structures, and …

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PDF] psu.edu

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

distance. The Wasserstein metric may be more easily applied in some applications …

2004

Wasserstein Distance —— Major Reference Works - Wiley ...

Oct 15, 2004 — Encyclopedia of Statistical Sciences. Wasserstein Distance. This is an outdated version. There is a newer version ...

2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

… metric setting, following some ideas introduced in [11, 5], and study in detail the case of the Wasserstein … structure of the Wasserstein space, to which the metric theory applies, and use …

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Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

distance. The Wasserstein metric may be more easily applied in some applications …

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

2004 zzz 15

[CITATION] Comment: Testing for Weibull scale families as a test case for Wasserstein correlation tests

T de Wet - 2000 - … 104, 2 IZDA, 28004 MADRID, SPA

<—2004———2004—— 20—

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

distance. The Wasserstein metric may be more easily applied in some applications …

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

Entropy dissipation and Wasserstein metric methods for the

M Di Francesco, PA Markowich - Partial Differential Equations …, 2004 - books.google.com

Burgers' equation with initial data in L'(R). In particular, after a time de-pendent scaling, we

provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards

an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis …

[PDF] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia …, 2004 - www-dimat.unipv.it

Page 1. A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein

spaces Giuseppe Savar ´e Department of Mathematics - University of Pavia and Institute of

Applied Mathematics and Information Technology, CNR, Pavia in collaboration with Ugo …

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures

L Ambrosio, N Gigli, G Savare - 2005 - Lectures in Mathematics, ETH Zurich …

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M Houda - Quantitative Methods in Economics, 2004 - pdfs.semanticscholar.org

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un

fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The

ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

2004

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - math.cmu.edu

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

基于 Wasserstein 距离的目标识别中的研究

赵春江，施文康，邓勇 - NCIRCS2004 第一届全国信息检索与内容 …, 2004 - cpfd.cnki.com.cn

Wasserstein 距离是定义在概率空间上的二阶矩. 首先分析了Wasserstein

距离的经典数学表达式, 和用于实际工程计算的经验公式. 然后举了一个简单的例子,

来说明Wasserstein 距离的实际作用. 通过实验和与Hausdorff 距离相比较可以看出, 完全可以把 …

[Chinese Research in Object Recognition Based on Wasserstein Distance]

2004 [PDF] cmu.edu

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - math.cmu.edu

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

[PDF] Wasserstein metrics and empirical distributions in stability of stochastic programs

M Houda - Quantitative Methods in Economics, 2004 - pdfs.semanticscholar.org

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un

fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The

ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

[CITATION] Wasserstein metrics and empirical distributions in stability of stochastic programs

H Michal - … of the International Conference Quantitative Methods …

<——2004————2004—— 30—

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …
Cited by 89 Related articles All 8 versions

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

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Entropy dissipation and Wasserstein metric methods for the

M Di Francesco, PA Markowich - Partial Differential Equations …, 2004 - books.google.com

Burgers' equation with initial data in L'(R). In particular, after a time de-pendent scaling, we

provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards

an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis …

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - math.cmu.edu

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

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L Ambrosio, N Gigli, G Savaré - Birkhäuser

Entropy dissipation and Wasserstein metric methods for the

M Di Francesco, PA Markowich - Partial Differential Equations …, 2004 - books.google.com

Burgers' equation with initial data in L'(R). In particular, after a time de-pendent scaling, we

provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards

an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis …

2004

Entropy dissipation and Wasserstein metric methods for the

M Di Francesco, PA Markowich - Partial Differential Equations …, 2004 - books.google.com

Burgers' equation with initial data in L'(R). In particular, after a time de-pendent scaling, we

provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards

an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis …

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

Cited by 1 Related articles All 7 versions
<——2004————2004—— 40—

PDF] researchgate.net

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

… where L denotes the maximum of the supports. Page 8. 24 1 5 Nonlinear friction equations

with viscosity An interesting application of Wasserstein metric comes out from the problem

of the numerical approximation of nonlinear friction equations 15 …

2004 see 2003

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

2004

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

2004 see 2003
Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

2004

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

2004

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear partial differential equations and integro–differential equations. Among others, we can describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-descent method in the Wasserstein metric, and prove global existence of energy-and momentum-conserving solutions. We also show that the solutions converge to the manifold …

2004

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

… Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

(2004) … INPROCEEDINGS{Carrillo04wassersteinmetric, author = {JA Carrillo and G. Toscani},

title = {Wasserstein metric and large-time asymptotics of nonlinear diffusion equations …

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and uniqueness result for Fokker-Planck Equations with time dependent point control. We prove existence for an approximate problem and then show convergence in the Wasserstein …

2004

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

<——2004————2004—— 50—

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and uniqueness result for Fokker-Planck Equations with time dependent point control. We prove existence for an approximate problem and then show convergence in the Wasserstein …

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications …

[PDF] fhi.sk

[PDF] Wasserstein metrics and empirical distributions in stability of stochastic programs

M Houda - Quantitative Methods in Economics, 2004 - fhi.sk

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear partial differential equations and integro–differential equations. Among others, we can describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

A ffourth-order nonlinear PDE as gradient flow of the ... - IMATI ...

https://www.yumpu.com › document › view › a-fourth-...

A fourth-order nonlinear PDE as gradient flow of theFisher information in ... 1. The fourth order equation and itsstructureA-HYKE2, april 2004 – p.3 ...

You've visited this page 2 times. Last visit: 3/7/21

[CITATION] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia, Italy, 2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

2004 see 2003

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

ithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

distance. The Wasserstein metric may be more easily applied in some applications …

[PDF] fhi.sk

[PDF] Wasserstein metrics and empirical distributions in stability of stochastic programs

M Houda - Quantitative Methods in Economics, 2004 - fhi.sk

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un

fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The

ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

A fourth-order nonlinear PDE as gradient flow of the - Yumpu

https://www.yumpu.com › document › view › a-fourth-...

A fourth-order nonlinear PDE as gradient flow of theFisher information in ... Gradient flows w.r.t. the Wasserstein distanceAmbient space: S :=nw ≥ 0 a.e. ...

[CITATION] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia, Italy, 2004

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

<——2004———2004—— 60—

JA Carrillo, G Toscani - … Physics: In Honour of the Salvatore Rionero …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

2004 see 2020, 2021 zzz 16

[CITATION] On Linear Optimization over Wasserstein Balls (2020)

MC Yue, D Kuhn, W Wiesemann - URL http://arxiv. org/abs, 2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

ourth-order nonlinear PDE as gradient flow of the ... - IMATI ...

www.yumpu.com › document › view › a-fourth-order-...

A fourth-order nonlinear PDE as gradient flow of theFisher information in ... Gradient flows w.r.t. the Wasserstein distanceAmbient space: S :=nw ≥ 0 a.e. in Ω ...

You've visited this page 2 times. Last visit: 3/7/21

[CITATION] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia, Italy, 2004

[PDF] Wasserstein metrics and empirical distributions in stability of stochastic programs

2004 [PDF] fhi.sk

M Houda - Quantitative Methods in Economics, 2004 - fhi.sk

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un

fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The

ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

2004

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

2004 [PDF] researchgate.net

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

2004

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

A fourth-order nonlinear PDE as gradient flow of the ... - IMATI ...

2004

https://www.yumpu.com › document › view › a-fourth-...

A fourth-order nonlinear PDE as gradient flow of theFisher information in ... Gradient flows w.r.t. the Wasserstein distanceAmbient space: S :=nw ≥ 0 a.e. in Ω ...

ATION] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia, Italy, 2004

WASSERSTEIN METRIC AND LARGE–TIME ASYMPTOTICS ...

<——2004————2004—— 70—

https://www.worldscientific.com › doi › abs

by JA CARRILLO · 2004 · Cited by 85 — Further examples include the approximation of nonlinear friction equations by adding viscosity, and the asymptotic behavior of degenerate convection-diffusion ...

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

[PDF] fhi.sk

[PDF] Wasserstein metrics and empirical distributions in stability of stochastic programs

M Houda - Quantitative Methods in Economics, 2004 - fhi.sk

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un

fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The

ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. New trends

JA Carrillo, G Toscani - in mathematical physics, 234–244, World Sci. Publ, 2004 - Citeseer

We review here various recent applications of Wassertein–type metrics to both nonlinear

partial differential equations and integro–differential equations. Among others, we can

describe the asymptotic behavior of nonlinear friction equations arising in the kinetic …

[CITATION] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

JACG Toscani - New trends in mathematical physics, World Sci. Publ …, 2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

2004

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

Entropy dissipation and Wasserstein metric methods for the

M Di Francesco, PA Markowich - … and Inverse Problems: Pan …, 2004 - books.google.com

Burgers' equation with initial data in L'(R). In particular, after a time de-pendent scaling, we

provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards

an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis …

Entropy dissipation and wasserstein metric methods for the viscous burgers’ equation: convergence to diffusive wavesAuthors:Di Francesco M., Markowich P.A.
Article, 2004
Publication:Contemporary Mathematics, 362, 2004, 145

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

distance. The Wasserstein metric may be more easily applied in some applications …

Entropy dissipation and Wasserstein metric methods for the

M Di Francesco, PA Markowich - Partial Differential Equations …, 2004 - books.google.com

Burgers' equation with initial data in L'(R). In particular, after a time de-pendent scaling, we

provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards

an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis …

2004 zzz 17

[CITATION] Polynomial Matrix Diagonalization Following Vaserstein

J Jozwiak - 2004

<——2004————2004—— 80—

2004

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

2004

[PDF] Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

L Petrelli - 2004 - Citeseer

Abstract We employ the Monge-Kantorovich mass transfer theory to obtain an existence and

uniqueness result for Fokker-Planck Equations with time dependent point control. We prove

existence for an approximate problem and then show convergence in the Wasserstein …

2004

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …
Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

L Ambrosio, N Gigli, G Savaré - … Nazionale dei Lincei. Classe di Scienze …, 2004 - eudml.org

Abstract top In this paper we summarize some of the main results of a forthcoming book on

this topic, where we examine in detail the theory of curves of maximal slope in a general

metric setting, following some ideas introduced in [11, 5], and study in detail the case of the …

Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration

AL Gibbs - 2004 - Taylor & Francis

In this paper, we show how the time for convergence to stationarity of a Markov chain can be

assessed using the Wasserstein metric, rather than the usual choice of total variation

distance. The Wasserstein metric may be more easily applied in some applications …

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

2004

[PDF] fhi.sk

[PDF] Wasserstein metrics and empirical distributions in stability of stochastic programs

M Houda - Quantitative Methods in Economics, 2004 - fhi.sk

Ab stract Prac ti cal eco no mic prob lems of ten ask for op ti mi za tion pro ce du res, not un

fre qu en tly with ran dom in puts le a ding thus to sto chas tic prog ra mming mo dels. The

ran dom ness is mo del led thro ugh the un der ly ing pro ba bi li ty dis tri bu tion, which is as …

2004

A fourth-order nonlinear PDE as gradient flow of the ... - IMATI ...

https://www.yumpu.com › document › view › a-fourth-...

A fourth-order nonlinear PDE as gradient flow of theFisher information in Wasserstein ... The fourth order equation and itsstructureA-HYKE2, april 2004 – p.3 ... Gradient flows w.r.t. the Wasserstein distanceAmbient space: S :=nw ≥ 0 a.e. in Ω ...

[CITATION] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia, Italy, 2004

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

2004

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

We study a model Boltzmann equation closely related to the BGK equation using a steepest-

descent method in the Wasserstein metric, and prove global existence of energy-and

momentum-conserving solutions. We also show that the solutions converge to the manifold …

2004

Wasserstein metric and large–time asymptotics of nonlinear diffusion equations

JA Carrillo, G Toscani - New Trends in Mathematical Physics: In …, 2004 - World Scientific

… In addition, these equations exhibit similarity solutions, which are in general of noticeable

importance to understand the cooling process of the granular flow … at In view of (16), it becomes

natural to look for the time evolution of the square of the Wasserstein metric …

<——2004————2004—— 90—

[2004.07162] On Linear Optimization over Wasserstein Balls

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

by MC Yue · 2020 · Cited by 18 — On Linear Optimization over Wasserstein Balls. Authors:Man-Chung Yue, Daniel Kuhn, Wolfram Wiesemann · Download PDF. Abstract: Wasserstein balls ...

Missing: MC ‎D ‎W

2004

EA Carlen, W Gangbo - Archive for rational mechanics and analysis, 2004 - Springer

… to the BGK equation using a steepest-descent method in the Wasserstein metric, and prove

… We show how the Wasserstein metric is natural for this problem because it is adapted to the …

<——2004————2004—— 92— end 2004

including 1 title with Vaserstein

start 2005 Wasserstein

Eulerian Calculus for the Contraction in the Wasserstein Distance

Felix Otto, ‎Michael Westdickenberg - 2005 - ‎No preview

Wasserstein space and Ricci flow.

J. Lott American Mathematical Society 2005

Meeting: 1007, Santa Barbara, California, SS 9A, Special Session on Ricci Flow/Riemannian Geometry. 1007-58-105. John Lott* (lott@umich.edu), Department ...

Wasserstein space and Ricci flow. Given a compact metric space X, its Wasserstein space is the space of probability measures on X, equipped with a certain.

2005 PDF

Flussi gradiente in spazi metrici e nello spazio di Wasserstein ...

https://media.accademiaxl.it › Ambrosio15-33

teor dei flussi gradiente in spazi metrici generali e nello spazio delle misure di probabilita¡ munito della distanza di Wasserstein quadratica.

20 pages

[CITATION] Flussi gradiente in spazi metrici e nello spazio di Wasserstein delle misure di probability

L AMBROSIO - Rendiconti della Accademia nazionale delle scienze …, 2005 - L'Accademia

[PDF] Flussi gradiente in spazi metrici e nello spazio di Wasserstein delle misure di probability

L AMBROSIO - … della Accademia nazionale delle scienze detta …, 2005 - media.accademiaxl.it

In questo articolo riassumiamo i principali risultati del libro [4], dedicato ad una teoria dei flussi gradiente in spazi metrici generali e nello spazio delle misure di probabilita¡ munito della distanza di Wasserstein quadratica. La sintesi che faremo dei risultati (largamente ispirata a [3] con qualche piccola aggiunta, modifica e aggiornamento) riflette la struttura del libro, con due parti che possono essere lette quasi indipendentemente: nella prima studiamo i flussi gradiente in spazi metrici (chiamandoli curve di massima pendenza, dato …

[Italian Gradient flows in metric spaces and in the Wasserstein space of probability measures]

Hamiltonian ODE's in the Wasserstein space of probability measures

LAW Gangbo - 2005 - calcvar.sns.it

Abstract: In this paper we consider a Hamiltonian $ H $ on ${\ cal P} _2 (* R*^{2d}) $, the set

of probability measures with finite quadratic moments on the phase space $* R*^{2d} $,

which is a metric space when endowed with the Wasserstein distance $ W_2. $ We study ...

All 12 versions Cite Save More

The Wasserstein Distance and its Behaviour along Geodesics

L Ambrosio, N Gigli, G Savaré - Gradient Flows: in Metric Spaces and in …, 2005 - Springer

In this chapter we endow Pp (X), when X is a separable Hilbert space, with a kind of

differential structure, consistent with the metric structure introduced in the previous chapter.

Our starting point is the analysis of absolutely continuous curves µt:(a, b)→ Pp (X) and of ...

[PDF] Contractions in the 2-wasserstein length space and thermalization of granular media, to appear in Archive for Rational Mechanics and Analysis (2005)

by José A. Carrillo , Robert J. Mccann , Cédric Villani

Abstract An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) — if uniformly controlled — will quantify contractivity (limit expansivity) of the flow.

Published 2006 MR22 9130 (2006j:76121)

Optimal quantizer performance and the Wasserstein distortion

S Matloub, DB O'Brien… - … , 2005. Proceedings. DCC …, 2005 - ieeexplore.ieee.org

Abstract The Wasserstein distortion has proved useful in a variety of mathematical, signal

processing and coding problems as a measure of how different two distributions are. In this

paper we provide an expression for the performance of the optimal entropy constrained ...

On constrained optimization in the Wasserstein metric

[PDF] from cmu.eduA Tudorascu - 2005 - math.cmu.edu

Abstract In this paper we prove the monotonicity of the second-order moments of the discrete

approximations to the heat equation arising from the Jordan-Kinderlehrer-Otto (JKO)

variational scheme [7]. This issue appears in the study of constrained optimization in the 2 ...

[PDF] Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

J.A. Carrillo, G. Toscani,

in New Trends in Mathematical Physics, (In Honour of the Salvatore Rionero 70th Birthday), 234-244,

(2005, Hardcover) World Scientific Publishing Company, Incorporated ISBN-10: 9812560777 | ISBN-13: 9789812560773
<——2005————— 2005——— -10—

MR2192294 (2007c:28003) Otto, Felix; Westdickenberg, Michael Eulerian calculus for the contraction in the Wasserstein distance. SIAM J. Math. Anal. 37 (2005), no. 4, 1227--1255 (electronic). 28A33

MR2305058 Ambrosio, L. Gradient flows in metric spaces and in the Wasserstein space of probability measures. (Italian) Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 29 (2005), no. 1, 15--33. 28A33 (49Q20)

Asymptotics for L-2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

By: Del Barrio, E; Gine, E; Utzet, F

BERNOULLI Volume: ‏ 11 Issue: ‏ 1 Pages: ‏ 131-189 Published: ‏ FEB 2005

Optimal quantizer performance and the Wasserstein distortion

Times Cited: 31

By: Matloub, S; O'Brien, DB; Gray, RM

Conference: IEEE Data Compression Conference Location: ‏ Snowbird, UT Date: ‏ MAR 29-31, 2005

Sponsor(s): ‏IEEE

DCC 2005: Data Compression Conference, Proceedings Book Series: ‏ IEEE DATA COMPRESSION CONFERENCE Pages: ‏ 243-250 Published: ‏ 2005

Times Cited: 1

2005 see 2004

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations

By: Carrillo, JA; Toscani, G

Conference: International Meeting on New Trends in Mathematical Physics Location: ‏ Naples, ITALY Date: ‏ JAN 24-25, 2003

NEW TRENDS IN MATHEMATICAL PHYSICS Pages: ‏ 234-244 Published: ‏ 2005

Times Cited: 41

Carrillo, J. A.; Toscani, G.

Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. (English) Zbl 1089.76055

Fergola, Paola (ed.) et al., New trends in mathematical physics. In honour of the Salvatore Rionero 70th birthday. Proceedings of the international meeting, Naples, Italy, January, 24–25 2003. Hackensack, NJ: World Scientific (ISBN 981-256-077-7/hbk ). 234-244 (2005).

MSC: 76R50 76T25 45K05 76-02

PDF BibTeX XML Cite

Eulerian calculus for the contraction in the Wasserstein distance

By: Otto, F; Westdickenberg, M

SIAM JOURNAL ON MATHEMATICAL ANALYSIS Volume: ‏ 37 Issue: ‏ 4 Pages: ‏ 1227-1255 Published: ‏ 2005

Times Cited: 52

2005 see 2004

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric

By: Carlen, EA; Gangbo, W

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS Volume: ‏ 172 Issue: ‏ 1 Pages: ‏ 21-64 Published: ‏ APR 2004

Times Cited: 31

Eulerian Calculus for the Contraction in the Wasserstein Distance

Felix Otto and Michael Westdickenberg

SIAM Journal on Mathematical Analysis Vol. 37, No. 4, pp. 1227–12552005

Eulerian calculus for the contraction in the Wasserstein distance

F Otto, M Westdickenberg - SIAM journal on mathematical analysis, 2005 - SIAM

We consider the porous medium equation on a compact Riemannian manifold and give a

new proof of the contraction of its semigroup in the Wasserstein distance. This proof is based

on the insight that the porous medium equation does not increase the size of infinitesimal …

2005 [PDF] projecteuclid.org

Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

E Del Barrio, E Giné, F Utzet - Bernoulli, 2005 - projecteuclid.org

Weighted L 2 functionals of the empirical quantile process appear as a component of many

test statistics, in particular in tests of fit to location-scale families of distributions based on

weighted Wasserstein distances. An essentially complete set of distributional limit theorems …

Optimal quantizer performance and the Wasserstein distortion

S Matloub, DB O'Brien, RM Gray - Data Compression …, 2005 - ieeexplore.ieee.org

The Wasserstein distortion has proved useful in a variety of mathematical, signal processing

and coding problems as a measure of how different two distributions are. In this paper we

provide an expression for the performance of the optimal entropy constrained quantizer in …

Cited by 1 Related articles All 5 versions
<——2005—–– 2005———20—

The Wasserstein Distance and its Behaviour along Geodesics

L Ambrosio, N Gigli, G Savaré - Gradient Flows: in Metric Spaces and in …, 2005 - Springer

In this chapter we endow Pp (X), when X is a separable Hilbert space, with a kind of

differential structure, consistent with the metric structure introduced in the previous chapter.

Our starting point is the analysis of absolutely continuous curves µt:(a, b)→ Pp (X) and of …

Contractions in the 2-wasserstein lenght space and thermalization of granular media

[PDF] cmu.edu

[PDF] On constrained optimization in the Wasserstein metric

A Tudorascu - 2005 - math.cmu.edu

In this paper we prove the monotonicity of the second-order moments of the discrete

approximations to the heat equation arising from the Jordan-Kinderlehrer-Otto (JKO)

variational scheme [7]. This issue appears in the study of constrained optimization in the 2 …

[PDF] recercat.cat

JA Carrillo de la Plata, RJ McCann, C Villani - 2005 - recercat.cat

… offers several advantages: 1) Wasserstein distance is the natural distance associated with

… of finite Wasserstein distance is much more general than the assumption of finite entropy; 3) …

Optimal quantizer performance and the Wasserstein distortion

S Matloub, DB O'Brien, RM Gray - Data Compression …, 2005 - ieeexplore.ieee.org

The Wasserstein distortion has proved useful in a variety of mathematical, signal processing

and coding problems as a measure of how different two distributions are. In this paper we

provide an expression for the performance of the optimal entropy constrained quantizer in …

Hamiltonian ODE's in the Wasserstein space of probability ...

del Barrio, Eustasio; Giné, Evarist; Utzet, Frederic

Hamiltonian ODE's in the Wasserstein space of probability measures. created by ambrosio on 07 Dec 2005 ... the set of probability measures with finite quadratic moments on the phase space ∗R∗2d ∗ R ∗ 2 d , which is a metric space ...

[CITATION] Hamiltonian ODE's in the Wasserstein space of probability measures

W Gangbo, L Ambrosio - 2005 - … . Gruppo di ricerca di Calcolo delle …

Asymptotics for L2 L2

functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances. (English) Zbl 1063.62072

Bernoulli 11, No. 1, 131-189 (2005).

MSC: 62G20 62G10 60F05 62E20

Hamiltonian ODE's in the Wasserstein space of probability ...

[CITATION] Hamiltonian ODE's in the Wasserstein space of probability measures

W Gangbo, L Ambrosio - 2005 - … . Gruppo di ricerca di Calcolo delle …

Eulerian calculus for the contraction in the Wasserstein distance

F Otto, M Westdickenberg - SIAM journal on mathematical analysis, 2005 - SIAM

We consider the porous medium equation on a compact Riemannian manifold and give a

new proof of the contraction of its semigroup in the Wasserstein distance. This proof is based

on the insight that the porous medium equation does not increase the size of infinitesimal …

The Wasserstein Distance and its Behaviour along Geodesics

L Ambrosio, N Gigli, G Savaré - Gradient Flows: in Metric Spaces and in …, 2005 - Springer

In this chapter we endow Pp (X), when X is a separable Hilbert space, with a kind of

differential structure, consistent with the metric structure introduced in the previous chapter.

Our starting point is the analysis of absolutely continuous curves µt:(a, b)→ Pp (X) and of …

All 2 versions
<—-2005———— 2005———- 30—

2005 see 2006 2008

Separability and completeness for the Wasserstein distance

link.springer.com › content › pdf

We give an elementary proof that the Wasserstein distances, which play a basic ... Let (X, d) be a separable complete metric space and P the set of Borel prob- ... 2005. 4. S. T. Rachev. Probability metrics and the stability of stochastic models.

[CITATION] Separability and Completeness for the Wasserstein distance

[CITATION] Separability and Completeness for the Wasserstein distance

F Bolley - Report available online via http://www. lsp. ups-tlse. fr …, 2005

[CITATION] Separability and Completeness for the Wasserstein distance

F Bolley - Report available online via http://www. lsp. ups-tlse. fr …, 2005

DF] On constrained optimization in the Wasserstein metric

A Tudorascu - 2005 - math.cmu.edu

In this paper we prove the monotonicity of the second-order moments of the discrete

approximations to the heat equation arising from the Jordan-Kinderlehrer-Otto (JKO)

variational scheme [7]. This issue appears in the study of constrained optimization in the 2 …

F Bolley - Report available online via http://www. lsp. ups-tlse. fr …, 2005

Eulerian calculus for the contraction in the Wasserstein distance

F Otto, M Westdickenberg - SIAM journal on mathematical analysis, 2005 - SIAM

We consider the porous medium equation on a compact Riemannian manifold and give a

new proof of the contraction of its semigroup in the Wasserstein distance. This proof is based

on the insight that the porous medium equation does not increase the size of infinitesimal …

2005 [PDF] projecteuclid.org

Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

E Del Barrio, E Giné, F Utzet - Bernoulli, 2005 - projecteuclid.org

… empirical quantile process appear as a component of many test statistics, in particular in

tests of fit to location–scale families of distributions based on weighted Wasserstein distances.

An essentially complete set of distributional limit theorems for the squared empirical quantile …

2005

Gradient Flows in Metric Spaces and in the ... - ResearchGate

https://www.researchgate.net › ... › Metric Space

Gradient Flows in Metric Spaces and in the Space of Probability Measures ... studied in the Wasserstein gradient flow setting by Ambrosio et al. [2005] .

CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures

L Ambrosio, N Gigli, G Savare - 2005 - Lectures in Mathematics, ETH Zurich …

[CITATION] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia, Italy, 2004

Cited by 15 Related articles
CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures

L Ambrosio, N Gigli, G Savare - 2005 - Lectures in Mathematics, ETH Zurich …

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures. Lectures in Mathematics, ETH Zurich

LANGG SAVAREÂ - 2005 - BirkhaÈuser

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures

L Ambrosio, N Gigli, G Savare - 2005 - Lectures in Mathematics, ETH Zurich …

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures. Lectures in Mathematics, ETH Zurich

LANGG SAVAREÂ - 2005 - BirkhaÈuser

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures

L Ambrosio, N Gigli, G Savare - 2005 - Lectures in Mathematics, ETH Zurich …

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures. Lectures in Mathematics,

2005

Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

E Del Barrio, E Giné, F Utzet - Bernoulli, 2005 - projecteuclid.org

Weighted L 2 functionals of the empirical quantile process appear as a component of many test statistics, in particular in tests of fit to location-scale families of distributions based on weighted Wasserstein distances. An essentially complete set of distributional limit theorems …

[CITATION] Asymptotics for L 2-functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances

E del Barrio, E Gine - Preprint, 2002

2005

Del Barrio , Giné , Utzet : Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances.

MR2121458 (2005k:62135) del Barrio, Eustasio; Giné, Evarist; Utzet, Frederic Asymptotics for $L_2$ functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances. Bernoulli 11 (2005), no. 1, 131--189. (Reviewer: Lajos Horváth) 62G30 (60F05).

Zbl 1063.62072

Optimal quantizer performance and the Wasserstein distortion

[PDF] On constrained optimization in the Wasserstein metric

A Tudorascu - 2005 - math.cmu.edu

In this paper we prove the monotonicity of the second-order moments of the discrete approximations to the heat equation arising from the Jordan-Kinderlehrer-Otto (JKO) variational scheme [7]. This issue appears in the study of constrained optimization in the 2 …

S Matloub, DB O'Brien, RM Gray - Data Compression …, 2005 - ieeexplore.ieee.org

The Wasserstein distortion has proved useful in a variety of mathematical, signal processing and coding problems as a measure of how different two distributions are. In this paper we provide an expression for the performance of the optimal entropy constrained quantizer in …

2005 [PDF] cmu.edu

[PDF] On constrained optimization in the Wasserstein metric

A Tudorascu - 2005 - math.cmu.edu

In this paper we prove the monotonicity of the second-order moments of the discrete

approximations to the heat equation arising from the Jordan-Kinderlehrer-Otto (JKO)

variational scheme [7]. This issue appears in the study of constrained optimization in the 2 …

<—-2005———— 2005———- 40—

year 2005

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics …

Path functionals over Wasserstein spaces

MR2250166 (2007j:49051) Brancolini, A.; Buttazzo, G.; Santambrogio, F. Path functionals over Wasserstein spaces. J. Eur. Math. Soc. (JEMS) 8 (2006), no. 3, 415--434. (Reviewer: Luigi De Pascale) 49Q20 (28A33 49J45 58E10 90B10). Zbl 1130.49036

A Brancolini, G Buttazzo, F Santambrogio - Journal of the European …, 2006 - ems-ph.org

Abstract. Given a metric space X we consider a general class of functionals which measure

the cost of a path in X joining two given points x0 and x1, providing abstract existence results

for optimal paths. The results are then applied to the case when X is a Wasserstein space of …

MR2287892 (2007k:35315) Carrillo, José A.; Di Francesco, Marco; Lattanzio, Corrado Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws. J. Differential Equations 231 (2006), no. 2, 425--458. (Reviewer: Yu. G. Rykov) 35L65 (35B40)

Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws

JA Carrillo, M Di Francesco, C Lattanzio - Journal of Differential Equations, 2006 - Elsevier

Abstract The aim of this paper is to analyze contractivity properties of Wasserstein-type

metrics for one-dimensional scalar conservation laws with nonnegative, L∞ and compactly

supported initial data and its implications on the long time asymptotics. The flux is assumed …

2006

arXiv:math/0612562 [pdf, ps, other]

Some geometric calculations on Wasserstein space

John Lott (Submitted on 19 Dec 2006 (v1), last revised 9 Apr 2007 (this version, v2))

MR2358290 (2009b:58014)

Lecture 1: Main Models & Basics of Wasserstein Distance

File Format: PDF/Adobe Acrobat

Presentation of models. Wasserstein Distance: Basics. Contractivity in 1D. Lecture 1: Main Models & Basics of. Wasserstein Distance. J. A. Carrillo ...

in 3rd SUMMER SCHOOL ON ''METHODS AND MODELS OF KINETIC THEORY'' (M&MKT 2006)

Porto Ercole (Grosseto, Italy) June 4-10, 2006

[PDF] uzh.ch

On Stein's factors for Poisson approximation in Wasserstein distance

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

[CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

Dynamic clustering of histograms using Wasserstein metric

[PDF] from psu.eduA Irpino, R Verde… - COMPSTAT, 2006 - Citeseer

In the present paper we present a new distance, based on the Wasserstein metric, in order

to cluster a set of data described by distributions with finite continue support. The proposed

distance allows to define a measure of inertia of data with respect a barycenter that ...

2006

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

[PDF] from arxiv.orgL Ambrosio… - Arxiv preprint math/0603435, 2006 - arxiv.org

Abstract: The geodesic problem in Wasserstein spaces with a metric perturbed by a

conformal factor is considered, and necessary optimality conditions are estabilished in a

case where this conformal factor favours the spreading of the probability measure along ...

<——2006———2006—— -10—

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto ...

Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 ... 0 (F−1 n (t) − F−1(t)) 2 dt − an,

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - math.sns.it

Dottorato di ricerca in Matematica e Statistica ... 1.1 Absolutely continuous curves in metric spaces

and metric derivative . . . . . 15 ... 1.3 Metric Sobolev spaces W1,p(I; X). . . . . . . . . . . . . . . . . . . . .

. . . . 17 ... 1.4 Borel probability measures, narrow topology and tightness . . . . . . . . . . . 19

Wasserstein distance on configuration space

2006 see 2007 2008 2009

L Decreusefond - arXiv preprint math/0602134, 2006 - arxiv.org

Abstract: We investigate here the optimal transportation problem on configuration space for

the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is

finite, there exists one unique optimal measure and that this measure is supported by the ...

(Submitted on 7 Feb 2006)

2006 see 2009

The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation

UGGSG Toscani - 2006 - cvgmt.sns.it

Despite the lack of a maximum principle for fourth order equations, nonnegative solutions can

be obtained as a limit of a variational approximation scheme by exploiting the particular structure

of this equation, which is the gradient flow of the Fisher Information functional with respect ...

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer

The Wasserstein gradient flow of the Fisher information ... - cvgmt

[CITATION] The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation

UGGSG Toscani - 2006

RICCI FLOW, ENTROPY AND OPTIMAL TRANSPORTATION∗ 1 ...

The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation. created by savare on 01 Sep 2006 modified on 25 Feb 2009.

[CITATION] The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation

UGGSG Toscani - 2006

2006 zzz 18

[CITATION] Diffusion is a 2-Wasserstein contraction on any manifold evolving by reverse Ricci flow

RJ McCann… - Preprint, 2006

Cited by 2 - Related articles

by RJ MCCANN - ‎2008 - ‎Cited by 79 - ‎Related articles

2-Wasserstein distance W2(ν, ˜ν,τ) between them evolves according to its defi- nition. (3). W2. 2 (ν, ˜ν,τ) = inf π∈Γ(ν,˜ν). ∫. M×M d2(x,y,τ) dπ(x,y). Date: March 14, 2008. ∗

This paper supercedes the earlier paper Diffusion is a 2-Wasserstein contraction on any manifold evolving by reverse Ricci flow (2006). c 2007, the ...

Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

[CITATION] Diffusion ia a 2–Wasserstein contraction on any manifold evolving by reverse Ricci flow

RJ McCann, P Topping - Preprint, 2006

CITATION] Diffusion is a 2-Wasserstein contraction on any manifold ...

www.sckool.org › leonid-vaserstein-interview › page=2

[CITATION] Diffusion is a 2-Wasserstein contraction on any manifold evolving by reverse Ricci flow. RJ McCann… - Preprint, 2006. Cited by 2 - Related articles

2006 see 2007

Wasserstein kernels for one-dimensional diffusion problems

by A Tudorascu - ‎2006 - ‎Cited by 2 - ‎Related articles

Sep 1, 2006 - implicit scheme. The concept of Wasserstein kernel associated with one-dimensional diffusion problems with Neumann boundary conditions is ...

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal

mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to

evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

2006 [PDF] psu.edu

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal

mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to

evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

2006 see 2008

[math/0602479] Spectral gaps in Wasserstein distances and the 2D ...

by M Hairer - ‎2006 - ‎Cited by 102 - ‎Related articles

Feb 21, 2006 - ... a general method to prove the existence of spectral gaps for Markov ... as well and hence can be seen as a type of 1-Wasserstein distance.

Spectral gaps in Wasserstein distances and the 2D ... - arXiv.org

arxiv.org › pdf › math pdf

ctral gap in a particular 1-Wasserstein distance. (In the sequel ... we concentrate on the two-dimensional stochastic Navier–Stokes equations on a torus t

by M Hairer · ‎2006 · ‎Cited by 140 · ‎Related articles
Cited by 4 Related articles

2006

Contractions in the 2-Wasserstein length space and thermalization of granular media

By: Carrillo, JA; McCann, RJ; Villani, CD

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS Volume: ‏ 179 Issue: ‏ 2 Pages: ‏ 217-263 Published: ‏ FEB 200

Times Cited: 172

[CITATION] Contraction in the 2-wasserstein metric length space and thermalization of granular media

JA Carrillo, RJ McCann, C Villani - To appear

Cited by 2 Related articles
<——2006————2006———— -20 ——

Spectral gaps in Wasserstein distances and the 2D stochastic ...

https://www.semanticscholar.org › paper › Spectral-gaps-i...

Feb 21, 2006 — Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations · Martin Hairer, Jonathan C. Mattingly · Published 21 ...

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

[PDF] Some geometric calculations on Wasserstein space

J Lott - arXiv preprint math/0612562, 2006 - arxiv.org

If M is a smooth compact Riemannian manifold then the Wasserstein space P2(M) is the space

of Borel probability measures on M, equipped with the Wasserstein metric W2. We refer to

[21] for background information on Wasserstein spaces. The Wasserstein space originated in …

By: Irpino, Antonio; Verde, Rosanna

Conference: 10th Jubilee Conference of the International-Federation-of-Classification-Societies Location: ‏ Univ Ljubljana, Ljubljana, SLOVENIA Date: ‏ JUL 25-29, 2006

Sponsor(s): ‏Int Federat Classificat Soc

DATA SCIENCE AND CLASSIFICATION Book Series: ‏ Studies in Classification Data Analysis and Knowledge Organization Pages: ‏ 185-+ Published: ‏ 2006

Times Cited: 33

2006 see 2007

[PDF] Some geometric calculations on Wasserstein space

J Lott - arXiv preprint math/0612562, 2006 - arxiv.org

If M is a smooth compact Riemannian manifold then the Wasserstein space P2(M) is the space

of Borel probability measures on M, equipped with the Wasserstein metric W2. We refer to

[21] for background information on Wasserstein spaces. The Wasserstein space originated in …

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

A Irpino, R Verde - Data science and classification, 2006 - Springer

Abstract Symbolic Data Analysis (SDA) aims to to describe and analyze complex and

structured data extracted, for example, from large databases. Such data, which can be

expressed as concepts, are modeled by symbolic objects described by multivalued …

2006

[PDF] Dynamic clustering of histograms using Wasserstein metric

A Irpino, R Verde, Y Lechevallier - COMPSTAT, 2006 - Citeseer

In the present paper we present a new distance, based on the Wasserstein metric, in order

to cluster a set of data described by distributions with finite continue support. The proposed

distance allows to define a measure of inertia of data with respect a barycenter that satisfies …

2006 see 2010 [PDF] semanticscholar.org

Path functionals over Wasserstein spaces

A Brancolini, G Buttazzo, F Santambrogio - Journal of the European …, 2006 - ems-ph.org

Given a metric space X we consider a general class of functionals which measure the cost of

a path in X joining two given points x0 and x1, providing abstract existence results for

optimal paths. The results are then applied to the case when X is a Wasserstein space of …

Path functionals over Wasserstein spaces

ABGBF Santambrogio - Journal: J. Eur. Math. Soc, 2006

On Stein's factors for Poisson approximation in Wasserstein distance

[PDF] uzh.ch

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal

mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to

evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws

JA Carrillo, M Di Francesco, C Lattanzio - Journal of Differential Equations, 2006 - Elsevier

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for

one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported

initial data and its implications on the long time asymptotics. The flux is assumed to be …

<——2006———2006———— 30—

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - arXiv preprint math/0603435, 2006 - arxiv.org

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

2006 [PDF] researchgate.net

Path functionals over Wasserstein spaces

A Brancolini, G Buttazzo, F Santambrogio - Journal of the European …, 2006 - ems-ph.org

Given a metric space X we consider a general class of functionals which measure the cost of

a path in X joining two given points x0 and x1, providing abstract existence results for

optimal paths. The results are then applied to the case when X is a Wasserstein space of …

Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - pdfs.semanticscholar.org

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

Separability and completeness for the Wasserstein distance

2006 see 2008

link.springer.com › chapter

by F Bolley · 2008 · Cited by 93 — We give an elementary proof that the Wasserstein distances, which play a basic role in optimal transportation issues, turn some, spaces of probability measures into separable complete metric spaces.

[CITATION] Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

F Bolley - Lecture Notes in Math. Springer, 2006

SEPARABILITY AND COMPLETENESS FOR THE ...

www.lpsm.paris › pageperso › bolley › wasserstein

PDF see 2008

Abstract. In this note we prove in an elementary way that the Wasserstein distances, ... Let (X, d) be a separable complete metric space and P be the set of Borel ...

by F BOLLEY · ‎Cited by 88 · ‎Related articles

[CITATION] Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

F Bolley - Lecture Notes in Math. Springer, 2006

2006

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - arXiv preprint math/0603435, 2006 - arxiv.org

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

2006 [PDF] uzh.ch

On Stein's factors for Poisson approximation in Wasserstein distance

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

[CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

Cited by 3 Related articles

2006

The Vasershtein distance as the stability criterion in robust estimation (Corresp.)

P Papantoni-Kazakos - IEEE Transactions on Information Theory, 2006 - dl.acm.org

In the models used by Hampel as well as by Gray and the author for the qualitative analysis

of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein

distance is proposed here as an alternative stability measure. This measure, in contrast to …

2006 [PDF] arxiv.org

[PDF] Some geometric calculations on Wasserstein space

J Lott - arXiv preprint math/0612562, 2006 - arxiv.org

… In terms of the weighted L2-spaces L2(M,ρ dvolM ) and Ω1 … One such relation was given in [17],

where it was heuristically shown that the geodesic distance coming from (2.4 … If c : [0, 1] →

P∞(M) is a smooth immersed curve then its length L(c) in the Wasserstein space P2(M …

[PDF] uzh.ch

On Stein's factors for Poisson approximation in Wasserstein distance

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

On Stein's factors for Poisson approximation in Wasserstein distance with non-linear transportation costs

ZW Liao, Y Ma, A Xia - arXiv preprint arXiv:2003.13976, 2020 - arxiv.org

We establish various bounds on the solutions to a Stein equation for Poisson approximation

in Wasserstein distance with non-linear transportation costs. The proofs are a refinement of

those in [Barbour and Xia (2006)] using the results in [Liu and Ma (2009)]. As a corollary, we …

[PDF] Trimester on Partial Differential Equations and Calculus of Variations

<——2006————2006——40—

[PDF] sns.it

M Struwe - 2006 - crm.sns.it

… provides one more link between optimal transportation and the theory of action- minimizing

measures … Euler–Poisson systems as energy minimizing paths in the Wasserstein space P2(R).

I will describe a … This extends the concept of the Euler-Poisson system to general measures …

Spectral gaps in Wasserstein distances and the 2D stochastic ...

2006 PDF

https://arxiv.org › pdf › math

by M Hairer · 2006 · Cited by 147 — spectral gap in a particular 1-Wasserstein distance. (In the sequel ... we concentrate on the two-dimensional stochastic Navier–Stokes equations on a torus to ...

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

MHJC MATTINGLY, M Hairer - Preprint, 2006

[CITATION] Spectral gaps in Wasserstein distances and the 2D Navier–Stokes equation

M Hairer, JC Mattingly - Ann. Probab, 2006

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - arXiv preprint math/0603435, 2006 - arxiv.org

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

year 2006

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

Spectral gaps in Wasserstein distances and the 2D stochastic ...

2006

2006 see 2008

http://citeseerx.ist.psu.edu › viewdoc › summary

by M Hairer · 2006 · Cited by 163 — CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We develop a general method that allows to show the existence of spectral gaps ...

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

MHJC MATTINGLY, M Hairer - Preprint, 2006

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

2006 [PDF] researchgate.net

A Irpino, R Verde - Data science and classification, 2006 - Springer

Abstract Symbolic Data Analysis (SDA) aims to to describe and analyze complex and

structured data extracted, for example, from large databases. Such data, which can be

expressed as concepts, are modeled by symbolic objects described by multivalued …

2006 [PDF] psu.edu

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws

JA Carrillo, M Di Francesco, C Lattanzio - Journal of Differential Equations, 2006 - Elsevier

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for

one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported

initial data and its implications on the long time asymptotics. The flux is assumed to be …

2006

Contractions in the 2-Wasserstein length space and thermalization of granular media

JA Carrillo, RJ McCann, C Villani - Archive for Rational Mechanics and …, 2006 - Springer

An algebraic decay rate is derived which bounds the time required for velocities to

equilibrate in a spatially homogeneous flow-through model representing the continuum limit

of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by …

< ——2006———2006——50—

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal

mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to

evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

2006 see 2009 [PDF] semanticscholar.org

Path functionals over Wasserstein spaces

A Brancolini, G Buttazzo, F Santambrogio - Journal of the European …, 2006 - ems-ph.org

Given a metric space X we consider a general class of functionals which measure the cost of

a path in X joining two given points x0 and x1, providing abstract existence results for

optimal paths. The results are then applied to the case when X is a Wasserstein space of …

[CITATION] Path functionals over Wasserstein spaces

ABGBF Santambrogio - Journal: J. Eur. Math. Soc, 2006

Contractions in the 2-Wasserstein length space and thermalization of granular media

2006 [PDF] uab.cat

JA Carrillo, RJ McCann, C Villani - Archive for Rational Mechanics and …, 2006 - Springer

An algebraic decay rate is derived which bounds the time required for velocities to

equilibrate in a spatially homogeneous flow-through model representing the continuum limit

of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by …

Spectral gaps in Wasserstein distances and the 2D stochastic ...

On Stein's factors for Poisson approximation in Wasserstein distance

by M Hairer · 2006 · Cited by 155 — Using the convergence result, we show that the stochastic Navier--Stokes equations' invariant measures depend continuously on the viscosity and ...

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

MHJC MATTINGLY, M Hairer - Preprint, 2006

[PDF] uzh.ch

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

[CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

year 2006

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

On Stein's factors for Poisson approximation in Wasserstein distance

[PDF] uzh.ch

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

[CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

[PDF] Dynamic clustering of histograms using Wasserstein metric

A Irpino, R Verde, Y Lechevallier - COMPSTAT, 2006 - Citeseer

In the present paper we present a new distance, based on the Wasserstein metric, in order

to cluster a set of data described by distributions with finite continue support. The proposed

distance allows to define a measure of inertia of data with respect a barycenter that satisfies …

A Tudorascu - pdfs.semanticscholar.org

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

< ——2006————2006——60—

Asymptotic power of goodness of fit tests based on Wasserstein distance

[PDF] Some geometric calculations on Wasserstein space

J Lott - arXiv preprint math/0612562, 2006 - arxiv.org

If M is a smooth compact Riemannian manifold then the Wasserstein space P2(M) is the space

of Borel probability measures on M, equipped with the Wasserstein metric W2. We refer to

[21] for background information on Wasserstein spaces. The Wasserstein space originated in …

2006

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws

JA Carrillo, M Di Francesco, C Lattanzio - Journal of Differential Equations, 2006 - Elsevier

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for

one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported

initial data and its implications on the long time asymptotics. The flux is assumed to be …

2006 [PDF] researchgate.net

Path functionals over Wasserstein spaces

A Brancolini, G Buttazzo… - Journal of the European …, 2006 - content.ems.press

Given a metric space X we consider a general class of functionals which measure the cost of

a path in X joining two given points x0 and x1, providing abstract existence results for

optimal paths. The results are then applied to the case when X is a Wasserstein space of …

[PDF] ens-rennes.fr

Path functionals over Wasserstein spaces

G Buttazzo, A Brancolini, F Santambrogio - Journal of the European …, 2006 - ems.press

Given a metric space X we consider a general class of functionals which measure the cost of

a path in X joining two given points x0 and x1, providing abstract existence results for

optimal paths. The results are then applied to the case when X is a Wasserstein space of …

2006

On Stein's factors for Poisson approximation in Wasserstein distance

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method

for normal approximation, and it has proved to be an extremely powerful tool for establishing

Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

[CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

www.jstor.org › stable

Spectral Gaps in Wasserstein Distances and the 2D ... - JStor

the stochastic Navier-Stokes equations' invariant measures depend continu ously on the viscosity ... Received May 2006; revised May 2007. Supported in part by ... Stochastic PDEs, Wasserstein distance, ergodicity, mixing, spectral gap. 2050 ...

by M Hairer · ‎2008 · ‎Cited by 140 · ‎Related articles

[CITATION] Spectral gaps in Wasserstein distances and the 2D Navier–Stokes equation

M Hairer, JC Mattingly - Ann. Probab, 2006

Asymptotic power of goodness of fit tests based on Wasserstein distance

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

MHJC MATTINGLY, M Hairer - Preprint, 2006

20 06 modified

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0, X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

On Stein's factors for Poisson approximation in Wasserstein distance

[PDF] uzh.chtheat

AD Barbour, A Xia - Bernoulli, 2006 - JSTOR

Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method for normal approximation, and it has proved to be an extremely powerful tool for establishing Poisson approximations to sums of dependent integer-valued random variables (see Barbour …

[CITATION] On Stein's factors for Poisson approximation in Wasserstein distance. Bernoulli 12 943–954

AD Barbour, A Xia - … (MathSciNet): MR2274850 Digital Object Identifier: doi, 2006

Asymptotic power of goodness of fit tests based on Wasserstein distance

2006

H Boistard - personales.unican.es

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

<——2006————2006——70—

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics. An extensive literature on this topic is already available, originating with the work of Otto and …

Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media

2006

358 citations*

2006 ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

José A. Carrillo ¹,Robert J. McCann ²,Cédric Villani ³

¹ Autonomous University of Barcelona ,² University of Toronto ,³ École normale supérieure de Lyon

Geometry

Convexity

View More (9+)

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical... View Full Abstract

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - arXiv preprint math/0603435, 2006 - arxiv.org

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These …

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

A Irpino, R Verde - Data science and classification, 2006 - Springer

Abstract Symbolic Data Analysis (SDA) aims to to describe and analyze complex and structured data extracted, for example, from large databases. Such data, which can be expressed as concepts, are modeled by symbolic objects described by multivalued …

[PDF] uab.cat

Contractions in the 2-Wasserstein length space and thermalization of granular media

JA Carrillo, RJ McCann, C Villani - Archive for Rational Mechanics and …, 2006 - Springer

An algebraic decay rate is derived which bounds the time required for velocities to

equilibrate in a spatially homogeneous flow-through model representing the continuum limit

of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by …

2006

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - arXiv preprint math/0603435, 2006 - arxiv.org

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal

mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to

evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

[PDF] Dynamic clustering of histograms using Wasserstein metric

A Irpino, R Verde, Y Lechevallier - COMPSTAT, 2006 - Citeseer

In the present paper we present a new distance, based on the Wasserstein metric, in order

to cluster a set of data described by distributions with finite continue support. The proposed

distance allows to define a measure of inertia of data with respect a barycenter that satisfies …

2006 [PDF] researchgate.net

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

A Irpino, R Verde - Data science and classification, 2006 - Springer

Abstract Symbolic Data Analysis (SDA) aims to to describe and analyze complex and

structured data extracted, for example, from large databases. Such data, which can be

expressed as concepts, are modeled by symbolic objects described by multivalued …

< ——2006————2006——80—

2006

Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

Hamiltonian ODE’s in the Wasserstein space of probability ...

2006 modified

www.math.ucla.edu › ~wgangbo › publications

Hamiltonian ODE’s in the Wasserstein space of probability measures L. AMBROSIO Scuola Normale Superiore di Pisa AND W. GANGBO Georgia Institute of Technology Abstract In this paper we consider a Hamiltonian H on P2(R2d), the set of probabil-ity measures with ﬁnite quadratic moments on the phase space R2d = Rd ×Rd, which is a metric space when endowed with the Wasserstein distance W2. We

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

A Irpino, R Verde - Data science and classification, 2006 - Springer

Abstract Symbolic Data Analysis (SDA) aims to to describe and analyze complex and

structured data extracted, for example, from large databases. Such data, which can be

expressed as concepts, are modeled by symbolic objects described by multivalued …

[PDF] uab.cat

Contractions in the 2-Wasserstein length space and thermalization of granular media

JA Carrillo, RJ McCann, C Villani - Archive for Rational Mechanics and …, 2006 - Springer

An algebraic decay rate is derived which bounds the time required for velocities to

equilibrate in a spatially homogeneous flow-through model representing the continuum limit

of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by …

2006 [PDF] psu.edu

[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - Citeseer

In this PhD Thesis we deal with some aspects of the applications of the theory of optimal

mass transportation (and the related Kantorowitch-Rubinstein-Wasserstein distance) to

evolution partial differential equations. Essentially, the Thesis is made up of three parts. The …

2006

A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

A Irpino, R Verde - Data science and classification, 2006 - Springer

Abstract Symbolic Data Analysis (SDA) aims to to describe and analyze complex and

structured data extracted, for example, from large databases. Such data, which can be

expressed as concepts, are modeled by symbolic objects described by multivalued …

[PDF] uab.cat

Contractions in the 2-Wasserstein length space and thermalization of granular media

JA Carrillo, RJ McCann, C Villani - Archive for Rational Mechanics and …, 2006 - Springer

An algebraic decay rate is derived which bounds the time required for velocities to

equilibrate in a spatially homogeneous flow-through model representing the continuum limit

of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by …

2006 [PDF] psu.edu

[PDF] Dynamic clustering of histograms using Wasserstein metric

A Irpino, R Verde, Y Lechevallier - COMPSTAT, 2006 - Citeseer

In the present paper we present a new distance, based on the Wasserstein metric, in order

to cluster a set of data described by distributions with finite continue support. The proposed

distance allows to define a measure of inertia of data with respect a barycenter that satisfies …

Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein

test is based on the statistic: n ∫ 1 … 0 (F−1 n (t) − F−1(t)) 2 dt − an … B2(t) − t(1 − t) …

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

Spectral gaps in Wasserstein distances and the 2D ... - arXivhttps://arxiv.org › pdf › math
https://arxiv.org › pdf › mathPDF
by M Hairer · 2006 · Cited by 157 — This work is motivated by the study of the two-dimen- sional stochastic Navier–Stokes equations on the torus. However, the results and techniques are

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

MHJC MATTINGLY, M Hairer - Preprint, 2006

Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations

<——2006———2006——90—

2006 see 2008

M Hairer, JC Mattingly - arXiv, 2006 - ui.adsabs.harvard.edu

We develop a general method to prove the existence of spectral gaps for Markov

semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for

this analysis is neither a weighted supremum norm nor an $ Ł^ p $-type norm, but involves …

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations.

M Hairer, JC Mattingly - Preprint

Spectral gaps in Wasserstein distances and the 2D stochastic ...

https://arxiv.org › pdf › math

https://arxiv.org › pdf › mathPDF

by M Hairer · 2006 · Cited by 161 — This work is motivated by the study of the two-dimen- sional stochastic Navier–Stokes equations on the torus. However, the results and techniques are more ...

Spectral gaps in Wasserstein distances and the 2D stochastic ...https://arxiv.org › math
https://arxiv.org › math
by M Hairer · 2006 · Cited by 160 — Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations. We develop a general method to prove the existence of spectral gaps for ...

[CITATION] Spectral gaps in Wasserstein distances and the 2D Navier–Stokes equation

M Hairer, JC Mattingly - Ann. Probab, 2006

Spectral gaps in Wasserstein distances and the 2D stochastic ...

Separability and completeness for the Wasserstein distance

by M Hairer · 2006 · Cited by 155 — Using the convergence result, we show that the stochastic Navier--Stokes equations' invariant measures depend continuously on the viscosity and ..

2006 see 2008

https://www.semanticscholar.org › paper › Separability-an...

We give an elementary proof that the Wasserstein distances, which play a basic role in optimal transportation issues, turn some, spaces of probability measures

[CITATION] Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

F Bolley - Lecture Notes in Math. Springer, 2006

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

[

2006

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - mathcs.emory.edu

Recent advances in evolutionary partial differential equations are based upon interpreting

the evolution as gradient flow/steepest descent with respect to Monge-Kantorovich metrics.

An extensive literature on this topic is already available, originating with the work of Otto and …

Spectral gaps in Wasserstein distances and the 2D ... - arXiv

2006 PDF

https://arxiv.org › pdf › math

by M Hairer · 2006 · Cited by 144 — Using the convergence result, we show that the stochastic. Navier–Stokes equations' invariant measures depend continuously on the viscosity and the structure of ...

[CITATION] Spectral gaps in Wasserstein distances and the 2D Navier–Stokes equation

M Hairer, JC Mattingly - Ann. Probab, 2006

2006

2006 PDF https://arxiv.org › pdf › math

by M Hairer · 2006 · Cited by 144 — spectral gap in a particular 1-Wasserstein distance. (In the sequel ... we concentrate on the two-dimensional stochastic Navier–Stokes equations on a torus to ...

[CITATION] Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

MHJC MATTINGLY, M Hairer - Preprint, 2006

ttps://arxiv.org › pdf › math

2006 PDF

arXiv:math/0604332v1 [math.AP] 14 Apr 2006

by F Bolley · 2006 · Cited by 29 — We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous Boltzmann kinetic equations in the Maxwellian ...

[CITATION] Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

F Bolley - Lecture Notes in Math. Springer, 2006

for quasi-split groups (of rank> 2) by Deodhar [8] in 1975, for several unitary groups by Bak [unpublished], for most classical groups by Vaserstein [29] in 1973.

2006

U Rehmann - Algebraic K-Theory. Proceedings of a Conference …, 2006 - books.google.com

198 known. In 1977, I found a generalization [22] to skew fields of Matsumoto's theorem

presenting K2 of a field and in a joint work with Stuhler [23], we pointed out a transfer

method for comparing K., of a (local or global) division algebra with the K2 of its center, a …

Zbl 1308.13014

2006 Vaserstein
or quasi-split groups (of rank> 2) by Deodhar [8] in 1975, for several unitary groups by Bak [unpublished], for most classical groups by Vaserstein [29] in 1973.

U Rehmann - … Conference Held at Oberwolfach, June 1980: Part 1, 2006 - books.google.com

198 known. In 1977, I found a generalization [22] to skew fields of Matsumoto's theorem

presenting K2 of a field and in a joint work with Stuhler [23], we pointed out a transfer

method for comparing K., of a (local or global) division algebra with the K2 of its center, a …

2006 see 2005 Peer-reviewed
Eulerian Calculus for the Contraction in the Wasserstein Distance

Authors:F. Otto, M. Westdickenberg
Article, 2006
Publication:SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 37, 2006, 1227
Publisher:2006

<——2006———2006——100—

On Stein‘s factors for Poisson approximation in Wasserstein distance

Authors:Barbour, A D (Creator), Xia, A (Creator)
Summary:We provide a probabilistic proof of various Stein's factors for Poisson approximation in terms of the Wasserstein distance
Downloadable Article, 2006
English
Publication:info:doi/10.3150/bj/1165269145
Publisher:International Statistical Institute, 2006

Wasserstein Distance
Encyclopedia Article, 2006
Publication:Encyclopedia of Statistical Sciences, 20060815
Publisher:2006

<——2006———2006——102— end 2006

including 2 titles with Vaserstein

and 1 title with Vasershtein

start 2007 Wasserstein

. arXiv:0706.1172 [pdf, ps, other]

Stein's method and Poisson process approximation for a class of Wasserstein metrics

Dominic Schuhmacher

Comments: Published in at this http URL the Bernoulli (this http URL) by the International Statistical Institute/Bernoulli Society (this http URL)

Journal-ref: Bernoulli 2009, Vol. 15, No. 2, 550-568

Subjects: Probability (math.PR)

arXiv:0704.0876 [pdf, ps, other]

Non-monotone convergence in the quadratic Wasserstein distance

Walter Schachermayer, Uwe Schmock, Josef Teichmann

Subjects: Probability (math.PR)

OPEN ACCESS

VORRICHTUNG ZUR VERHÜTUNG VON WASSERSTEIN IN WASSERFÜHRENDEN SYSTEMEN

by SCHULZE, CHRISTEL

06/2007

PatentCitation Online

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arXiv:0704.0704 [pdf, ps, other]

Entropic Measure and Wasserstein Diffusion

Max-K von Renesse, Karl-Theodor Sturm

Subjects: Probability (math.PR); Analysis of PDEs (math.AP)

online

OPEN ACCESS

Entropic Measure and Wasserstein Diffusion

by von Renesse, Max-K; Sturm, Karl-Theodor

04/2007

We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy...

Journal ArticleFull Text Online

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arXiv:math/0006044 [pdf, ps, other]

Particle Approximation of the Wasserstein Diffusion

Sebastian Andres, Max-K. von Renesse

(Submitted on 14 Dec 2007)

online

OPEN ACCESS

Particle Approximation of the Wasserstein Diffusion

by Andres, Sebastian; von Renesse, Max-K

12/2007

We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process converges to the...

Journal ArticleFull Text Online

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IRPINO A., VERDE R. (2007). Clustering linear models using Wasserstein distance. In: classification and data analysis 2007, book of short paper. cladag 2007. macerata. 12-14 september 2007. (pp. 107-110). ISBN/ISSN: 978-88-6056-020-9. MACERATA: eum (ITALY).

Clustering Linear Models Using Wasserstein Distance | SpringerLink

by A Irpino - ‎2010 - ‎Related articles

Nov 25, 2009 - Clustering Linear Models Using Wasserstein Distance. Authors; Authors ... Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS) ... We show the properties of the proposed metric and an application to real data using a dynamic clustering algorithm.

Histogram based segmentation using Wasserstein distances

Scale Space and Variational Methods in Computer Vision

Tony Chan, Selim Esedoglu and Kangyu Ni

Lecture Notes in Computer Science, 2007, Volume 4485/2007, 697-708,

[PDF] from unicaen.fr

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Wasserstein Space and Fokker-Planck Equation

S Fang - 2007 Wiley China 方诗赞

Fang Shi-Chan -Wasserstein Space and Fokker-Planck Equation

[CITATION] Wasserstein Space and Fokker-Planck Equation

S Fang - 2007

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S Fang - 2007

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S Fang - 2007

Weighted L2-Wasserstein Goodness-of-Fit Statistics

[PDF] from unipd.itT de Wet - stat.unipd.it

Abstract: In two recent papers, del Barrio et al.[2] and del Barrio et al.[3], the authors

introduced and studied a new class of goodness-of-fit statistics for location-scale families,

based on L2-functionals of the empirical quantile process. These functionals measure the ...

[CITATION] Weighted L2-Wasserstein Goodness-of-Fit Statistics

T de Wet

Wasserstein space over the Wiener space Shizan FANGa, b Jinghai SHAOb, c Karl-Theodor STURMc a: IMB, BP 47870, Université de Bourgogne, 21078 Dijon …

[PDF] from u-bourgogne.frS FANG, J SHAO… - math.u-bourgogne.fr

Abstract The goal of this paper is to study optimal transportation problems and gradient flows

of probability measures on the Wiener space, based on and extending fundamental results

of Feyel-Ustünel. Carrying out the program of Ambrosio-Gigli-Savaré, we present a ...

Curve assolutamente continue negli spazi di Wasserstein con applicazioni all'equazione di continuità e ad equazioni di diffusione non lineare

S Lisini - Bollettino dell unione matematica italiana. Sezione A: …, 2007 - dialnet.unirioja.es

Información del artículo Curve assolutamente continue negli spazi di Wasserstein con applicazioni

all'equazione di continuità e ad equazioni di diffusione non lineare. ...

<——2007————2007———-10—

Calculus of variations.—Necessary optimality conditions for geodesics in weighted Wasserstein spaces,

by LUIGI AMBROSIO and FILIPPO SANTAMBROGIO, …

Rend. Lincei Mat. Appl. 18 (2007), 23–37

[PDF] from ems-ph.org RLM Appl - ems-ph.org

ABSTRACT.—The geodesic problem in Wasserstein spaces with a metric perturbed by a

conformal factor is considered, and necessary optimality conditions are established in a

case where this conformal factor favours the spreading of the probability measure along ...

MR2339442 (2009d:35215) Carrillo, J. A.; Di Francesco, M.; Lattanzio, C. Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 10 (2007), no. 2, 277--292. 35L65 (28A33)

Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws

[PDF] from uab.esJA Carrillo, M Di Francesco… - Boll. Unione Mat. Ital. Ser. B …, 2007 - mat.uab.es

Abstract. In this work, recent results concerning the long time asymptotics of one–

dimensional scalar conservation laws with probability densities as initial data are reviewed

and further applied to the case of viscous conservation laws with nonlinear degenerate ...

Contractivity and asymptotics in Wasserstein metrics for (viscous) nonlinear scalar conservation laws.

[PDF] from univaq.itM Di Francesco - Equadiff, 2007 - matematica.univaq.it

Our idea follows the paper of Carrillo–Di Francesco–Toscani (ARMA 2006) for nonlinear

diffusion equations ut=∆ φ (u), where the solution u is rescaled by its own second moment.

We require the additional assumption on f∃ α∈(0, 1), r↦→ f (r) 1− α is convex on (0,+∞).( ...

Histogram Based Segmentation Using Wasserstein Distances ...

2007

Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973

Tony F. Chan, Selim Esedoglu, Kangyu Ni Published 2007 in SSVM

We developed variational models for image segmentation that incorporate histogram information into level set based curve evolution techniques. The novelty is ...

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

MR2255281 (2007k:35255) Carrillo, J. A.; Di Francesco, M.; Toscani, G. Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering. Proc. Amer. Math. Soc. 135 (2007), no. 2, 353--363 (electronic). (Reviewer: Ross Pinsky) 35K57 (35B40 35K15)

[PDF] STRICT CONTRACTIVITY OF THE 2-WASSERSTEIN DISTANCE FOR ...

by JA CARRILLO - ‎Cited by 34 - ‎Related articles

tion having the same center of mass decays to zero for large times. As a ... one–dimensional porous medium equation towards well centered self–similar .... algebraic rate of decay to zero of the 2-Wasserstein distance between any two so-.

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Characterization of absolutely continuous curves in Wasserstein spaces

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Let X be a separable, complete metric space and [equation] be the space of Borel probability measures with finite moment of order p > 1, metrized by the ...

[PDF]

CHARACTERIZATION OF ABSOLUTELY CONTINUOUS CURVES IN ...

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arXiv 2006

[PDF] Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - Rendiconti Lincei-Matematica e …, 2007 - ems-ph.org

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are established in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

MR2343987 (2008f:35211) Tudorascu, Adrian Wasserstein kernels for one-dimensional diffusion problems. Nonlinear Anal. 67 (2007), no. 9, 2553--2572. (Reviewer: Toka Diagana) 35K57 (35D05 35R35 49M25)

Wasserstein kernels for one-dimensional diffusion problems ...

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The concept of Wasserstein kernel associated with one-dimensional diffusion problems with Neumann boundary conditions is introduced. On the basis of this, ...

Wasserstein kernels for one-dimensional diffusion problems ...

www.sciencedirect.com › science › article › abs › pii

The concept of Wasserstein kernel associated with one-dimensional diffusion problems with Neumann boundary conditions is introduced. On the basis of this, ...

by A Tudorascu - ‎2007

On the Jordan-Kinderlehrer-Otto variational scheme and ... - WVU Math

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Aug 16, 2007 - heat equation arising from the Jordan-Kinderlehrer-Otto (JKO) variational scheme. This issue ap- pears in the study of constrained optimization ...

Characterization of absolutely continuous curves in Wasserstein spaces

By: Lisini, Stefano

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Volume: ‏ 28 Issue: ‏ 1 Pages: ‏ 85-120 Published: ‏ JAN 2007

Times Cited: 48 4.

<——2007———2007———-20

Contractivity and asymptotics in wasserstein for viscous nonlinear scalar conservations laws

EXISTENCE OF PARTICULAR OPTIMAL TRANSPORTS FOR THEW1 WASSERSTEIN DISTANCE

2007 Bollettino dell unione matematica italiana. Sezione B: articoli di ricerca matematica

José Antonio Carrillo , M. Di Francesco , C. Lattanzio

The Wasserstein Gradient Flow of the Fisher Information and ...

2007 T. Champion , L. De Pascale , P. Juutinen

2007

cdn.vanderbilt.edu › sites › 2014/02 › abstr.UGO_.pdf

The Wasserstein Gradient Flow of the Fisher. Information and the Quantum Drift-Diffusion. Equation. Ugo Gianazza. September 12, 2007. Abstract. I will present ...

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2007

Entropic Measure and Wasserstein Diffusion

5 citations*

2007 ARXIV: PROBABILITY

Mentoring at the University of Pennsylvania: results of a faculty survey.

133 citations*

2007 JOURNAL OF GENERAL INTERNAL MEDICINE

Alan G. Wasserstein ,D. Alex Quistberg ,Judy A. Shea

University of Pennsylvania

Job satisfaction

Faculty development

View More (26+)

Research suggests mentoring is related to career satisfaction and success. Most studies have focused on junior faculty. To explore multiple aspects of mentoring at an academic medical center in relation to faculty rank, track, and gender. Cross-sectional mail survey in mid-2003. Faculty members, 1,4... View Full Abstract

online OPEN ACCESS

Non-monotone convergence in the quadratic Wasserstein distance

by Schachermayer, Walter; Schmock, Uwe; Teichmann, Josef

04/2007

We give an easy counter-example to Problem 7.20 from C. Villani's book on mass transport: in general, the quadratic Wasserstein distance between $n$-fold...

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Characterization of absolutely continuous curves in Wasserstein spaces

S Lisini - Calculus of Variations and Partial Differential …, 2007 - Springer

Let X be a separable, complete metric space and P _ p (X) be the space of Borel probability

measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this

paper we prove that every absolutely continuous curve with finite p-energy in the space P …

Histogram based segmentation using Wasserstein distances

T Chan, S Esedoglu, K Ni - International Conference on Scale Space and …, 2007 - Springer

In this paper, we propose a new nonparametric region-based active contour model for clutter

image segmentation. To quantify the similarity between two clutter regions, we propose to

compare their respective histograms using the Wasserstein distance. Our first segmentation …

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

[PDF] Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws

JA Carrillo, M Di Francesco… - … Mat. Ital. Sez. B Artic. Ric …, 2007 - researchgate.net

In this work, recent results concerning the long time asymptotics of one–dimensional scalar

conservation laws with probability densities as initial data are reviewed and further applied

to the case of viscous conservation laws with nonlinear degenerate diffusions. The non …

[PDF] wvu.edu

Wasserstein kernels for one-dimensional diffusion problems

A Tudorascu - Nonlinear Analysis: Theory, Methods & Applications, 2007 - Elsevier

We treat the evolution as a gradient flow with respect to the Wasserstein distance on a

special manifold and construct the weak solution for the initial-value problem by using a time-

discretized implicit scheme. The concept of Wasserstein kernel associated with one …

<——2007———2007———-30—

[PDF] cnrs.fr

[PDF] Wasserstein space over the Wiener space Shizan FANGa, b Jinghai SHAOb, c Karl-Theodor STURMc a: IMB, BP 47870, Université de Bourgogne, 21078 Dijon …

S FANG, J SHAO, KT STURM - fang.perso.math.cnrs.fr

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel-Ustünel. Carrying out the program of Ambrosio-Gigli-Savaré, we present a complete …

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

2007 see 2006

9 citations* for all

9 citations*

2007 RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI

Luigi Ambrosio ,Filippo Santambrogio

Scuola Normale Superiore di Pisa

Geodesic

View More (6+)

Abstract: The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the curve to pass through spread probability measures. These conditions have the form o... View Full Abstract

2007 zzz 19

[CITATION] Wasserstein distance for clustering interval data

A Irpino, R Verde - GFKL 2007, 2007 - iris.unicampania.it

IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti

della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati

della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili … Wasserstein …

Particle Approximation of the Wasserstein Diffusion

2007

Institutional leadership and faculty response: fostering professionalism at the University of Pennsylvania School of Medicine.

2007 ARXIV: PROBABILITY

27 citations*

2007 ACADEMIC MEDICINE

Alan G. Wasserstein ,Patrick J. Brennan ,Arthur H. Rubenstein

University of Pennsylvania

Continuing medical education

Curriculum

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Fostering professionalism requires institutional leadership and faculty buy-in. At the University of Pennsylvania School of Medicine, policies and educational programs were developed to enhance professionalism in three areas: conduct of clinical trials, relations with pharmaceutical manufacturers, a... View Full Abstract

2007

The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-Diffusion Equation

U Gianazza - 2007 - my.vanderbilt.edu

Page 1. The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-Diffusion

Equation Ugo Gianazza September 12, 2007 Abstract I will present a global existence result

for nonnegative variational so- lutions to the “quantum drift diffusion” evolution equation ∂tu + …

On Wasserstein geometry of the space of Gaussian measures

A Takatsu - arXiv preprint arXiv:0801.2250, 2008 - arxiv.org

The space of Gaussian measures on a Euclidean space is geodesically convex in the $ L^

2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian

measures are parameterized by means and covariance matrices. By restricting to the space …

2007

Characterization of absolutely continuous curves in Wasserstein spaces

S Lisini - Calculus of Variations and Partial Differential …, 2007 - Springer

… of Borel probability measures, metrized by the so-called 2-Kantorovitch–Rubinstein–Wasser-

stein distance (for … Characterization of absolutely continuous curves in Wasserstein spaces 89 …

of these results is relative to the theory of Monge–Kantorovitch in Wiener spaces (see [16 …

Eficacia asintotica tests relacionados con el estadística de Wasserstein

H Boistard - 2007 - theses.fr

Résumé Le test d'ajustement basé sur la distance de Wasserstein est un test bien adapté aux familles de localisation et changement d'échelle. La distribution asymptotique sous hypothèse nulle est connue depuis les travaux de del Barrio et al.(1999, 2000). Le thème de …

2007 see 2008
e Wasserstein Gradient Flow of the Fisher Information and ...

cdn.vanderbilt.edu › sites › 2014/02 › abstr.UGO_.pdf

PDF 2007

The Wasserstein Gradient Flow of the Fisher. Information and the Quantum Drift-Diffusion. Equation. Ugo Gianazza. September 12, 2007. Abstract. I will present ...

by U Gianazza · ‎2007 · ‎Cited by 154 · ‎Related articles

2007 [PDF] psu.edu

Histogram based segmentation using Wasserstein distances

T Chan, S Esedoglu, K Ni - International Conference on Scale Space and …, 2007 - Springer

… model for clutter image segmentation. To quantify the similarity between two clutter regions,

we propose to compare their respective histograms using the Wasserstein distance. Our first

segmentation model is based on minimizing the Wasserstein distance between the object (…

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

<——2007———2007———-40—

Entropic Measure and Wasserstein Diffusion

by MK von Renesse · 2007 · Cited by 85 — The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or ...

[CITATION] Entropic Measure and Wasserstein Diffusion. 2007

MK von Renesse, KT Sturm - Preprint

[PDF] Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws

JA Carrillo, M Di Francesco… - … Mat. Ital. Sez. B Artic. Ric …, 2007 - researchgate.net

In this work, recent results concerning the long time asymptotics of one–dimensional scalar

conservation laws with probability densities as initial data are reviewed and further applied

to the case of viscous conservation laws with nonlinear degenerate diffusions. The non …

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

Histogram based segmentation using Wasserstein distances

T Chan, S Esedoglu, K Ni - International Conference on Scale Space and …, 2007 - Springer

In this paper, we propose a new nonparametric region-based active contour model for clutter

image segmentation. To quantify the similarity between two clutter regions, we propose to

compare their respective histograms using the Wasserstein distance. Our first segmentation …

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

[CITATION] Wasserstein distance for clustering interval data

A Irpino, R Verde - GFKL 2007, 2007 - iris.unicampania.it

IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti

della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati

della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili … Wasserstein …

Wasserstein kernels for one-dimensional diffusion problems

A Tudorascu - Nonlinear Analysis: Theory, Methods & Applications, 2007 - Elsevier

We treat the evolution as a gradient flow with respect to the Wasserstein distance on a

special manifold and construct the weak solution for the initial-value problem by using a time-

discretized implicit scheme. The concept of Wasserstein kernel associated with one …

[PDF] ams.org
Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

Histogram based segmentation using Wasserstein distances

54 citations*

2007 LECTURE NOTES IN COMPUTER SCIENCE

Tony F. Chan ,Selim Esedoĝlu ,Kangyu Ni

Histogram

Segmentation

View More (3+)

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

Wasserstein kernels for one-dimensional diffusion problems

A Tudorascu - Nonlinear Analysis: Theory, Methods & Applications, 2007 - Elsevier

We treat the evolution as a gradient flow with respect to the Wasserstein distance on a special manifold and construct the weak solution for the initial-value problem by using a time-discretized implicit scheme. The concept of Wasserstein kernel associated with one …

2007

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported solutions of the one-dimensional porous medium equation having the same center of mass decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

<——2007———2007———-50—

[PDF] Wasserstein space over the Wiener space Shizan FANGa, b Jinghai SHAOb, c Karl-Theodor STURMc a: IMB, BP 47870, Université de Bourgogne, 21078 Dijon …

S FANG, J SHAO, KT STURM - Citeseer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel-Ustünel. Carrying out the program of Ambrosio-Gigli-Savaré, we present a complete …

Eficacia asintotica tests relacionados con el estadística de Wasserstein

H Boistard - 2007 - theses.fr

Résumé Le test d'ajustement basé sur la distance de Wasserstein est un test bien adapté

aux familles de localisation et changement d'échelle. La distribution asymptotique sous

hypothèse nulle est connue depuis les travaux de del Barrio et al.(1999, 2000). Le thème de …

2007 modified 2012, 2021

[PDF] Wasserstein space over the Wiener space Shizan FANGa, b Jinghai SHAOb, c Karl-Theodor STURMc a: IMB, BP 47870, Université de Bourgogne, 21078 Dijon …

S FANG, J SHAO, KT STURM - Citeseer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel-Ustünel. Carrying out the program of Ambrosio-Gigli-Savaré, we present a complete …

Images for Eficiencia asintótica de tests relacionados con el estadístico de Wasserstein

2007

[CITATION] Eficiencia asintótica de tests relacionados con el estadístico de Wasserstein

H Boistard - 2007

Eficiencia asintótica de tests relacionados con el estadístico de Wasserstein

Author:Hélène Boistard
Thesis, Dissertation, 2007
Spanish
Publisher:[s.n.], [S.l.], 2007
[Spanish Asymptotic efficiency of tests related to the Wasserstein statistic]

Histogram based segmentation using Wasserstein distances

T Chan, S Esedoglu, K Ni - International Conference on Scale Space and …, 2007 - Springer

In this paper, we propose a new nonparametric region-based active contour model for clutter

image segmentation. To quantify the similarity between two clutter regions, we propose to

compare their respective histograms using the Wasserstein distance. Our first segmentation …

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

2007

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

2007

Histogram based segmentation using Wasserstein distances

T Chan, S Esedoglu, K Ni - International Conference on Scale Space and …, 2007 - Springer

In this paper, we propose a new nonparametric region-based active contour model for clutter

image segmentation. To quantify the similarity between two clutter regions, we propose to

compare their respective histograms using the Wasserstein distance. Our first segmentation …

2007 [PDF] wvu.edu

Wasserstein kernels for one-dimensional diffusion problems

A Tudorascu - Nonlinear Analysis: Theory, Methods & Applications, 2007 - Elsevier

We treat the evolution as a gradient flow with respect to the Wasserstein distance on a

special manifold and construct the weak solution for the initial-value problem by using a time-

discretized implicit scheme. The concept of Wasserstein kernel associated with one …

2007 zzz 20

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

2007

Hamiltonian ODEs in the Wasserstein space of probability ...

onlinelibrary.wiley.com › doi › abs

Apr 30, 2007 · In this paper we consider a Hamiltonian H on 𝒫 2 (ℝ 2d ), the set of probability measures with finite quadratic moments on the phase space ℝ 2d = ℝ d × ℝ d, which is a metric space when endowed with the Wasserstein distance W2. We study the initial value problem d μ t / dt + ∇ · (𝕁 dvt μ t) = 0, where 𝕁 d is the canonical symplectic matrix, μ 0 is prescribed, and vt is a tangent vector to 𝒫 2 (ℝ 2d) at μ t, belonging to ∂ H (μ t ), the subdifferential of H at ...

Author: Luigi Ambrosio, Wilfrid Gangbo

<——2007———2007———-60—

2007 [PDF] researchgate.net

[PDF] Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws

JA Carrillo, M Di Francesco… - … Mat. Ital. Sez. B Artic. Ric …, 2007 - researchgate.net

In this work, recent results concerning the long time asymptotics of one–dimensional scalar

conservation laws with probability densities as initial data are reviewed and further applied

to the case of viscous conservation laws with nonlinear degenerate diffusions. The non …

Characterization of absolutely continuous curves in Wasserstein spaces

S Lisini - Calculus of variations and partial differential equations, 2007 - Springer

Let X be a separable, complete metric space and P _ p (X) be the space of Borel probability

measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this

paper we prove that every absolutely continuous curve with finite p-energy in the space P …

2007

[PDF] Curve assolutamente continue negli spazi di Wasserstein con applicazioni all'equazione di continuità e ad equazioni di diffusione non lineare

S Lisini - Bollettino dell unione matematica italiana. Sezione A …, 2007 - bdim.eu

Questa tesi di dottorato si colloca nell'ambito delle applicazioni della teoria del trasporto

ottimo di massa, e della conseguente distanza di Wasserstein, alle equazioni alle derivate

parziali di tipo evolutivo. L'interpretazione di alcune equazioni di diffusione come flusso …

Characterization of absolutely continuous curves in Wasserstein spaces

S Lisini - Calculus of variations and partial differential equations, 2007 - Springer

Let X be a separable, complete metric space and P _ p (X) be the space of Borel probability

measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this

paper we prove that every absolutely continuous curve with finite p-energy in the space P …

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - … of the American Mathematical …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

2007

Gradient Flows of Probability Measures - UCSB Math

https://web.math.ucsb.edu › ~kcraig › math › Ambr...

https://web.math.ucsb.edu › ~kcraig › math › Ambr...PDF

by L Ambrosio · 2007 · Cited by 77 — 2 Metric and differentiable structure of the Wasserstein space. 13. 2.1 Absolutely continuous maps and metric derivative . . . . .

2007 [PDF] ems.press

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - Rendiconti Lincei-Matematica e …, 2007 - ems.press

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

2007 [PDF] wvu.edu

Wasserstein kernels for one-dimensional diffusion problems

A Tudorascu - Nonlinear Analysis: Theory, Methods & Applications, 2007 - Elsevier

We treat the evolution as a gradient flow with respect to the Wasserstein distance on a

special manifold and construct the weak solution for the initial-value problem by using a time-

discretized implicit scheme. The concept of Wasserstein kernel associated with one …

Characterization of absolutely continuous curves in Wasserstein spaces

S Lisini - Calculus of variations and partial differential equations, 2007 - Springer

Let X be a separable, complete metric space and P _ p (X) be the space of Borel probability

measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this

paper we prove that every absolutely continuous curve with finite p-energy in the space P …

[PDF] ems.press

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

L Ambrosio, F Santambrogio - Rendiconti Lincei-Matematica e …, 2007 - ems.press

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

<——2007———2007———-70—

[PDF] Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws

JA Carrillo, M Di Francesco… - … Mat. Ital. Sez. B Artic. Ric …, 2007 - researchgate.net

In this work, recent results concerning the long time asymptotics of one–dimensional scalar

conservation laws with probability densities as initial data are reviewed and further applied

to the case of viscous conservation laws with nonlinear degenerate diffusions. The non …

[PDF] bdim.eu

[PDF] Curve assolutamente continue negli spazi di Wasserstein con applicazioni all'equazione di continuità e ad equazioni di diffusione non lineare

S Lisini - Bollettino dell unione matematica italiana. Sezione A …, 2007 - bdim.eu

Questa tesi di dottorato si colloca nell'ambito delle applicazioni della teoria del trasporto

ottimo di massa, e della conseguente distanza di Wasserstein, alle equazioni alle derivate

parziali di tipo evolutivo. L'interpretazione di alcune equazioni di diffusione come flusso …

[PDF] Curve assolutamente continue negli spazi di Wasserstein con applicazioni all'equazione di continuità e ad equazioni di diffusione non lineare

2007 [PDF] bdim.eu

S Lisini - … italiana. Sezione A: la matematica nella società e nella …, 2007 - bdim.eu

Questa tesi di dottorato si colloca nell'ambito delle applicazioni della teoria del trasporto

ottimo di massa, e della conseguente distanza di Wasserstein, alle equazioni alle derivate

parziali di tipo evolutivo. L'interpretazione di alcune equazioni di diffusione come flusso …

Eficacia asintotica tests relacionados con el estadística de Wasserstein

[Ltalian Absolutely continuous curves in Wasserstein spaces with applications to the continuity equation and non-linear diffusion equations]

2007

H Boistard - 2007 - theses.fr

Résumé Le test d'ajustement basé sur la distance de Wasserstein est un test bien adapté

aux familles de localisation et changement d'échelle. La distribution asymptotique sous

hypothèse nulle est connue depuis les travaux de del Barrio et al.(1999, 2000). Le thème de …

[Spanish Asymptotic efficacy tests related to the Wasserstein statistic]

2007

Eficacia asintotica tests relacionados con el estadística de ...

https://www.semanticscholar.org › Ef...

https://www.semanticscholar.org › Ef... · Translate this page

Le test d'ajustement base sur la distance de Wasserstein est un test bien ... Eficacia asintotica tests relacionados con el estadística de Wasserstein.

Missing: Eficiencia ‎| Must include: Eficiencia

[CITATION] Eficiencia asintótica de tests relacionados con el estadístico de Wasserstein

H Boistard - 2007

[Spanish Asymptotic efficiency of tests related to the Wasserstein statistic ]

2007

[PDF] Curve assolutamente continue negli spazi di Wasserstein con applicazioni all'equazione di continuità e ad equazioni di diffusione non lineare

S Lisini - Bollettino dell unione matematica italiana. Sezione A …, 2007 - bdim.eu

Questa tesi di dottorato si colloca nell'ambito delle applicazioni della teoria del trasporto

ottimo di massa, e della conseguente distanza di Wasserstein, alle equazioni alle derivate

parziali di tipo evolutivo. L'interpretazione di alcune equazioni di diffusione come flusso …

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

2007

[PDF] ems.press

L Ambrosio, F Santambrogio - Rendiconti Lincei-Matematica e …, 2007 - ems.press

The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor

is considered, and necessary optimality conditions are estabilished in a case where this

conformal factor favours the spreading of the probability measure along the curve. These …

2007

Characterization of absolutely continuous curves in Wasserstein spaces

S Lisini - Calculus of variations and partial differential equations, 2007 - Springer

Let X be a separable, complete metric space and P _ p (X) be the space of Borel probability

measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this

paper we prove that every absolutely continuous curve with finite p-energy in the space P …

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J Carrillo, M Di Francesco, G Toscani - Proceedings of the American …, 2007 - ams.org

We show that the Euclidean Wasserstein distance between two compactly supported

solutions of the one-dimensional porous medium equation having the same center of mass

decays to zero for large times. As a consequence, we detect an improved $ L^ 1$-rate of …

2007 [PDF] psu.edu

Histogram based segmentation using Wasserstein distances

T Chan, S Esedoglu, K Ni - International Conference on Scale Space and …, 2007 - Springer

In this paper, we propose a new nonparametric region-based active contour model for clutter

image segmentation. To quantify the similarity between two clutter regions, we propose to

compare their respective histograms using the Wasserstein distance. Our first segmentation …

[CITATION] Poster Presentations-3 Image Segmentation and Visual Grouping-Histogram Based Segmentation Using Wasserstein Distances

T Chan, S Esedoglu, K Ni - Lecture Notes in …, 2007 - Berlin: Springer-Verlag, 1973-

<——2007———2007———-80—

2007 see 2006

Some Geometric Calculations on Wasserstein Space

164 citations* for all

160 citations*

2007 COMMUNICATIONS IN MATHEMATICAL PHYSICS

John Lott

University of Michigan

Scalar curvature

Exponential map (Riemannian geometry)

View More (8+)

We compute the Riemannian connection and curvature for the Wasserstein space of a smooth compact Riemannian manifold.

Absolutely continuous curves in Wasserstein spaces : with applications to continuity equation and to nonlinear diffusion equations : dottorato di ricerca in matematica e statistica : tesi di dottoratoShow more

Authors:Stefano Lisini, Università degli studi (Pavia).
Print Book, 2007?]
English
Publisher:2007?]

On Stein's factors for poisson aproximation in Wasserstein distance

Authors:Andrew D. Barbour, Aihua Xia
Print Book, 2007
English
Publisher:University of Zurich, Institute of Mathematics, Zürich, 2007

<——2007———2007———-83— end 2007

start 2008 titles with Wasserstein

2008 PDF

Wasserstein Space Over the Wiener Space Shizan Fang ...

http://webdoc.sub.gwdg.de › serien › sfb611

by S Fang · Cited by 47 — Abstract. The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, ...

26 pages

arXiv:0906.2280 [pdf, ps, other]

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

Aldéric Joulin

Comments: Published in at this http URL the Bernoulli (this http URL) by the International Statistical Institute/Bernoulli Society (this http URL)

Journal-ref: Bernoulli 2009, Vol. 15, No. 2, 532-549

Subjects: Statistics Theory (math.ST)

arXiv:0812.4847 [pdf, ps, other]

Polynomial birth-death distribution approximation in Wasserstein distance

Aihua Xia, Fuxi Zhang

Comments: 16 pages

Journal-ref: Journal of Theoretical Probability 22 (2009), 294--310.

Subjects: Probability (math.PR)

2008 see 2010 2011 book

arXiv:0807.1065 [pdf, ps, other]

Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini

Comments: Version 2. Improved presentation, slight technical changes. To appear in Memoirs AMS

Subjects: Analysis of PDEs (math.AP); Symplectic Geometry (math.SG)

arXiv:0801.2455 [pdf, other]

Eulerian calculus for the displacement convexity in the Wasserstein distance

Sara Daneri, Giuseppe Savare

Journal-ref: SIAM J. Math. Anal. 40 (2008), 1104-1122

Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)

2008

arXiv:0801.2250 [pdf, ps, other]

On Wasserstein geometry of the space of Gaussian measures

On Wasserstein geometry of the space of Gaussian measures

Comments: 15pages, 1figures

Subjects: Differential Geometry (math.DG); Probability (math.PR)

[PDF] from arxiv.orgA Takatsu - Arxiv preprint arXiv:0801.2250, 2008 - arxiv.org

Abstract: The space of Gaussian measures on a Euclidean space is geodesically convex in

the $ L^ 2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian

measures are parameterized by means and covariance matrices. By restricting to the ...

Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance

by R Verde - ‎2008 - ‎Cited by 29 - ‎Related articles

Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance. Authors ... representation of large data sets: Fisher vs piecewise linear approximations.

Title: Dynamic clustering of interval data using a Wasserstein-based distance

Author(s): Irpino, A; Verde, R

Source: PATTERN RECOGNITION LETTERS Volume: 29 Issue: 11 Pages: 1648-1658 Published: 2008

Cone structure of $ L^ 2$-Wasserstein spaces

[PDF] from arxiv.orgA Takatsu… - Arxiv preprint arXiv:0812.2752, 2008 - arxiv.org

Abstract: The purpose of this paper is to understand the geometric structure of the $ L^ 2$-

Wasserstein space $\ pp $ over the Euclidean space. For this sake, we focus on its cone

structure. One of our main results is that the $ L^ 2$-Wasserstein space over a Polish ...

publ. 1912

[CITATION] Cone structure of L2-Wasserstein spaces, Preprint (2008)

A Takatsu, T Yokota - Available at arXiv

Euler–Poisson Systems as Action-Minimizing Paths in the ...

Eulerian calculus for the displacement convexity in the Wasserstein distance

Jul 17, 2008 — Euler–Poisson Systems as Action-Minimizing Paths in the ... Gangbo W.: Hamiltonian ODE in the Wasserstein spaces of probability measures.

<——2008—————————2008———-10—

MR2452882 (2009k:58072) Daneri, Sara; Savaré, Giuseppe Eulerian calculus for the displacement convexity in the Wasserstein distance. SIAM J. Math. Anal. 40 (2008), no. 3, 1104--1122. (Reviewer: Chloé Jimenez) 58J65 (49J10)

[PDF] from arxiv.orgS Daneri… - Arxiv preprint arXiv:0801.2455, 2008 - arxiv.org

Abstract: In this paper we give a new proof of the (strong) displacement convexity of a class

of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci

curvature bound. Our approach does not rely on existence and regularity results for ...

All 22 versions

Model reduction of stochastic processes using Wasserstein pseudometrics

[PDF] from ntnu.noD Thorsley… - American Control Conference, 2008, 2008 - ieeexplore.ieee.org

Abstract We consider the problem of finding reduced models of stochastic processes. We

use Wasserstein pseudometrics to quantify the difference between processes. The method

proposed in this paper is applicable to any continuous-time stochastic process with output, ...

A geometric study of Wasserstein spaces: Euclidean spaces

[PDF] from arxiv.orgB Kloeckner - Arxiv preprint arXiv:0804.3505, 2008 - arxiv.org

Abstract: We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an

intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the

case of the line, there exists a (unique)" exotic" isometric flow. This contrasts with the case ...

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows aeXiv

[PDF] from arxiv.orgJW Portegies… - Arxiv preprint arXiv:0812.1269, 2008 - arxiv.org

Abstract: We develop a gradient-flow framework based on the Wasserstein metric for a

parabolic moving-boundary problem that models crystal dissolution and precipitation. In

doing so we derive a new weak formulation for this moving-boundary problem and we ..

.arXiv:0812.1269 [pdf, ps, other]

A New Interval Data Distance Based on the Wasserstein Metric

R Verde… - Data Analysis, Machine Learning and Applications, 2008 - Springer

Interval data allow statistical units to be described by means of interval values, whereas their

representation by single values appears to be too reductive or inconsistent, that is, unable to

keep the uncertainty usually inherent to the observed data. In the present paper, we ...

A new interval data distance based on the Wasserstein metric

By: Verde, Rosanna; Irpino, Antonio

Conference: 31st Annual Conference of the German-Classification-Society Location: ‏ Albert Ludwigs Univ, Freiburg, GERMANY Date: ‏ MAR 07-09, 2007

Sponsor(s): ‏German Classificat Soc

DATA ANALYSIS, MACHINE LEARNING AND APPLICATIONS Book Series: ‏ Studies in Classification Data Analysis and Knowledge Organization Pages: ‏ 705-712 Published: ‏ 2008

Times Cited: 4

2008

[PDF] A geometric study of the Wasserstein space of the line

[PDF] from inria.frB Kloeckner - Preprint, 2008 - hal.inria.fr

The concept of optimal transportation raised recently a growing interest in link with the

geometry of metric spaces. In particular the L2 Wasserstein space W2 (X) have been used in

[6] and [8, 9] to define certain curvature conditions on a metric space X. Many useful ...

Kantorovich‐Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology

J Pousin - AIP Conference Proceedings, 2008 - link.aip.org

Determining the influence of a biological species to the evolution of an other one strongly

depends on the choice of mathematical models in biology. In this work we consider the case

of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma, ...

Introduction to Wasserstein Spaces

[PDF] from bnu.edu.cnS Fang - 2008 - math.bnu.edu.cn

Page 1. Introduction to Wasserstein Spaces Shizan Fang Stochastic research Center, Beijing

Normal University Beijing, 100875, China ... The purpose of this lecture is to understand the

geometric structure of P2(Rd). 1 Wasserstein Space (P2(Rd), W2) 1.1 Wasserstein distance ...

ll 4 versions [PDF] qucosa.de

Ordinary Least Squares for Histogram Data Based on Wasserstein Distance

R Verde… - COMPSTAT'2010 Book of Abstracts, 2008 - www-roc.inria.fr

Abstract. Histogram data is a kind of symbolic representation which allows to describe an

individual by an empirical frequency distribution. In this paper we introduce a linear

regression model for histogram variables. We present a new Ordinary Least Squares ...

MR2350420 (2009e:60010) Clement, Philippe; Desch, Wolfgang An elementary proof of the triangle inequality for the Wasserstein metric. Proc. Amer. Math. Soc. 136 (2008), no. 1, 333--339 (electronic). (Reviewer: Luigi De Pascale) 60B05 (49Q20)

An elementary proof of the triangle inequality for the Wasserstein metric

P Clement, W Desch - Proceedings of the American Mathematical Society, 2008 - ams.org

We give an elementary proof for the triangle inequality of the $ p $-Wasserstein metric for

probability measures on separable metric spaces. Unlike known approaches, our proof does

not rely on the disintegration theorem in its full generality; therefore the additional …

<——2008————2008———-20—

MR2358290 (2009b:58014) Lott, John Some geometric calculations on Wasserstein space. Comm. Math. Phys. 277 (2008), no. 2, 423--437. (Reviewer: Cédric Villani) 58B20 (58J65)

arXiv 2007

2008 see 2006 arXiv

MR2386101 (2009g:60007) Decreusefond, L. Wasserstein distance on configuration space. Potential Anal. 28 (2008), no. 3, 283--300. (Reviewer: Ali Süleyman Üstünel) 60B05 (60H07)

MR2389987 (2008m:35140) Tudorascu, Adrian On the Jordan-Kinderlehrer-Otto variational scheme and constrained optimization in the Wasserstein metric. Calc. Var. Partial Differential Equations 32 (2008), no. 2, 155--173. 35K15 (35A15 35A35 46E35 46N20 49J45 49M25)

preprint 2007

MR2403310 (2010a:49064) Champion, Thierry; De Pascale, Luigi; Juutinen, Petri The $\infty$-Wasserstein distance: local solutions and existence of optimal transport maps. SIAM J. Math. Anal. 40 (2008), no. 1, 1--20. 49Q20 (49K30)

Wasserstin Distance - e p u b s . s i a m . o r g

by T Champion - ‎2008 - ‎Cited by 78 - ‎Related articles

1, pp. 1–20. THE o-WASSERSTEIN DISTANCE: LOCAL SOLUTIONS AND. EXISTENCE OF OPTIMAL TRANSPORT MAPS. ∗. THIERRY CHAMPION† , LUIGI ...

MR2417812 (2009e:53038) Figalli, A.; Juillet, N. Absolute continuity of Wasserstein geodesics in the Heisenberg group. J. Funct. Anal. 255 (2008), no. 1, 133--141. (Reviewer: Cédric Villani) 53C17 (22E25 49Q15)

Absolute continuity of Wasserstein geodesics in the Heisenberg group

by A FIGALLI - ‎Cited by 27 - ‎Related articles

geodesic is unique, the absolute continuity of Wasserstein geodesic also holds ... In particular, optimal transportation in the Heisenberg group Hn has been.

MR2478676 Hairer, Martin; Mattingly, Jonathan C. Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations. Ann. Probab. 36 (2008), no. 6, 2050--2091. 35Q35 (35R60 47D07 60H15 76D05 76M35)

Hairer , Mattingly : Spectral gaps in Wasserstein distances and the 2D ...

by M Hairer - ‎2008 - ‎Cited by 102 - ‎Related articles

We develop a general method to prove the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the type of norm we ...

Spectral gaps in Wasserstein distances and the 2D stochastic ...

projecteuclid.org › euclid.aop

Volume 36, Number 6 (2008), 2050-2091. Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations. Martin Hairer and Jonathan

by M Hairer · ‎2008 · ‎Cited by 140 · ‎Related articles

MR2482206 Ambrosio, Luigi; Gigli, Nicola Construction of the parallel transport in the Wasserstein space. Methods Appl. Anal. 15 (2008), no. 1, 1--29. (Reviewer: Koji Kikuchi) 49Q20 (28A33 35K55 47J35)

CONSTRUCTION OF THE PARALLEL TRANSPORT ... - Project Euclid

by L Ambrosio - ‎2008 - ‎Cited by 24 - ‎Related articles

Abstract. In this paper we study the problem of parallel transport in the Wasserstein spaces. 乡2(Rd). We show that the parallel transport exists along a class of ...

Zbl 1179.28009

Construction of the Parallel Transport in the Wasserstein Space

Author

Authors:Ambrosio, Luigi (Creator), Gigli, Nicola (Creator)
Computer Program, 2008-03
English
Publisher:International Press of Boston, 2008-03

2008 28

MR2483740 Bolley, F. Separability and completeness for the Wasserstein distance. Séminaire de probabilités XLI, 371--377, Lecture Notes in Math., 1934, Springer, Berlin, 2008. 60B05

Separability and completeness for the Wasserstein distance ...

by F Bolley - ‎2008 - ‎Cited by 66 - ‎Related articles

We give an elementary proof that the Wasserstein distances, which play a basic role in optimal transportation issues, turn some, spaces of probability measures ...

Separability and completeness for the Wasserstein distance ...

hal.archives-ouvertes.fr › hal-00453...

François Bolley. Separability and completeness for the Wasserstein distance. Séminaire de Probabilités XLI,, Lecture notes in mathematics, 2008, 1934, ...

MR2481677 Gangbo, Wilfrid; Nguyen, Truyen; Tudorascu, Adrian Hamilton-Jacobi equations in the Wasserstein space. Methods Appl. Anal. 15 (2008), no. 2, 155--183. 49L25 (47Jxx 82C40)

Hamilton-Jacobi equations in the Wasserstein space. - Project Euclid

by W Gangbo - ‎2008 - ‎Cited by 67 - ‎Related articles

Abstract. We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. ... Hamilton-Jacobi equations in infinite dimension, viscosity solutions, mass transfer, Wasserstein metric.

MR2487455 Walczuk, Anna Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric. [Central limit theorem for an additive functional of a Markov process, stable in the Wasserstein metric] Ann. Univ. Mariae Curie-Skƚodowska Sect. A 62 (2008), 149--159. 60J25 (60F05)

Central limit theorem for an additive functional of a Markov process ...

by A Walczuk - ‎2008 - ‎Cited by 5 - ‎Related articles

"Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric." Annales UMCS, Mathematica 62.1 (2008): 149-159.

<——2008—————————2008———- 30—

MR2443374 (2010b:60009) Clément, Philippe; Desch, Wolfgang Wasserstein metric and subordination. Studia Math. 189 (2008), no. 1, 35--52. (Reviewer: Paul Raynaud de Fitte) 60B05 (28A33 47D06 54E35)

Wasserstein metric and subordinationAll - IM PAN

by P Clément - ‎2008 - ‎Cited by 1 - ‎Related articles

Wasserstein metric and subordination. Volume 189 / 2008. Philippe Clément, Wolfgang Desch Studia Mathematica 189 (2008), 35-52 MSC: Primary 60B05; ...

Wasserstein metric and subordination

Author

Authors:Clement P., Desch W.
Article, 2008
Publication:Studia Mathematica, 189, 2008 12 01, 35
Publisher:2008

MR2509579 Verde, Rosanna; Irpino, Antonio Comparing histogram data using a Mahalanobis-Wasserstein distance. COMPSTAT 2008---Proceedings in Computational Statistics, 77--89, Physica-Verlag/Springer, Heidelberg, 2008. 62G09 (62H11). Zbl 1147.62054

Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance

by R Verde - ‎2008 - ‎Cited by 38 - ‎Related articles

In this paper, we present a new distance for comparing data described by histograms. The distance is a generalization of the classical Mahalanobis distance for ...

Cone structure of L²-Wasserstein spaces

A Takatsu, T Yokota - arXiv preprint arXiv:0812.2752, 2008 - arxiv.org

The purpose of this paper is to understand the geometric structure of the $ L^ 2$-Wasserstein space $\pp $ over the Euclidean space. For this sake, we focus on its cone structure. One of our main results is that the $ L^ 2$-Wasserstein space over a Polish space …

Wasserstein metric and subordination

published 2012

By: Clement, Philippe; Desch, Wolfgang

STUDIA MATHEMATICA Volume: ‏ 189 Issue: ‏ 1 Pages: ‏ 35-52 Published: ‏

Absolute continuity of Wasserstein geodesics in the Heisenberg group

By: Figalli, A.; Juillet, N.

JOURNAL OF FUNCTIONAL ANALYSIS Volume: ‏ 255 Issue: ‏ 1 Pages: ‏ 133-141 Published: ‏ JUL 1 2008 Times Cited: 15

On the Jordan-Kinderlehrer-Otto variational scheme and constrained optimization in the Wasserstein metric

By: Tudorascu, Adrian

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Volume: ‏ 32 Issue: ‏ 2 Pages: ‏ 155-173 Published: ‏ JUN 2008

Times Cited: 6

22018

List of talks, presentations and attendances of Goncalo dos Reis

https://www.maths.ed.ac.uk › ~gdosrei › talks

AMRC Reesearch Seminar, Sheffield, 8 Dec 2022; Applied Mathematics ...

Wasserstein calculus and related topics, Edinburgh (UK), 19 - 23 November 2018 ...

Wasserstein Calculus and Related Topics | ICMS

https://www.icms.org.uk › workshops › wasserstein-calc...

Wasserstein Calculus and Related Topics ... This workshop reviewed and consolidated knowledge on stochastic calculus in Wasserstein space and assessed its ...

Alexander Davie, University of Edinburgh: Mult...

Alvin Tse, University of Edinburgh: Weak Parti...

William Salkeld, University of Edinburgh: Differ...

2018

List of talks, presentations and attendances of Goncalo dos Reis

https://www.maths.ed.ac.uk › ~gdosrei › talks

AMRC Reesearch Seminar, Sheffield, 8 Dec 2022; Applied Mathematics ...

Wasserstein calculus and related topics, Edinburgh (UK), 19 - 23

November 2018 ...

2018
A Wasserstein GAN model with the total variational regularizationAuthors:Zhang, Lijun (Creator), Zhang, Yujin (Creator), Gao, Yongbin (Creator)
Summary:It is well known that the generative adversarial nets (GANs) are remarkably difficult to train. The recently proposed Wasserstein GAN (WGAN) creates principled research directions towards addressing these issues. But we found in practice that gradient penalty WGANs (GP-WGANs) still suffer from training instability. In this paper, we combine a Total Variational (TV) regularizing term into the WGAN formulation instead of weight clipping or gradient penalty, which implies that the Lipschitz constraint is enforced on the critic network. Our proposed method is more stable at training than GP-WGANs and works well across varied GAN architectures. We also present a method to control the trade-off between image diversity and visual quality. It does not bring any computation burdenShow more
Downloadable Archival Material, 2018-12-03
Undefined
Publisher:2018-12

Model reduction of stochastic processes using Wasserstein pseudometrics

By: Thorsley, David; Klavins, Eric

Conference: American Control Conference 2008 Location: ‏ Seattle, WA Date: ‏ JUN 11-13, 2008

Sponsor(s): ‏IEEE

2008 AMERICAN CONTROL CONFERENCE, VOLS 1-12 Book Series: ‏ Proceedings of the American Control Conference Pages: ‏ 1374-1381 Published: ‏ 2008

Times Cited: 8 12.

<——2008———2008———- 40 —

Some geometric calculations on Wasserstein space

By: Lott, John

COMMUNICATIONS IN MATHEMATICAL PHYSICS Volume: ‏ 277 Issue: ‏ 2 Pages: ‏ 423-437 Published: ‏ JAN 2008

Times Cited: 47

Hamiltonian ODEs in the wasserstein space of probability measures

By: Ambrosio, Luigi; Gangbo, Wilfred

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Volume: ‏ 61 Issue: ‏ 1 Pages: ‏ 18-53 Published: ‏ JAN 2008

Times Cited: 56

Comparing histogram data using a Mahalanobis-Wasserstein distance

By: Verde, Rosanna; Irpino, Antonio

Conference: 18th Symposium on Computational Statistics (COMSTAT 2008) Location: ‏ Oporto, PORTUGAL Date: ‏ AUG 24-29, 2008

Sponsor(s): ‏Univ Porto, Fac Econ; PSE; FCT; FEUP; Banco Portugal; SPM; Caixa Geral Depositos; SPE; CLAD; ifcs

COMPSTAT 2008: PROCEEDINGS IN COMPUTATIONAL STATISTICS Pages: ‏ 77-89 Published: ‏ 2008

Times Cited: 20

Kantorovich‐Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology

J Pousin - AIP Conference Proceedings, 2008 - aip.scitation.org

Determining the influence of a biological species to the evolution of an other one strongly

depends on the choice of mathematical models in biology. In this work we consider the case

of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma …

The Wasserstein Distance and its Behaviour along Geodesics

Book Author(s): Ambrosio, L; Gigli, N; Savare, G

GRADIENT FLOWS IN METRIC SPACES AND IN THE SPACE OF PROBABILITY MEASURES, SECOND EDITION Book Series: ‏ Lectures in Mathematics Pages: ‏ 151-165 Published: ‏ 2008

Kantorovich-Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology

By: Pousin, Jerome

Conference: International Conference on Numerical Analysis and Applied Mathematics Location: ‏ Psalidi, GREECE Date: ‏ SEP 16-20, 2008

Sponsor(s): ‏Greek Minist Educ & Religious Affairs; European Soc Computat Methods Sci & Engn

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS Book Series: ‏ AIP CONFERENCE PROCEEDINGS Volume: ‏ 1048 Pages: ‏ 440-445 Published: ‏ 2008

An elementary proof of the triangle inequality for the Wasserstein metric

By: Clement, Philippe; Desch, Wolfgang

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume: ‏ 136 Issue: ‏ 1 Pages: ‏ 333-339 Published: ‏ 2008

The infinity-Wasserstein distance: Local solutions and existence of optimal transport maps

Times Cited: 6

By: Champion, Thierry; De Pascale, Luigi; Juutinen, Petri

SIAM JOURNAL ON MATHEMATICAL ANALYSIS Volume: ‏ 40 Issue: ‏ 1 Pages: ‏ 1-20 Published: ‏ 2008 Times Cited: 43 21.

EULERIAN CALCULUS FOR THE DISPLACEMENT CONVEXITY IN THE WASSERSTEIN DISTANCE

By: Daneri, Sara; Savare, Giuseppe

SIAM JOURNAL ON MATHEMATICAL ANALYSIS Volume: ‏ 40 Issue: ‏ 3 Pages: ‏ 1104-1122 Published: ‏ 2008

Times Cited: 58

e Wasserstein Gradient Flow of the Fisher Information and ...

Kantorovich‐Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology

Oct 21, 2008 — The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation ... of this equation, which is the gradient flow of the (perturbed) Fisher information functional ... Elsevier, Amsterdam (2006).

by U Gianazza · ‎2009 · ‎Cited by 154 · ‎Related articles

<—–2008————2008———- 50—

J Pousin - AIP Conference Proceedings, 2008 - aip.scitation.org

Determining the influence of a biological species to the evolution of an other one strongly

depends on the choice of mathematical models in biology. In this work we consider the case

of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma …

The logarithmic Sobolev inequality for the Wasserstein diffusion

link.springer.com › content › pdf

Oct 14, 2008 — and Sturm (Entropic measure and Wasserstein diffusion. Ann Probab, 2008) satis- fies a logarithmic Sobolev inequality. This implies ...

by M Döring · ‎20

The logarithmic Sobolev inequality for the Wasserstein diffusion

Oct 14, 2008 — ... (Entropic measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev inequality. This implies hypercontractivity of ...

by M Döring · ‎2009 · ‎Cited by 20 · ‎Related articles

[CITATION] The Logarithmic Sobolev Inequality for the Wasserstein Diffusion (2008)

M Döring, W Stann

Hamilton-Jacobi equations in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Methods and Applications …, 2008 - projecteuclid.org

… choices of V,U0 : M → R reveal that the characteristics for (2) are paths in AC2 … These systems

of equations appear in Fluid Mechanics and the one-dimensional Euler- Poisson system (see …

In the last section, motivated by the study of the Euler- Poisson system on the real line, we …

2008

The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation

U Gianazza, G Savaré, G Toscani - Archive for Rational Mechanics and …, 2008 - infona.pl

We prove the global existence of non-negative variational solutions to the “drift diffusion”

evolution equation $${{\partial_t} u+ div\left (u {\mathrm {D}}\left (2\frac {\Delta\sqrt u}{\sqrt u}-

{f}\right)\right)= 0} $$ under variational boundary condition. Despite the lack of a maximum …

Dynamic clustering of interval data using a Wasserstein-based distance

A Irpino, R Verde - Pattern Recognition Letters, 2008 - Elsevier

Interval data allow statistical units to be described by means of intervals of values, whereas their representation by means of a single value appears to be too reductive or inconsistent. In the present paper, we present a Wasserstein-based distance for interval data, and we …

Hamilton-Jacobi equations in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Methods and Applications …, 2008 - projecteuclid.org

We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the

Wasserstein space. We prove existence of solutions for the Cauchy problem for certain

Hamiltonians defined on the Wasserstein space over the real line. In order to illustrate the …

Hamiltonian ODEs in the Wasserstein space of probability measures

L Ambrosio, W Gangbo - … on Pure and Applied Mathematics: A …, 2008 - Wiley Online Library

In this paper we consider a Hamiltonian H on 𝒫2 (ℝ2d), the set of probability measures with

finite quadratic moments on the phase space ℝ2d= ℝd× ℝd, which is a metric space when

endowed with the Wasserstein distance W2. We study the initial value problem …

Eulerian calculus for the displacement convexity in the Wasserstein distance

S Daneri, G Savaré - SIAM Journal on Mathematical Analysis, 2008 - SIAM

In this paper we give a new proof of the (strong) displacement convexity of a class of integral

functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature

bound. Our approach does not rely on existence and regularity results for optimal transport …

Dynamic clustering of interval data using a Wasserstein-based distance

A Irpino, R Verde - Pattern Recognition Letters, 2008 - Elsevier

Interval data allow statistical units to be described by means of intervals of values, whereas

their representation by means of a single value appears to be too reductive or inconsistent.

In the present paper, we present a Wasserstein-based distance for interval data, and we …

Dynamic clustering of interval data using a Wasserstein-based distance

R VERDE, A IRPINO - 2008 - iris.unicampania.it

Interval data allow statistical units to be described by means of intervals of values, whereas

their representation by means of a single value appears to be too reductive or inconsistent.

In the present paper, we present a Wasserstein-based distance for interval data, and we …

<—–2008———2008———-60—

Hamiltonian ODEs in the Wasserstein space of probability measures

141 citations*

2008 COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Luigi Ambrosio ¹,Wilfrid Gangbo ²

¹ Scuola Normale Superiore, Faculty of Sciences, Piazza dei Cavalieri 7, 56126 Pisa, Italy,² Georgia Institute of Technology

Symplectic matrix

View More (9+)

In this paper we consider a Hamiltonian H on P 2 (R 2d ), the set of probability measures with finite quadratic moments on the phase space R 2d = R d × R d , which is a metric space when endowed with the Wasserstein distance W 2 . We study the initial value problem dμ t /dt+∇·(J d V t μ t ) = 0, w... View Full Abstract

Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

M Hairer, JC Mattingly - The Annals of Probability, 2008 - projecteuclid.org

We develop a general method to prove the existence of spectral gaps for Markov

semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for

this analysis is neither a weighted supremum norm nor an $\L^{p} $-type norm, but involves …

A Wasserstein approach to the one-dimensional sticky particle system

L Natile, G Savaré - SIAM journal on mathematical analysis, 2009 - SIAM

We present a simple approach for studying the one-dimensional pressureless Euler system

via adhesion dynamics in the Wasserstein space P_2(R) of probability measures with finite

quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we …

Comparing histogram data using a Mahalanobis–Wasserstein distance

R Verde, A Irpino - COMPSTAT 2008, 2008 - Springer

In this paper, we present a new distance for comparing data described by histograms. The

distance is a generalization of the classical Mahalanobis distance for data described by

correlated variables. We define a way to extend the classical concept of inertia and …

[PDF] intlpress.com

[PDF] Construction of the parallel transport in the Wasserstein space

L Ambrosio, N Gigli - Methods and Applications of Analysis, 2008 - intlpress.com

1. Introduction. In the last few years, starting from the seminal papers [14, 4, 12, 9], the geometric

and differential properties of the space 乡2(Rd) of probability measures in Rd with finite quadratic

moments, endowed with the quadratic optimal transportation distance, have been deeply …

An elementary proof of the triangle inequality for the Wasserstein metric

P Clement, W Desch - Proceedings of the American Mathematical Society, 2008 - ams.org

We give an elementary proof for the triangle inequality of the $ p $-Wasserstein metric for

probability measures on separable metric spaces. Unlike known approaches, our proof does

not rely on the disintegration theorem in its full generality; therefore the additional …

Wasserstein distance on configuration space

L Decreusefond - Potential Analysis, 2008 - Springer

We investigate here the optimal transportation problem on configuration space for the

quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is

finite, there exists one unique optimal measure and that this measure is supported by the …

On Wasserstein geometry of the space of Gaussian measures

A Takatsu - arXiv preprint arXiv:0801.2250, 2008 - arxiv.org

The space of Gaussian measures on a Euclidean space is geodesically convex in the $ L^

2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian

measures are parameterized by means and covariance matrices. By restricting to the space …

Absolute continuity of Wasserstein geodesics in the Heisenberg group

A Figalli, N Juillet - Journal of Functional Analysis, 2008 - Elsevier

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot,

Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2)(2004) 261–

301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is …

[PDF] ntnu.no

Model reduction of stochastic processes using Wasserstein pseudometrics

D Thorsley, E Klavins - 2008 American Control Conference, 2008 - ieeexplore.ieee.org

We consider the problem of finding reduced models of stochastic processes. We use

Wasserstein pseudometrics to quantify the difference between processes. The method

proposed in this paper is applicable to any continuous-time stochastic process with output …

<——2008——————2008———- 70 —

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic

moving-boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

M Di Francesco, M Wunsch - Monatshefte für Mathematik, 2008 - Springer

We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems

arising in semiconductor device modeling and plasma physics in one space dimension. In

particular, we prove that, under certain structural assumptions on the external potentials and …

A new interval data distance based on the Wasserstein metric

R Verde, A Irpino - Data Analysis, Machine Learning and Applications, 2008 - Springer

Interval data allow statistical units to be described by means of interval values, whereas their

representation by single values appears to be too reductive or inconsistent, that is, unable to

keep the uncertainty usually inherent to the observed data. In the present paper, we present …

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to

the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This

issue appears in the study of constrained optimization in the 2-Wasserstein metric performed …

2008 Full View

Wasserstein metric and subordination

[CITATION] Wasserstein metric and subordination.(2008)

P Clément, W Desch - 2008

[PDF] A geometric study of the Wasserstein space of the line

[CITATION] Wasserstein metric and subordination Philippe Clément

I MATEMATYCZNY - Studia Math, 2008

2008 [PDF] psu.edu

B Kloeckner - Preprint, 2008 - Citeseer

The concept of optimal transportation raised recently a growing interest in link with the

geometry of metric spaces. In particular the L2 Wasserstein space W2 (X) have been used in

[6] and [8, 9] to define certain curvature conditions on a metric space X. Many useful …

[PDF] bnu.edu.cn

[PDF] Introduction to Wasserstein Spaces

S Fang - 2008 - math0.bnu.edu.cn

Page 1.

[PDF] unipd.it

[PDF] Weighted L2-Wasserstein Goodness-of-Fit Statistics

T de Wet - stat.unipd.it

In two recent papers, del Barrio et al.[2] and del Barrio et al.[3], the authors introduced and

studied a new class of goodness-of-fit statistics for location-scale families, based on L2-

functionals of the empirical quantile process. These functionals measure the Wasserstein …

Hamiltonian ODEs in the Wasserstein space of probability measures

141 citations*

2008 COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Luigi Ambrosio ¹,Wilfrid Gangbo ²

¹ Scuola Normale Superiore, Faculty of Sciences, Piazza dei Cavalieri 7, 56126 Pisa, Italy,² Georgia Institute of Technology

Symplectic matrix

View More (9+)

In this paper we consider a Hamiltonian H on P 2 (R 2d ), the set of probability measures with finite quadratic moments on the passerstein

Eulerian Calculus for the Displacement Convexity in the Wasserstein Distancehase space R 2d = R d × R d , which is a metric space when endowed with the Wasserstein distance W 2 . We study the initial value problem dμ t /dt+∇·(J d V t μ t ) = 0, w... View Full Abstract

2008 see 2007, 2009 zzz 21

[CITATION] Entropic measure and Wasserstein diffusion, to appear in Ann

MK von Renesse, KT Sturm - 2008 - Probab

Cited by 2 Related articles see 2007, 2009

[CITATION] Entropic measure and Wasserstein diffusion, to appear in Ann

MK von Renesse, KT Sturm - 2008 - Probab

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

<——2008———2008———- 80—

2008 [PDF] wvu.edu

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to

the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This

issue appears in the study of constrained optimization in the 2-Wasserstein metric performed …

2008 thesis
<Die> Wärmeleitungsgleichung auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum = <The> heat equation on manifolds as a gradient flow in the Wasserstein spaceShow more

Author:Matthias Erbar
Thesis, Dissertation, 2008
German
Publisher:2008
2008 see 2010

[CITATION] Die Wärmeleitungsgleichung auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum

M Erbar - 2008 - Master's thesis, Bonn Universität

[CITATION] … auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum: The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - 2008

[CITATION] Die Wärmeleitungsgleichung auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum

M Erbar - 2008 - Master's thesis, Bonn Universität

Model reduction of stochastic processes using Wasserstein pseudometrics

[CITATION] Die Wärmeleitungsgleichung auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum: The heat equation on manifolds as a gradient flow in the …

M Erbar - 2008

[CITATION] … auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum: The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - 2008

[CITATION] … auf Mannigfaltigkeiten als Gradientenfluss im Wassersteinraum: The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - 2008

2008 [PDF] ntnu.no

D Thorsley, E Klavins - 2008 American Control Conference, 2008 - ieeexplore.ieee.org

We consider the problem of finding reduced models of stochastic processes. We use Wasserstein pseudometrics to quantify the difference between processes. The method proposed in this paper is applicable to any continuous-time stochastic process with output …

2008 see 2006

Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

M Hairer, JC Mattingly - The Annals of Probability, 2008 - projecteuclid.org

We develop a general method to prove the existence of spectral gaps for Markov

semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for

this analysis is neither a weighted supremum norm nor an $\L^{p} $-type norm, but involves

the derivative of the observable as well and hence can be seen as a type of 1-Wasserstein

distance. This turns out to be a suitable approach for infinite-dimensional spaces where the

usual Harris or Doeblin conditions, which are geared toward total variation convergence …

2008 [PDF] psu.edu

Hamiltonian ODEs in the Wasserstein space of probability measures

L Ambrosio, W Gangbo - … on Pure and Applied Mathematics: A …, 2008 - Wiley Online Library

In this paper we consider a Hamiltonian H on 𝒫2 (ℝ2d), the set of probability measures with

finite quadratic moments on the phase space ℝ2d= ℝd× ℝd, which is a metric space when

endowed with the Wasserstein distance W2. We study the initial value problem …

Hamiltonian ODEs in the Wasserstein space of probability measures

L Ambrosio, W Gangbo - … on Pure and Applied Mathematics: A …, 2008 - Wiley Online Library

In this paper we consider a Hamiltonian H on 𝒫2 (ℝ2d), the set of probability measures with finite quadratic moments on the phase space ℝ2d= ℝd× ℝd, which is a metric space when endowed with the Wasserstein distance W2. We study the initial value problem …

2008 [PDF] intlpress.com

[PDF] Construction of the parallel transport in the Wasserstein space

L Ambrosio, N Gigli - Methods and Applications of Analysis, 2008 - intlpress.com

1. Introduction. In the last few years, starting from the seminal papers [14, 4, 12, 9], the geometric and differential properties of the space 乡2(Rd) of probability measures in Rd with finite quadratic moments, endowed with the quadratic optimal transportation distance, have been deeply …

2008

Construction of the parallel transport in the Wasserstein space

N Gigli, L Ambrosio - 2008 - iris.sissa.it

In this paper we study the problem of parallel transport in the Wasserstein spaces P_2 (R^ d). We show that the parallel transport exists along a class of curves whose velocity field is sufficiently smooth, and that we call regular. Furthermore, we show that the class of regular …

2008 [PDF] psu.edu

[PDF] A geometric study of the Wasserstein space of the line

B Kloeckner - Preprint, 2008 - Citeseer

The concept of optimal transportation raised recently a growing interest in link with the geometry of metric spaces. In particular the L2 Wasserstein space W2 (X) have been used in [6] and [8, 9] to define certain curvature conditions on a metric space X. Many useful …

On Wasserstein geometry of the space of Gaussian measures

A Takatsu - arXiv preprint arXiv:0801.2250, 2008 - arxiv.org

The space of Gaussian measures on a Euclidean space is geodesically convex in the $ L^ 2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space …

<———2008——————2008———- 90—

The logarithmic Sobolev inequality for the Wasserstein diffusion

search.proquest.com › openview

by M Döring · 2009 · Cited by 20 — Ann Probab, 2008) satises a logarithmic Sobolev inequality. This implies hypercontractivity of the associated transition semigroup. We also study functional ...

[CITATION] The Logarithmic Sobolev Inequality for the Wasserstein Diffusion (2008)

M Döring, W Stannat - Preprint, to appear in PTRF

Cited by 2 Related articles see 2009

2008

Hamilton-Jacobi equations in the Wasserstein space

94 citations*

2008 METHODS AND APPLICATIONS OF ANALYSIS

Wilfrid Gangbo ¹,Truyen Nguyen ²,Adrian Tudorascu ¹

¹ Georgia Institute of Technology ,² University of Akron

Real line

View More (7+)

We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. We prove existence of solutions for the Cauchy problem for certain Hamil- tonians defined on the Wasserstein space over the real line. In order to illustrate the link between HJE in the Wasser... View Full Abstract

Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

M Di Francesco, M Wunsch - Monatshefte für Mathematik, 2008 - Springer

We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems

arising in semiconductor device modeling and plasma physics in one space dimension. In

particular, we prove that, under certain structural assumptions on the external potentials and …

2008 [PDF] bnu.edu.cn

[PDF] Introduction to Wasserstein Spaces

S Fang - 2008 - math0.bnu.edu.cn

Page 1. Introduction to Wasserstein Spaces Shizan Fang Stochastic research Center, Beijing

Normal University Beijing, 100875, China June-July 2008 The topic on the heat equation ∂ut

∂t − ∆ut = 0 on Rd is classical; but the porous medium equation ∂ut ∂t − (∆um t )=0 m = 1 (0.1) …

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic

moving-boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

2008

Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance

126 citations* for all

126 citations*

2008 SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Sara Daneri ¹,Giuseppe Savaré ²

¹ International School for Advanced Studies ,² University of Pavia

Geodesic convexity

Ricci curvature

View More (8+)

Inasserstein

Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manif... View Full Abstract

2008

Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations

2006 ARXIV: PROBABILITY

The $\infty$-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

108 citations*

2008 SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Thierry Charles Champion ,Luigi De Pascale ,P. Juutinen

Institut de Mathématiques de Toulon - EA 2134

Monotonic function

View More (5+)

We consider the non-nonlinear optimal transportation problem of minimizing the cost functional $\mathcal{C}_\infty(\lambda) = \operatornamewithlimits{\lambda-ess\,sup}_{(x,y) \in \Omega^2} |y-x|$ in the set of probability measures on $\Omega^2$ having prescribed marginals. This corresponds to the qu... View Full Abstract

Eulerian calculus for the displacement convexity in the Wasserstein distance

S Daneri, G Savaré - SIAM Journal on Mathematical Analysis, 2008 - SIAM

In this paper we give a new proof of the (strong) displacement convexity of a class of integral

functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature

The -Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

T Champion, L De Pascale, P Juutinen - SIAM Journal on Mathematical …, 2008 - SIAM

We consider the non-nonlinear optimal transportation problem of minimizing the cost

functional C_∞(λ)=λ-ess\,sup_(x,y)∈Ω^2|yx| in the set of probability measures on Ω^2

having prescribed marginals. This corresponds to the question of characterizing the …

Cited by 120 Related articles All 11 versions

The $\inft$-Wasserstein…

Wasserstein distance on configuration space

L Decreusefond - Potential Analysis, 2008 - Springer

We investigate here the optimal transportation problem on configuration space for the

quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is

finite, there exists one unique optimal measure and that this measure is supported by the …

<——2008——————2008———- 100—

An elementary proof of the triangle inequality for the Wasserstein metric

P Clement, W Desch - Proceedings of the American Mathematical Society, 2008 - ams.org

We give an elementary proof for the triangle inequality of the $ p $-Wasserstein metric for

probability measures on separable metric spaces. Unlike known approaches, our proof does

not rely on the disintegration theorem in its full generality; therefore the additional …

A new interval data distance based on the Wasserstein metric

R Verde, A Irpino - Data Analysis, Machine Learning and Applications, 2008 - Springer

Interval data allow statistical units to be described by means of interval values, whereas their

representation by single values appears to be too reductive or inconsistent, that is, unable to

keep the uncertainty usually inherent to the observed data. In the present paper, we present …

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to

the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This

issue appears in the study of constrained optimization in the 2-Wasserstein metric performed …

Wasserstein metric and subordination

P Clément, W Desch - Studia Mathematica, 2008 - infona.pl

Let $(X, d_X) $, $(Ω, d_ {Ω}) $ be complete separable metric spaces. Denote by 𝓟 (X) the

space of probability measures on X, by $ W_ {p} $ the p-Wasserstein metric with some

p∈[1,∞), and by $ 𝓟_ {p}(X) $ the space of probability measures on X with finite …

[CITATION] Wasserstein metric and subordination.(2008)

P Clément, W Desch - 2008

Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein space

[CITATION] Wasserstein metric and subordination Philippe Clément

I MATEMATYCZNY - Studia Math, 2008

2008

(PDF) Euler–Poisson Systems as Action-Minimizing Paths in ...

Jul 17, 2008 — Euler–Poisson Systems as Action-Minimizing Paths in the ... Gangbo W.: Hamiltonian ODE in the Wasserstein spaces of probability measures.

www.researchgate.net › publication › 225752681_Euler-...

Feb 7, 2016 — Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein Space. June 2009; Archive for Rational Mechanics and Analysis ...

2008

Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

M Di Francesco, M Wunsch - Monatshefte für Mathematik, 2008 - Springer

We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems

arising in semiconductor device modeling and plasma physics in one space dimension. In

particular, we prove that, under certain structural assumptions on the external potentials and …

[PDF] bnu.edu.cn

[PDF] Introduction to Wasserstein Spaces

S Fang - 2008 - math0.bnu.edu.cn

Page 1. Introduction to Wasserstein Spaces Shizan Fang Stochastic research Center, Beijing

Normal University Beijing, 100875, China June-July 2008 The topic on the heat equation ∂ut

∂t − ∆ut = 0 on Rd is classical; but the porous medium equation … Kantorovich problem: when …

Absolute continuity of Wasserstein geodesics in the Heisenberg group

A Figalli, N Juillet - Journal of Functional Analysis, 2008 - Elsevier

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot,

Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2)(2004) 261–

301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is …

2008

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic

moving-boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

2008

Hamilton-Jacobi equations in the Wasserstein space

94 citations*

2008 METHODS AND APPLICATIONS OF ANALYSIS

Wilfrid Gangbo ¹,Truyen Nguyen ²,Adrian Tudorascu ¹

¹ Georgia Institute of Technology ,² University of Akron

Real line

View More (7+)

<——2008——————2008———- 110—

2008

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savaré and …

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic

moving-boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic

moving-boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

2008 see 209906

Separability and completeness for the Wasserstein distance

108 citations*

2008 SÉMINAIRE DE PROBABILITÉS XLI,, LECTURE NOTES IN MATHEMATICS

François Bolley

École normale supérieure de Lyon

Metric space

Completeness (order theory)

View More (6+)

We give an elementary proof that the Wasserstein distances, which play a basic role in optimal transportation issues, turn some, spaces of prob

2008 114

SEPARABILITY AND COMPLETENESS FOR THE WASSERSTEIN DISTANCE

F Bolley - Lecture Notes in Math, 2006 pdf

Separability and completeness for the Wasserstein distance

F Bolley - Séminaire de probabilités XLI, 2008 - Springer

Ecole Normale Supérieure de Lyon, Umpa (UMR 5669) 46 allée d'Italie, F-69364 Lyon cedex

7 Current address: Institut de Mathématiques, LSP (UMR C5583) Université Paul Sabatier, Route

de Narbonne, F-31062 Toulouse cedex 9 e-mail: bolley@cict.fr … Summary. We give an elementary

proof that the Wasserstein distances, which play a basic role in optimal transportation

issues, turn some spaces of probability measures into separable complete metric spaces …

Let (X, d) be a separable complete metric space and P the set of Borel prob- ability measures …

[CITATION] Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

F Bolley - Lecture Notes in Math. Springer, 2006
ited by 100 Related articles All 11 versions

3008

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic moving-boundary problem that models crystal dissolution and precipitation. In doing so we derive a new weak formulation for this moving-boundary problem and we show that this …

2008 [PDF] intlpress.com

Construction of the parallel transport in the Wasserstein space

L Ambrosio, N Gigli - Methods and Applications of Analysis, 2008 - projecteuclid.org

1. Introduction. In the last few years, starting from the seminal papers [14, 4, 12, 9], the geometric

and differential properties of the space 乡2(Rd) of probability measures in Rd with finite quadratic

moments, endowed with the quadratic optimal transportation distance, have been deeply …

Construction of the parallel transport in the Wasserstein space

N Gigli, L Ambrosio - 2008 - iris.sissa.it

In this paper we study the problem of parallel transport in the Wasserstein spaces P_2 (R^

d). We show that the parallel transport exists along a class of curves whose velocity field is

sufficiently smooth, and that we call regular. Furthermore, we show that the class of regular …

2008

Hamilton-Jacobi equations in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Methods and Applications …, 2008 - projecteuclid.org

We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. We prove existence of solutions for the Cauchy problem for certain Hamiltonians defined on the Wasserstein space over the real line. In order to illustrate the …

2008

On Wasserstein geometry of the space of Gaussian measures

A Takatsu - arXiv preprint arXiv:0801.2250, 2008 - arxiv.org

The space of Gaussian measures on a Euclidean space is geodesically convex in the $ L^ 2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space …

2008 [PDF] arxiv.org

Wasserstein distance on configuration space

L Decreusefond - Potential Analysis, 2008 - Springer

We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is finite, there exists one unique optimal measure and that this measure is supported by the …

<——2008——————2008———- 120—

2008

A new interval data distance based on the Wasserstein metric

R Verde, A Irpino - Data Analysis, Machine Learning and Applications, 2008 - Springer

Interval data allow statistical units to be described by means of interval values, whereas their representation by single values appears to be too reductive or inconsistent, that is, unable to keep the uncertainty usually inherent to the observed data. In the present paper, we present …

2008 [PDF] wvu.edu

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This issue appears in the study of constrained optimization in the 2-Wasserstein metric performed …

Hamilton-Jacobi equations in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Methods and Applications …, 2008 - projecteuclid.org

We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. We prove existence of solutions for the Cauchy problem for certain Hamiltonians defined on the Wasserstein space over the real line. In order to illustrate the …

The -Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

T Champion, L De Pascale, P Juutinen - SIAM Journal on Mathematical …, 2008 - SIAM

We consider the non-nonlinear optimal transportation problem of minimizing the cost functional C_∞(λ)=λ-ess\,sup_(x,y)∈Ω^2|yx| in the set of probability measures on Ω^2 having prescribed marginals. This corresponds to the question of characterizing the …

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to

the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This

issue appears in the study of constrained optimization in the 2-Wasserstein metric performed …

Absolute continuity of Wasserstein geodesics in the Heisenberg group

A Figalli, N Juillet - Journal of Functional Analysis, 2008 - Elsevier

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot,

Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2)(2004) 261–

301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is …

2008 [PDF] sciencedirect.com

Absolute continuity of Wasserstein geodesics in the Heisenberg group

A Figalli, N Juillet - Journal of Functional Analysis, 2008 - Elsevier

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot,

Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2)(2004) 261–

301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is …

2008 [PDF] wvu.edu

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to

the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This

issue appears in the study of constrained optimization in the 2-Wasserstein metric performed …

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

JW Portegies, MA Peletier - arXiv preprint arXiv:0812.1269, 2008 - arxiv.org

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic

moving-boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

<——2008——————2008———- 130—

Dynamic clustering of interval data using a Wasserstein-based distance

A Irpino, R Verde - Pattern Recognition Letters, 2008 - Elsevier

Interval data allow statistical units to be described by means of intervals of values, whereas

their representation by means of a single value appears to be too reductive or inconsistent.

In the present paper, we present a Wasserstein-based distance for interval data, and we …

2008

Comparing histogram data using a Mahalanobis–Wasserstein distance

R Verde, A Irpino - COMPSTAT 2008, 2008 - Springer

In this paper, we present a new distance for comparing data described by histograms. The

distance is a generalization of the classical Mahalanobis distance for data described by

correlated variables. We define a way to extend the classical concept of inertia and …

2008 [PDF] ntnu.no

Model reduction of stochastic processes using Wasserstein pseudometrics

D Thorsley, E Klavins - 2008 American Control Conference, 2008 - ieeexplore.ieee.org

We consider the problem of finding reduced models of stochastic processes. We use

Wasserstein pseudometrics to quantify the difference between processes. The method

proposed in this paper is applicable to any continuous-time stochastic process with output …

2008

The -Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

T Champion, L De Pascale, P Juutinen - SIAM Journal on Mathematical …, 2008 - SIAM

We consider the non-nonlinear optimal transportation problem of minimizing the cost

functional C_∞(λ)=λ-ess\,sup_(x,y)∈Ω^2|yx| in the set of probability measures on Ω^2

having prescribed marginals. This corresponds to the question of characterizing the …

2008 [PDF] intlpress.com

[PDF] Construction of the parallel transport in the Wasserstein space

L Ambrosio, N Gigli - Methods and Applications of Analysis, 2008 - intlpress.com

1. Introduction. In the last few years, starting from the seminal papers [14, 4, 12, 9], the geometric

and differential properties of the space 乡2(Rd) of probability measures in Rd with finite quadratic

moments, endowed with the quadratic optimal transportation distance, have been deeply …

Construction of the parallel transport in the Wasserstein space

N Gigli, L Ambrosio - 2008 - iris.sissa.it

In this paper we study the problem of parallel transport in the Wasserstein spaces P_2 (R^

d). We show that the parallel transport exists along a class of curves whose velocity field is

sufficiently smooth, and that we call regular. Furthermore, we show that the class of regular …

2008

A new interval data distance based on the Wasserstein metric

R Verde, A Irpino - Data Analysis, Machine Learning and Applications, 2008 - Springer

Interval data allow statistical units to be described by means of interval values, whereas their

representation by single values appears to be too reductive or inconsistent, that is, unable to

keep the uncertainty usually inherent to the observed data. In the present paper, we present …

An elementary proof of the triangle inequality for the Wasserstein metric

P Clement, W Desch - Proceedings of the American Mathematical Society, 2008 - ams.org

We give an elementary proof for the triangle inequality of the $ p $-Wasserstein metric for

probability measures on separable metric spaces. Unlike known approaches, our proof does

not rely on the disintegration theorem in its full generality; therefore the additional …

Kantorovich‐Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in

Biology

J Pousin - AIP Conference Proceedings, 2008 - aip.scitation.org

Determining the influence of a biological species to the evolution of an other one strongly

depends on the choice of mathematical models in biology. In this work we consider the case

of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma …

Model reduction of stochastic processes using Wasserstein pseudometrics

2008 [PDF] ntnu.no

D Thorsley, E Klavins - 2008 American Control Conference, 2008 - ieeexplore.ieee.org

We consider the problem of finding reduced models of stochastic processes. We use

Wasserstein pseudometrics to quantify the difference between processes. The method

proposed in this paper is applicable to any continuous-time stochastic process with output …

Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

M Di Francesco, M Wunsch - Monatshefte für Mathematik, 2008 - Springer

We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems

arising in semiconductor device modeling and plasma physics in one space dimension. In

particular, we prove that, under certain structural assumptions on the external potentials and …

<——2008——————2008———- 140—

2008 [PDF] arxiv.org

Eulerian calculus for the displacement convexity in the Wasserstein distance

S Daneri, G Savaré - SIAM Journal on Mathematical Analysis, 2008 - SIAM

In this paper we give a new proof of the (strong) displacement convexity of a class of integral

functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature

bound. Our approach does not rely on existence and regularity results for optimal transport …

Hamiltonian ODEs in the Wasserstein space of probability measures

L Ambrosio, W Gangbo - … on Pure and Applied Mathematics: A …, 2008 - Wiley Online Library

In this paper we consider a Hamiltonian H on 𝒫2 (ℝ2d), the set of probability measures with

finite quadratic moments on the phase space ℝ2d= ℝd× ℝd, which is a metric space whenHamiltonian ODEs in the Wasserstein space of probability measures - Ambrosio - 2008 - Communications on ...

endowed with the Wasserstein distance W2. We study the initial value problem …

2008 [PDF] semanticscholar.org

The -Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

T Champion, L De Pascale, P Juutinen - SIAM Journal on Mathematical …, 2008 - SIAM

We consider the non-nonlinear optimal transportation problem of minimizing the cost

functional C_∞(λ)=λ-ess\,sup_(x,y)∈Ω^2|yx| in the set of probability measures on Ω^2

having prescribed marginals. This corresponds to the question of characterizing the …

A new interval data distance based on the Wasserstein metric

R Verde, A Irpino - Data Analysis, Machine Learning and Applications, 2008 - Springer

Interval data allow statistical units to be described by means of interval values, whereas their

representation by single values appears to be too reductive or inconsistent, that is, unable to

keep the uncertainty usually inherent to the observed data. In the present paper, we present …

2008

Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

M Di Francesco, M Wunsch - Monatshefte für Mathematik, 2008 - Springer

We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems

arising in semiconductor device modeling and plasma physics in one space dimension. In

particular, we prove that, under certain structural assumptions on the external potentials and …

2008

Hamiltonian ODEs in the Wasserstein space of probability measures

L Ambrosio, W Gangbo - … Issued by the Courant Institute of …, 2008 - Wiley Online Library

In this paper we consider a Hamiltonian H on 𝒫2 (ℝ2d), the set of probability measures with

finite quadratic moments on the phase space ℝ2d= ℝd× ℝd, which is a metric space when

endowed with the Wasserstein distance W2. We study the initial value problem …

Dynamic clustering of interval data using a Wasserstein-based distance

A Irpino, R Verde - Pattern Recognition Letters, 2008 - Elsevier

Interval data allow statistical units to be described by means of intervals of values, whereas

their representation by means of a single value appears to be too reductive or inconsistent.

In the present paper, we present a Wasserstein-based distance for interval data, and we …

The -Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

T Champion, L De Pascale, P Juutinen - SIAM Journal on Mathematical …, 2008 - SIAM

We consider the non-nonlinear optimal transportation problem of minimizing the cost

functional C_∞(λ)=λ-ess\,sup_(x,y)∈Ω^2|yx| in the set of probability measures on Ω^2

having prescribed marginals. This corresponds to the question of characterizing the …

An elementary proof of the triangle inequality for the Wasserstein metric

P Clement, W Desch - Proceedings of the American Mathematical Society, 2008 - ams.org

We give an elementary proof for the triangle inequality of the $ p $-Wasserstein metric for

probability measures on separable metric spaces. Unlike known approaches, our proof does

not rely on the disintegration theorem in its full generality; therefore the additional …

[PDF] intlpress.com

[PDF] Construction of the parallel transport in the Wasserstein space

L Ambrosio, N Gigli - Methods and Applications of Analysis, 2008 - intlpress.com

1. Introduction. In the last few years, starting from the seminal papers [14, 4, 12, 9], the geometric

and differential properties of the space 乡2(Rd) of probability measures in Rd with finite quadratic

moments, endowed with the quadratic optimal transportation distance, have been deeply …

Construction of the parallel transport in the Wasserstein space

N Gigli, L Ambrosio - 2008 - iris.sissa.it

In this paper we study the problem of parallel transport in the Wasserstein spaces P_2 (R^

d). We show that the parallel transport exists along a class of curves whose velocity field is

sufficiently smooth, and that we call regular. Furthermore, we show that the class of regular …

<——2008———2008———- 150—

On Wasserstein geometry of the space of Gaussian measures

A Takatsu - arXiv preprint arXiv:0801.2250, 2008 - arxiv.org

The space of Gaussian measures on a Euclidean space is geodesically convex in the $ L^

2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian

measures are parameterized by means and covariance matrices. By restricting to the space …

[PDF] ntnu.no

Model reduction of stochastic processes using Wasserstein pseudometrics

D Thorsley, E Klavins - 2008 American Control Conference, 2008 - ieeexplore.ieee.org

We consider the problem of finding reduced models of stochastic processes. We use

Wasserstein pseudometrics to quantify the difference between processes. The method

proposed in this paper is applicable to any continuous-time stochastic process with output …

Kantorovich‐Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology

[PDF] A geometric study of the Wasserstein space of the line

B Kloeckner - Preprint, 2008 - Citeseer

The concept of optimal transportation raised recently a growing interest in link with the

geometry of metric spaces. In particular the L2 Wasserstein space W2 (X) have been used in

[6] and [8, 9] to define certain curvature conditions on a metric space X. Many useful …

J Pousin - AIP Conference Proceedings, 2008 - aip.scitation.org

Determining the influence of a biological species to the evolution of an other one strongly

depends on the choice of mathematical models in biology. In this work we consider the case

of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma …

Hamiltonian systems and the calculus of differential forms on the Wasserstein space

Peer-reviewed
Wasserstein metric convergence method for Fokker-Planck equations with point controlsAuthors:Luca Petrelli, Anthony J. Kearsley
Summary:Monge-Kantorovich mass transfer theory is employed to obtain an existence and uniqueness result for solutions to Fokker-Planck Equations with time dependent point control. Existence for an approximate problem is established together with a convergence analysis in the Wasserstein distance through equivalence with weak- ⋆ convergenceShow more
Article, 2009
Publication:Applied Mathematics Letters, 22, 200907, 1130
Publisher:2009

2009 [PDF] gatech.edu

HK Kim - 2009 - smartech.gatech.edu

This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian

systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in

the work of Ambrosio and Gangbo. We regularize H via Moreau-Yosida approximation to get …

<——2009—————2009——— 80—

www.nsf.gov › awardsearch › showAward

award#0901449 - Calculus of Variations and Hamilton-Jacobi ...

Aug 30, 2009 — ... program lies in the development of an appropriate theory for calculus of variations and Hamilton-Jacobi equations in the Wasserstein space.

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. すべて. 本文あり. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics). 高津飛鳥 …

Entropic measure and Wasserstein diffusion

MK von Renesse, KT Sturm - The Annals of Probability, 2009 - projecteuclid.org

We construct a new random probability measure on the circle and on the unit interval which

in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It

satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of …

2009

The logarithmic Sobolev inequality for the Wasserstein diffusion

M Döring, W Stannat - Probability theory and related fields, 2009 - Springer

We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all

probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic

measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev …

Approximation of homogeneous measures in the 2-Wasserstein metric

S Dostoglou, JD Kahl - Mathematical Physics Electronic Journal, 2009 - dialnet.unirioja.es

It is shown that, on certain weighted spaces of vector fields on R3, any homogeneous

measure of finite energy density and dissipation can be approximated in the second

Wasserstein distance by homogeneous measures supported by finite trigonometric …

Cite Cited by 2 Related articles All 11 versions

[CITATION] Approximation of homogeneous measures in the 2-Wasserstein metric Math

S Dostoglou, JD Kahl - Phys. Electron. J,

2009 [PDF] tue.nl

[PDF] Numerical algorithm for computation of the 2-Wasserstein distance, and applications to the foundations of diffusion

S Srivastava, MA Peletier - 2009 - pure.tue.nl

This work is intended to solve the optimal mass transfer problem formulated in the fluid

mechanics framework, and to study some of the applications. Starting with a brief historical

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Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

year

[CITATION] Gradient flows on Wasserstein spaces over compact Alexandrov spaces, to appear in Amer

S Ohta - J. Math

Local histogram based segmentation using the Wasserstein distance

2009 [PDF] springer.com

K Ni, X Bresson, T Chan, S Esedoglu - International journal of computer …, 2009 - Springer

… More specifically, the region data encourages segmentation so that local histograms within

each region are approximately homogeneous. … We use Wasserstein distance with exponent

1 to determine the dissimilarity between two histograms. The Wasserstein distance is a metric …

2009 [PDF] cambridge.org

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces $ X $ with curvature

bounded below. The gradient flow of a geodesically convex functional on the quadratic …

Gromov‐Hausdorff stable signatures for shapes using persistence

F Chazal, D Cohen‐Steiner, LJ Guibas… - Computer Graphics …, 2009 - Wiley Online Library

… In this case, stability is guaranteed under small perturbations in the Gromov‐Wasserstein distance

(Section 5 … combinatorial problems akin to the quadratic assignment problem (which is NP hard),

the construction of easily computable Gromov‐Hausdorff stable invariants is …

] inria.fr

<——2009—————2009——— 90—

2009 see 2010 2012 2019

Gradient flows in Wasserstein spaces and ... - Numdam

www.numdam.org › SEDP_2009-2010____A27_0

PDF

Gradient flows in Wasserstein spaces and applications to crowd movement. Séminaire É. ... spaces, and finally in the space of probability measures endowed with the ... Gigli-Savaré, we propose an approach where the optimality conditions for.

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The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

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We establish the convergence of a vortex system towards equations similar to the 2D Euler

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[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

A new approach based on Wasserstein distances, which are numerical costs of an optimal

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We propose and analyze a nonparametric region-based active contour model for

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Wasserstein distance for the fusion of multisensor multitarget particle filter clouds

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In a multisensor multitarget tracking application, the evaluation of the cost of assigning

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Non-monotone convergence in the quadratic Wasserstein distance

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1 Vienna University of Technology Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria email:

wschach@fam.tuwien.ac.at 2 Vienna University of Technology Wiedner Hauptstrasse 8–10,

1040 Vienna, Austria email: schmock@fam.tuwien.ac.at 3 Vienna University of Technology Wiedner …

Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance

A Xia, F Zhang - Journal of Theoretical Probability, 2009 - Springer

The polynomial birth–death distribution (abbreviated, PBD) on ℐ={0, 1, 2,…} or ℐ={0, 1, 2,…,

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Stein's method and Poisson process approximation for a class of Wasserstein metrics

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Based on Stein's method, we derive upper bounds for Poisson process approximation in the

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between point measures. For the case p= 1, this construction yields the metric d 2 introduced …

[HTML] Wasserstein metric convergence method for Fokker–Planck equations with point controls

L Petrelli, AJ Kearsley - Applied mathematics letters, 2009 - Elsevier

Monge–Kantorovich mass transfer theory is employed to obtain an existence and

uniqueness result for solutions to Fokker–Planck Equations with time dependent point

control. Existence for an approximate problem is established together with a convergence …

Cited by 1 Related articles All 9 versions
<——2009———2009——— 100 —

Wasserstein distances for vortices approximation of Euler-type equations

M Hauray - Mathematical Models and Methods in Applied …, 2009 - World Scientific

We establish the convergence of a vortex system towards equations similar to the 2D Euler

equation in vorticity formulation. The only but important difference is that we use singular

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Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

… We establish the existence of Euclidean tangent cones on Wasserstein spaces over compact …

By using this Riemannian structure, we formulate and construct gradient flows of functions on …

is a Riemannian manifold of nonnegative sectional curvature, then our gradient flow of the …

2009

Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

2009 [HTML] sciencedirect.com

[HTML] Wasserstein metric convergence method for Fokker–Planck equations with point controls

L Petrelli, AJ Kearsley - Applied mathematics letters, 2009 - Elsevier

Monge–Kantorovich mass transfer theory is employed to obtain an existence and

uniqueness result for solutions to Fokker–Planck Equations with time dependent point

control. Existence for an approximate problem is established together with a convergence …

2009 [PDF] projecteuclid.org

Stein's method and Poisson process approximation for a class of Wasserstein metrics

D Schuhmacher - Bernoulli, 2009 - projecteuclid.org

Based on Stein's method, we derive upper bounds for Poisson process approximation in the

L 1-Wasserstein metric d 2 (p), which is based on a slightly adapted L p-Wasserstein metric

between point measures. For the case p= 1, this construction yields the metric d 2 introduced …

[CITATION] Stein's method and Poisson process approximation for a class of Wasserstein metrics. Bernoulli 15 550–568

D Schuhmacher - … (MathSciNet): MR2543874 Digital Object Identifier: doi, 2009

Bernoulli 15 550–568

Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance

A Xia, F Zhang - Journal of Theoretical Probability, 2009 - Springer

The polynomial birth–death distribution (abbreviated, PBD) on ℐ={0, 1, 2,…} or ℐ={0, 1, 2,…,

m} for some finite m introduced in Brown and Xia (Ann. Probab. 29: 1373–1403, 2001) is the

equilibrium distribution of the birth–death process with birth rates {α i} and death rates {β i} …

Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

[PDF] leidenuniv.nl

[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

… 4 3. Implementation 7 3.1. Calculation of Wasserstein distances 7 3.2. Bootstrapping and binning

7 3.3 … 28 A.3. Dilations and similarity transformations 29 A.4. Weighted coordinates 29 A.5.

Residuals of Wasserstein distances 30 A.6. Optimization of generalized cost 31 …

Spectral Gromov-Wasserstein distances for shape matching

F Mémoli - 2009 IEEE 12th International Conference on …, 2009 - ieeexplore.ieee.org

… Methods based on Heat Diffusion have also been used to analyze graphs (See [1] and … therein),

where signatures similar to the HKS have been proven useful in graph classification and

comparison … As a result, their method can potentially be used to classify shapes under- going …

Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

<——2009—————2009——— 110—

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer

We prove the global existence of non-negative variational solutions to the “drift diffusion”

evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under

variational boundary condition. Despite the lack of a maximum principle for fourth order …

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

2009 [PDF] tue.nl

[PDF] Numerical algorithm for computation of the 2-Wasserstein distance, and applications to the foundations of diffusion

S Srivastava, MA Peletier - 2009 - pure.tue.nl

This work is intended to solve the optimal mass transfer problem formulated in the fluid

mechanics framework, and to study some of the applications. Starting with a brief historical

overview of the optimal mass transfer problem (classical Monge problem and its relaxed …

2019 see 2009 2010
Gradient flows in Wasserstein spaces and applications to ...

www.numdam.org › SEDP_2009-2010____A27_0

by F Santambrogio · Cited by 13 — 2009-2010. Filippo Santambrogio. Gradient flows in Wasserstein spaces and applications to crowd movement. Séminaire É. D. P. (2009-2010), Exposé n° XXVII, ...

[CITATION] Gradient flows in Wasserstein spaces and applications to crowd movement, Séminaire XEDP, 2009-2010

F Santambrogio - Exp. No. XXVII, 2012

Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

2009

The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer

We prove the global existence of non-negative variational solutions to the “drift diffusion”

evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under

variational boundary condition. Despite the lack of a maximum principle for fourth order

equations, non-negative solutions can be obtained as a limit of a variational approximation

scheme by exploiting the particular structure of this equation, which is the gradient flow of

the (perturbed) Fisher information functional\fancyscript F^ f (u):=\frac 12 ∫\left| D\log …

Entropic measure and Wasserstein diffusion

MK von Renesse, KT Sturm - Annals of probability, 2009 - projecteuclid.org

We construct a new random probability measure on the circle and on the unit interval which

in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It

satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of …

Wasserstein distances for vortices approximation of Euler-type equations

M Hauray - Mathematical Models and Methods in Applied …, 2009 - World Scientific

We establish the convergence of a vortex system towards equations similar to the 2D Euler equation in vorticity formulation. The only but important difference is that we use singular kernel of the type x⊥/| x| α+ 1, with α< 1, instead of the Biot–Savard kernel x⊥/| x| 2. This …

<——2009———2009———120—

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

2009 [HTML] sciencedirect.com

[HTML] Wasserstein metric convergence method for Fokker–Planck equations with point controls

L Petrelli, AJ Kearsley - Applied mathematics letters, 2009 - Elsevier

Monge–Kantorovich mass transfer theory is employed to obtain an existence and uniqueness result for solutions to Fokker–Planck Equations with time dependent point control. Existence for an approximate problem is established together with a convergence …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

2009 [PDF] arxiv.org

Non-monotone convergence in the quadratic Wasserstein distance

W Schachermayer, U Schmock… - Séminaire de Probabilités …, 2009 - Springer

1 Vienna University of Technology Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria email: wschach@fam.tuwien.ac.at 2 Vienna University of Technology Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria email: schmock@fam.tuwien.ac.at 3 Vienna University of Technology Wiedner …

2009 [HTML] sciencedirect.com

[HTML] Wasserstein metric convergence method for Fokker–Planck equations with point controls

L Petrelli, AJ Kearsley - Applied mathematics letters, 2009 - Elsevier

Monge–Kantorovich mass transfer theory is employed to obtain an existence and uniqueness result for solutions to Fokker–Planck Equations with time dependent point control. Existence for an approximate problem is established together with a convergence …

Spectral Gromov-Wasserstein distances for shape matching

F Mémoli - 2009 IEEE 12th International Conference on …, 2009 - ieeexplore.ieee.org

We introduce a spectral notion of distance between shapes and study its theoretical properties. We show that our distance satisfies the properties of a metric on the class of isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if …

2009 [PDF] gatech.edu

Hamiltonian systems and the calculus of differential forms on the Wasserstein space

HK Kim - 2009 - smartech.gatech.edu

This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in the work of Ambrosio and Gangbo. We regularize H via Moreau-Yosida approximation to get …

2009 modified

[PDF] Gromov-Wasserstein stable signatures for object matching and the role of persistence

F Mémoli - geometrica.saclay.inria.fr

Page 1. 1 Gromov-Wasserstein stable signatures for object matching and the role of persistence

Facundo Mémoli memoli@math.stanford.edu Page 2. 2 Some definitions.. • Let (Z, d) be a compact

metric space. • For closed A, B ⊂ Z, we define the Hausdorff distance as: d Z H (A, B) = max(max …

2009 see 2016 [PDF] osu.edu

Spectral Gromov-Wasserstein distances for shape matching

F Mémoli - 2009 IEEE 12th International Conference on …, 2009 - ieeexplore.ieee.org

<——2009—————2009——— 130—

22009 thesis
Hamiltonian systems and the calculus of differential forms on the Wasserstein spaceAuthor:Hwa Kil Kim
Abstract:This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in the work of Ambrosio and Gangbo. We regularize H via Moreau-Yosida approximation to get H[subscript Tau] and denote by μ[subscript Tau] a solution of system with the new Hamiltonian H[subscript Tau] . Suppose H[subscript Tau] converges to H as τ tends to zero. We show μ[subscript Tau] converges to μ and μ is a solution of a Hamiltonian system which is corresponding to the Hamiltonian H. At the end of first part, we give a sufficient condition for the uniqueness of Hamiltonian systems. In the second part, we develop a general theory of differential forms on the Wasserstein space. Our main result is to prove an analogue of Green's theorem for 1-forms and show that every closed 1-form on the Wasserstein space is exact. If the Wasserstein space were a manifold in the classical sense, this result wouldn't be worthy of mention. Hence, the first cohomology group, in the sense of de Rham, vanishesShow more
Thesis, Dissertation, 2009
English
Publisher:Georgia Institute of Technology, Atlanta, Ga., 200

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of positively curved Markov jump processes. In particular, our main result generalizes the tail …

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … (MathSciNet): MR2543873 Digital Object Identifier: doi, 2009

[CITATION] A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … (MathSciNet): MR2543873 Digital Object Identifier: doi, 2009

[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

A new approach based on Wasserstein distances, which are numerical costs of an optimal transportation problem, allows to analyze nonlinear phenomena in a robust manner. The long-term behavior is reconstructed from time series, resulting in a probability distribution …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

Euler–Poisson systems as action-minimizing paths in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Archive for rational mechanics and …, 2009 - Springer

This paper uses a variational approach to establish existence of solutions (σ t, vt) for the 1-d

Euler–Poisson system by minimizing an action. We assume that the initial and terminal

points σ 0, σ T are prescribed in P _2 (R), the set of Borel probability measures on the real …

3009

A View on Optimal Transport from Noncommutative Geometry
https://arxiv.org › math
by F D'Andrea · 2009 · Cited by 38 — Abstract: We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, ...

2009 see 2010

A Wasserstein approach to the one-dimensional sticky particle system

L Natile, G Savaré - SIAM journal on mathematical analysis, 2009 - SIAM

We present a simple approach for studying the one-dimensional pressureless Euler system

via adhesion dynamics in the Wasserstein space P_2(R) of probability measures with finite

quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we …

[CITATION] A Wasserstein approach to the one-dimensional sticky particle system

LNG Savaré - 2009 - Submitted

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

Stein's method and Poisson process approximation for a class of Wasserstein metrics

D Schuhmacher - Bernoulli, 2009 - projecteuclid.org

Based on Stein's method, we derive upper bounds for Poisson process approximation in the

L 1-Wasserstein metric d 2 (p), which is based on a slightly adapted L p-Wasserstein metric

between point measures. For the case p= 1, this construction yields the metric d 2 introduced …

CITATION] Stein's method and Poisson process approximation for a class of Wasserstein metrics. Bernoulli 15 550–568

D Schuhmacher - … (MathSciNet): MR2543874 Digital Object Identifier: doi, 2009

Distilled Wasserstein Learning for Word Embedding and Topic ...

Entropic measure and Wasserstein diffusion

MK von Renesse, KT Sturm - Annals of probability, 2009 - projecteuclid.org

We construct a new random probability measure on the circle and on the unit interval which

in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It

satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of …

<——2009—————2009——— 140—

https://proceedings.neurips.cc › paper › hash

by A Montanari · 2009 · Cited by 83 — We propose a novel Wasserstein method with a distillation mechanism, yielding join

2009 [PDF] tue.nl

[PDF] Numerical algorithm for computation of the 2-Wasserstein distance, and applications to the foundations of diffusion

S Srivastava, MA Peletier - 2009 - pure.tue.nl

This work is intended to solve the optimal mass transfer problem formulated in the fluid

mechanics framework, and to study some of the applications. Starting with a brief historical

overview of the optimal mass transfer problem (classical Monge problem and its relaxed …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of

the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to

porous medium equations. We give an explicit expression of the solution to the porous …

Local histogram based segmentation using the Wasserstein distance

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

K Ni, X Bresson, T Chan, S Esedoglu - International journal of computer …, 2009 - Springer

We propose and analyze a nonparametric region-based active contour model for

segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel

intensity is independently identically distributed. Our proposed energy functional consists of …

2009 [PDF] springer.com

Local histogram based segmentation using the Wasserstein distance

K Ni, X Bresson, T Chan, S Esedoglu - International journal of computer …, 2009 - Springer

We propose and analyze a nonparametric region-based active contour model for

segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel

intensity is independently identically distributed. Our proposed energy functional consists of …

2009

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

[CITATION] A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … Reviews (MathSciNet): MR2543873 Digital Object …, 2009

2009

The logarithmic Sobolev inequality for the Wasserstein diffusion

M Döring, W Stannat - Probability theory and related fields, 2009 - Springer

We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all

probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic

measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev …

2009 [PDF] inria.fr

[PDF] Gromov-Wasserstein stable signatures for object matching and the role of persistence

F Mémoli - geometrica.saclay.inria.fr

Page 1. 1 Gromov-Wasserstein stable signatures for object matching and the role of persistence

Facundo Mémoli memoli@math.stanford.edu Page 2. 2 Some definitions.. • Let (Z, d) be a

compact metric space. • For closed A, B ⊂ Z, we define the Hausdorff distance as: d Z H (A, B) …

A Wasserstein approach to the one-dimensional sticky particle system

L Natile, G Savaré - SIAM journal on mathematical analysis, 2009 - SIAM

We present a simple approach for studying the one-dimensional pressureless Euler system

via adhesion dynamics in the Wasserstein space P_2(R) of probability measures with finite

quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we …

[CITATION] A Wasserstein approach to the one-dimensional sticky particle system

LNG Savaré - 2009 - Submitted

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

2009

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

[CITATION] A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … (MathSciNet): MR2543873 Digital Object Identifier: doi, 2009

<——2009—————2009——— 150—

[HTML] Wasserstein metric convergence method for Fokker–Planck equations with point controls

L Petrelli, AJ Kearsley - Applied mathematics letters, 2009 - Elsevier

Monge–Kantorovich mass transfer theory is employed to obtain an existence and

uniqueness result for solutions to Fokker–Planck Equations with time dependent point

control. Existence for an approximate problem is established together with a convergence …

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

[CITATION] A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … (MathSciNet): MR2543873 Digital Object Identifier: doi, 2009

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of

the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to

porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

Hamiltonian systems and the calculus of differential forms on the Wasserstein spaceHamiltonian ODEs in the Wasserstein space of probability measures - Ambrosio - 2008 - Communications on ...

HK Kim - 2009 - smartech.gatech.edu

This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian

systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in

the work of Ambrosio and Gangbo. We regularize H via Moreau-Yosida approximation to get …

Local histogram based segmentation using the Wasserstein distance

K Ni, X Bresson, T Chan, S Esedoglu - International journal of computer …, 2009 - Springer

We propose and analyze a nonparametric region-based active contour model for

segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel

intensity is independently identically distributed. Our proposed energy functional consists of …

2009

The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer

We prove the global existence of non-negative variational solutions to the “drift diffusion”

evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under

variational boundary condition. Despite the lack of a maximum principle for fourth order …

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

[CITATION] A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … (MathSciNet): MR2543873 Digital Object Identifier: doi, 2009

The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer

We prove the global existence of non-negative variational solutions to the “drift diffusion”

evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under

variational boundary condition. Despite the lack of a maximum principle for fourth order …

Wasserstein distances for vortices approximation of Euler-type equations

M Hauray - Mathematical Models and Methods in Applied …, 2009 - World Scientific

We establish the convergence of a vortex system towards equations similar to the 2D Euler

equation in vorticity formulation. The only but important difference is that we use singular

kernel of the type x⊥/| x| α+ 1, with α< 1, instead of the Biot–Savard kernel x⊥/| x| 2. This …

<——2009—————2009——— 160—

Hamiltonian systems and the calculus of differential forms on the Wasserstein space

HK Kim - 2009 - smartech.gatech.edu

This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian

systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in

the work of Ambrosio and Gangbo. We regularize H via Moreau-Yosida approximation to get …

Wasserstein distance for the fusion of multisensor multitarget particle filter clouds

D Danu, T Kirubarajan, T Lang - 2009 12th International …, 2009 - ieeexplore.ieee.org

In a multisensor multitarget tracking application, the evaluation of the cost of assigning

particle filter clouds of different sensors as being estimates of the same target is an essential

part in the particle cloud association. This paper treats the problem of evaluating the cost of …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of

the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to

porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

Approximation of homogeneous measures in the 2-Wasserstein metric

S Dostoglou, JD Kahl - Mathematical Physics Electronic Journal, 2009 - dialnet.unirioja.es

It is shown that, on certain weighted spaces of vector fields on R3, any homogeneous

measure of finite energy density and dissipation can be approximated in the second

Wasserstein distance by homogeneous measures supported by finite trigonometric …

[CITATION] Approximation of homogeneous measures in the 2-Wasserstein metric Math

S Dostoglou, JD Kahl - Phys. Electron. J, 2009

[PDF] Numerical algorithm for computation of the 2-Wasserstein distance, and applications to the foundations of diffusion

[PDF] tue.nl

S Srivastava, MA Peletier - 2009 - pure.tue.nl

This work is intended to solve the optimal mass transfer problem formulated in the fluid

mechanics framework, and to study some of the applications. Starting with a brief historical

overview of the optimal mass transfer problem (classical Monge problem and its relaxed …

2009

[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

A new approach based on Wasserstein distances, which are numerical costs of an optimal

transportation problem, allows to analyze nonlinear phenomena in a robust manner. The

long-term behavior is reconstructed from time series, resulting in a probability distribution …

[PDF] Gromov-Wasserstein stable signatures for object matching and the role of persistence

F Mémoli - geometrica.saclay.inria.fr

… Haven't been able to explain or relate to too many pre-existing practical approaches to object

matching. There's a plethora of methods: it would be nice to understand inter-relation between

them. • Furthermore, the GH distance is a ”pessimistic” measure of similarity: it is based on …

2009

Entropic measure and Wasserstein diffusion

MK von Renesse, KT Sturm - Annals of probability, 2009 - projecteuclid.org

We construct a new random probability measure on the circle and on the unit interval which

in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It

satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of …

Local histogram based segmentation using the Wasserstein distance

K Ni, X Bresson, T Chan, S Esedoglu - International journal of computer …, 2009 - Springer

We propose and analyze a nonparametric region-based active contour model for

segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel

intensity is independently identically distributed. Our proposed energy functional consists of …

The wasserstein distances

C Villani - Optimal Transport, 2009 - Springer

Assume, as before, that you are in charge of the transport of goods be- tween producers and

consumers, whose respective spatial distributions are modeled by probability measures. The

farther producers and con- sumers are from each other, the more difficult will be your job, and …

<——2009—————2009——— 170—

A Wasserstein approach to the one-dimensional sticky particle system

L Natile, G Savaré - SIAM journal on mathematical analysis, 2009 - SIAM

We present a simple approach for studying the one-dimensional pressureless Euler system

via adhesion dynamics in the Wasserstein space P_2(R) of probability measures with finite

quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we …

[CITATION] A Wasserstein approach to the one-dimensional sticky particle system

LNG Savaré - 2009 - Submitted

Euler–Poisson systems as action-minimizing paths in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Archive for rational mechanics and …, 2009 - Springer

This paper uses a variational approach to establish existence of solutions (σ t, vt) for the 1-d

Euler–Poisson system by minimizing an action. We assume that the initial and terminal

points σ 0, σ T are prescribed in P _2 (R), the set of Borel probability measures on the real …

The logarithmic Sobolev inequality for the Wasserstein diffusion

M Döring, W Stannat - Probability theory and related fields, 2009 - Springer

We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all

probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic

measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev …

Non-monotone convergence in the quadratic Wasserstein distance

W Schachermayer, U Schmock… - Séminaire de Probabilités …, 2009 - Springer

1 Vienna University of Technology Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria email:

wschach@fam.tuwien.ac.at 2 Vienna University of Technology Wiedner Hauptstrasse 8–10,

1040 Vienna, Austria email: schmock@fam.tuwien.ac.at 3 Vienna University of Technology Wiedner …

2009

Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance

A Xia, F Zhang - Journal of Theoretical Probability, 2009 - Springer

The polynomial birth–death distribution (abbreviated, PBD) on ℐ={0, 1, 2,…} or ℐ={0, 1, 2,…,

m} for some finite m introduced in Brown and Xia (Ann. Probab. 29: 1373–1403, 2001) is the

equilibrium distribution of the birth–death process with birth rates {α i} and death rates {β i} …

2009 see 2010 zzz 24

[CITATION] Wasserstein space over the Wiener space, to appear in Probab

S Fang, J Shao, KT Sturm - Theory Related Fields, 2009

[CITATION] Wasserstein space over the Wiener space, to appear in Probab

S Fang, J Shao, KT Sturm - Theory Related Fields, 2009

Spectral Gromov-Wasserstein distances for shape matching

2009

F Mémoli - 2009 IEEE 12th International Conference on …, 2009 - ieeexplore.ieee.org

We introduce a spectral notion of distance between shapes and study its theoretical

properties. We show that our distance satisfies the properties of a metric on the class of

isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if …

2009

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

2009

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

[HTML] Wasserstein metric convergence method for Fokker–Planck equations with point controls

L Petrelli, AJ Kearsley - Applied mathematics letters, 2009 - Elsevier

Monge–Kantorovich mass transfer theory is employed to obtain an existence and

uniqueness result for solutions to Fokker–Planck Equations with time dependent point

control. Existence for an approximate problem is established together with a convergence …

2009

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

<——2009—————2009——— 180—

2009

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

A Wasserstein approach to the one-dimensional sticky particle system

L Natile, G Savaré - SIAM journal on mathematical analysis, 2009 - SIAM

We present a simple approach for studying the one-dimensional pressureless Euler system

via adhesion dynamics in the Wasserstein space P_2(R) of probability measures with finite

quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we …

[CITATION] A Wasserstein approach to the one-dimensional sticky particle system

LNG Savaré - 2009 - Submitted

Euler–Poisson systems as action-minimizing paths in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Archive for rational mechanics and …, 2009 - Springer

This paper uses a variational approach to establish existence of solutions (σ t, vt) for the 1-d

Euler–Poisson system by minimizing an action. We assume that the initial and terminal

points σ 0, σ T are prescribed in P _2 (R), the set of Borel probability measures on the real …

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

Non-monotone convergence in the quadratic Wasserstein distance

W Schachermayer, U Schmock… - Séminaire de Probabilités …, 2009 - Springer

1 Vienna University of Technology Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria email:

wschach@fam.tuwien.ac.at 2 Vienna University of Technology Wiedner Hauptstrasse 8–10,

1040 Vienna, Austria email: schmock@fam.tuwien.ac.at 3 Vienna University of Technology Wiedner …

2009

Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance

A Xia, F Zhang - Journal of Theoretical Probability, 2009 - Springer

The polynomial birth–death distribution (abbreviated, PBD) on ℐ={0, 1, 2,…} or ℐ={0, 1, 2,…,

m} for some finite m introduced in Brown and Xia (Ann. Probab. 29: 1373–1403, 2001) is the

equilibrium distribution of the birth–death process with birth rates {α i} and death rates {β i} …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of

the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to

porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

Approximation of homogeneous measures in the 2-Wasserstein metric

S Dostoglou, JD Kahl - Mathematical Physics Electronic Journal, 2009 - dialnet.unirioja.es

It is shown that, on certain weighted spaces of vector fields on R3, any homogeneous

measure of finite energy density and dissipation can be approximated in the second

Wasserstein distance by homogeneous measures supported by finite trigonometric …

[CITATION] Approximation of homogeneous measures in the 2-Wasserstein metric Math

S Dostoglou, JD Kahl - Phys. Electron. J, 2009

[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

A new approach based on Wasserstein distances, which are numerical costs of an optimal

transportation problem, allows to analyze nonlinear phenomena in a robust manner. The

long-term behavior is reconstructed from time series, resulting in a probability distribution …

[PDF] tue.nl

[PDF] Numerical algorithm for computation of the 2-Wasserstein distance, and applications to the foundations of diffusion

S Srivastava, MA Peletier - 2009 - pure.tue.nl

This work is intended to solve the optimal mass transfer problem formulated in the fluid

mechanics framework, and to study some of the applications. Starting with a brief historical

overview of the optimal mass transfer problem (classical Monge problem and its relaxed …

<——2009—————2009——— 190—

2009

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

A Joulin - Bernoulli, 2009 - projecteuclid.org

The purpose of this paper is to extend the investigation of Poisson-type deviation

inequalities started by Joulin (Bernoulli 13 (2007) 782–798) to the empirical mean of

positively curved Markov jump processes. In particular, our main result generalizes the tail …

[CITATION] A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli 15 532–549

A Joulin - … (MathSciNet): MR2543873 Digital Object Identifier: doi, 2009

A Wasserstein approach to the one-dimensional sticky particle system

L Natile, G Savaré - SIAM journal on mathematical analysis, 2009 - SIAM

We present a simple approach for studying the one-dimensional pressureless Euler system

via adhesion dynamics in the Wasserstein space P_2(R) of probability measures with finite

quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we …

[CITATION] A Wasserstein approach to the one-dimensional sticky particle system

LNG Savaré - 2009 - Submitted

[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

2009

[PDF] leidenuniv.nl

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

… its natu- ral measure with arbitrary precision (22); in the case of finite time series this … In the following

we assume that the reconstruction process has been performed, so let x … the long- term behavior

of dynamical systems quantitatively, we employ the Wasserstein distances of …

[PDF] gatech.edu

Hamiltonian systems and the calculus of differential forms on the Wasserstein space

HK Kim - 2009 - smartech.gatech.edu

This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian

systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in

the work of Ambrosio and Gangbo. We regularize H via Moreau-Yosida approximation to get …

2009

Wasserstein distances for vortices approximation of Euler-type equations

M Hauray - Mathematical Models and Methods in Applied …, 2009 - World Scientific

We establish the convergence of a vortex system towards equations similar to the 2D Euler

equation in vorticity formulation. The only but important difference is that we use singular

kernel of the type x⊥/| x| α+ 1, with α< 1, instead of the Biot–Savard kernel x⊥/| x| 2. This …

2009

Stein's method and Poisson process approximation for a class of Wasserstein metrics

D Schuhmacher - Bernoulli, 2009 - projecteuclid.org

Based on Stein's method, we derive upper bounds for Poisson process approximation in the

L 1-Wasserstein metric d 2 (p), which is based on a slightly adapted L p-Wasserstein metric

between point measures. For the case p= 1, this construction yields the metric d 2 introduced …

[CITATION] Stein's method and Poisson process approximation for a class of Wasserstein metrics. Bernoulli 15 550–568

D Schuhmacher - … (MathSciNet): MR2543874 Digital Object Identifier: doi, 2009

[CITATION] Approximation for the Wasserstein distance

N Belili, H Heinich - COMPTES RENDUS …,

2009

Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance

A Xia, F Zhang - Journal of Theoretical Probability, 2009 - Springer

The polynomial birth–death distribution (abbreviated, PBD) on ℐ={0, 1, 2,…} or ℐ={0, 1, 2,…,

m} for some finite m introduced in Brown and Xia (Ann. Probab. 29: 1373–1403, 2001) is the

equilibrium distribution of the birth–death process with birth rates {α i} and death rates {β i} …

2009

Approximation of homogeneous measures in the 2-Wasserstein metric

S Dostoglou, JD Kahl - Mathematical Physics Electronic Journal, 2009 - dialnet.unirioja.es

It is shown that, on certain weighted spaces of vector fields on R3, any homogeneous

measure of finite energy density and dissipation can be approximated in the second

Wasserstein distance by homogeneous measures supported by finite trigonometric …

[CITATION] Approximation of homogeneous measures in the 2-Wasserstein metric Math

S Dostoglou, JD Kahl - Phys. Electron. J, 2009

2002 - ELSEVIER FRANCE-EDITIONS …

Wasserstein distance for the fusion of multisensor multitarget particle filter clouds

D Danu, T Kirubarajan, T Lang - … on Information Fusion, 2009 - ieeexplore.ieee.org

In a multisensor multitarget tracking application, the evaluation of the cost of assigning

particle filter clouds of different sensors as being estimates of the same target is an essential

part in the particle cloud association. This paper treats the problem of evaluating the cost of …

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of

the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to

porous medium equations. We give an explicit expression of the solution to the porous …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

ISSN. 巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索.

CiNii窓口業務の再開について. Wasserstein geometry of non-linear Fokker-Planck type equations …

<——2009—————2009——— 200—

Euler–Poisson systems as action-minimizing paths in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Archive for rational mechanics and …, 2009 - Springer

This paper uses a variational approach to establish existence of solutions (σ t, vt) for the 1-d

Euler–Poisson system by minimizing an action. We assume that the initial and terminal

points σ 0, σ T are prescribed in P _2 (R), the set of Borel probability measures on the real …

2009

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

2009

[PDF] WASSERSTEIN DISTANCES IN THE ANALYSIS OF TIME SERIES AND DYNAMICAL SYSTEMS TECHNICAL REPORT MI-2009-12

M MUSKULUS, S VERDUYN-LUNEL - 2009 - math.leidenuniv.nl

A new approach based on Wasserstein distances, which are numerical costs of an optimal

transportation problem, allows to analyze nonlinear phenomena in a robust manner. The

long-term behavior is reconstructed from time series, resulting in a probability distribution …

2009 [PDF] osu.edu

Spectral Gromov-Wasserstein distances for shape matching

F Mémoli - 2009 IEEE 12th International Conference on …, 2009 - ieeexplore.ieee.org

We introduce a spectral notion of distance between shapes and study its theoretical

properties. We show that our distance satisfies the properties of a metric on the class of

isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if …

2009

Local histogram based segmentation using the Wasserstein distance

K Ni, X Bresson, T Chan, S Esedoglu - International journal of computer …, 2009 - Springer

We propose and analyze a nonparametric region-based active contour model for

segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel

intensity is independently identically distributed. Our proposed energy functional consists of …

2009

2009 [PDF] kyoto-u.ac.jp

Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

2009 [PDF] academia.edu

The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer

We prove the global existence of non-negative variational solutions to the “drift diffusion”

evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under

variational boundary condition. Despite the lack of a maximum principle for fourth order …

2009 [PDF] tue.nl

[PDF] Numerical algorithm for computation of the 2-Wasserstein distance, and applications to the foundations of diffusion

S Srivastava, MA Peletier - 2009 - pure.tue.nl

This work is intended to solve the optimal mass transfer problem formulated in the fluid

mechanics framework, and to study some of the applications. Starting with a brief historical

overview of the optimal mass transfer problem (classical Monge problem and its relaxed …

2009 [PDF] kyoto-u.ac.jp

Gradient flows on Wasserstein spaces over compact Alexandrov spaces

S Ohta - American journal of mathematics, 2009 - muse.jhu.edu

We establish the existence of Euclidean tangent cones on Wasserstein spaces over

compact Alexandrov spaces of curvature bounded below. By using this Riemannian

structure, we formulate and construct gradient flows of functions on such spaces. If the …

2009 [PDF] wvu.edu

Euler–Poisson systems as action-minimizing paths in the Wasserstein space

W Gangbo, T Nguyen, A Tudorascu - Archive for rational mechanics and …, 2009 - Springer

This paper uses a variational approach to establish existence of solutions (σ t , v t ) for the 1-d

Euler–Poisson system by minimizing an action. We assume that the initial and terminal points

σ 0 , σ T are prescribed in $${\mathcal {P}_2(\mathbb {R})}$$ , the set of Borel probability …

<——2009———2009——— 210—

Duality on gradient estimates and Wasserstein controls

Newborn screening for Krabbe disease: the New York State model.

2009 ARXIV: PROBABILITY

203 citations*

2009 PEDIATRIC NEUROLOGY

Patricia K. Duffner ¹,Michele Caggana ²,Joseph J. Orsini ²,David A. Wenger ³,Marc C. Patterson ⁴ see all 28 authors

¹ State University of New York System ,² New York State Department of Health ,³ Department of Neurology, Jefferson Medical College, Philadelphia, Pennsylvania,⁴ Mayo Clinic

Krabbe disease

Newborn screening

View More (37+)

Krabbe disease is a rare inherited neurologic disorder affecting the central and peripheral nervous systems. The disease has four phenotypes: early infantile, later onset, adolescent, and adult. The only known treatment is hematopoietic stem cell transplantation, which is, in the early infantile for... View Full Abstract

2009

Entropic measure and Wasserstein diffusion

87 citations* for all

82 citations*

2009 ANNALS OF PROBABILITY

Max-K. von Renesse ,Karl-Theodor Sturm

[PDF] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational Problems and Related Topics)

Probability theory

View More (8+)

We construct a new random probability measure on the circle and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interv... View Full Abstract

2009

A Takatsu - 数理解析研究所講究録, 2009 - repository.kulib.kyoto-u.ac.jp

This note is a survey of the author's preprint [17], which concerns the geometric structure of

the $(l $-Gaussian measures in terms of $ L^{2}-$ Wasserstein geometry and solutions to …

[CITATION] Wasserstein geometry of non-linear Fokker-Planck type equations (Variational problems and related topics)

高津飛鳥 - 数理解析研究所講究録, 2009 - ci.nii.ac.jp

… 検索. すべて. 本文あり. 詳細検索. すべて. 本文あり. 閉じる. タイトル. 著者名. 著者ID. 著者所属. 刊行物名.

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2009

Newborn screening for Krabbe disease: the New York State model

…, JM Provenzale, SJ Rothman, MP Wasserstein - Pediatric …, 2009 - Elsevier

… A rapid and accurate technique for assessing galactocerebrosidase activity and performing

DNA mutation analysis had been developed. Interpreting these results was limited, however, …

2009 cComputer Program,

Stein’s method and Poisson process approximation for a class of Wasserstein metricsAuthor:Schuhmacher, Dominic (Creator)
Summary:Based on Stein’s method, we derive upper bounds for Poisson process approximation in the L1-Wasserstein metric d2(p), which is based on a slightly adapted Lp-Wasserstein metric between point measures. For the case p=1, this construction yields the metric d2 introduced in [Barbour and Brown Stochastic Process. Appl. 43 (1992) 9–31], for which Poisson process approximation is well studied in the literature. We demonstrate the usefulness of the extension to general p by showing that d2(p)-bounds control differences between expectations of certain pth order average statistics of point processes. To illustrate the bounds obtained for Poisson process approximation, we consider the structure of 2-runs and the hard core model as concrete examplesShow more
Computer Program, 2009-05
English
Publisher:Bernoulli Society for Mathematical Statistics and Probability, 2009-05
Access Free

2009

2009 Computer Program,
Entropic measure and Wasserstein diffusionAuthors:von Renesse, Max-K. (Creator), Sturm, Karl-Theodor (Creator)
Summary:We construct a new random probability measure on the circle and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval, respectively. The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or the unit interval) by Dirichlet form methods. The first one is closely related to Malliavin’s Brownian motion on the homeomorphism group. The second one is a probability valued stochastic perturbation of the heat flow, whose intrinsic metric is the quadratic Wasserstein distance. It may be regarded as the canonical diffusion process on the Wasserstein spaceShow more
Computer Program, 2009-05
English
Publisher:The Institute of Mathematical Statistics, 2009-05
Access Free

2009 grant

Calculus of Variations and Hamilton-Jacobi Equations in the Wasserstein Space

Award Number:0901449; Principal Investigator:Truyen Nguyen; Co-Principal Investigator:; Organization:University of Akron;NSF Organization:DMS Start Date:09/01/2009; Award Amount:$70,907.00; Relevance:86.11;

2009 grant

Calculus of Variations and Evolutive Systems on the Wasserstein Space

Award Number:0901070; Principal Investigator:Andrzej Swiech; Co-Principal Investigator:; Organization:Georgia Tech Research Corporation;NSF Organization:DMS Start Date:08/15/2009; Award Amount:$204,030.00; Relevance:77.74;

Peer-reviewed
Stein's method and Poisson process approximation for a class of Wasserstein metricsAuthor:Dominic Schuhmacher
Summary:Based on Stein???s method, we derive upper bounds for Poisson process approximation in the L1-Wasserstein metric d2(p), which is based on a slightly adapted Lp-Wasserstein metric between point measures. For the case p=1, this construction yields the metric d2 introduced in [Barbour and Brown Stochastic Process. Appl. 43 (1992) 9???31], for which Poisson process approximation is well studied in the literature. We demonstrate the usefulness of the extension to general p by showing that d2(p)-bounds control differences between expectations of certain pth order average statistics of point processes. To illustrate the bounds obtained for Poisson process approximation, we consider the structure of 2-runs and the hard core model as concrete examplesShow more
Downloadable Article
Publication:Bernoulli, 15, 2009-05, 550
Related articles All 14 versions

Entropic measure and Wasserstein diffusionAuthors:Max-K. von Renesse, Karl-Theodor Sturm
Summary:We construct a new random probability measure on the circle and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval, respectively. The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or the unit interval) by Dirichlet form methods. The first one is closely related to Malliavin’s Brownian motion on the homeomorphism group. The second one is a probability valued stochastic perturbation of the heat flow, whose intrinsic metric is the quadratic Wasserstein distance. It may be regarded as the canonical diffusion process on the Wasserstein spaceShow more
Downloadable Article
Publication:https://projecteuclid.org/euclid.aop/1245434030Ann. Probab., 37, 2009-05, 1114
<—–2009———2009———222—

Peer-reviewed
Local Histogram Based Segmentation Using the Wasserstein DistanceAuthors:Kangyu Ni, Xavier Bresson, Tony Chan, Selim Esedoglu
Summary:We propose and analyze a nonparametric region-based active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel intensity is independently identically distributed. Our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region-based image term that uses histograms of pixel intensity to distinguish different regions. More specifically, the region data encourages segmentation so that local histograms within each region are approximately homogeneous. An advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem. We use Wasserstein distance with exponent 1 to determine the dissimilarity between two histograms. The Wasserstein distance is a metric and is able to faithfully measure the distance between two histograms, compared to many pointwise distances. Moreover, it is insensitive to oscillations, and therefore our model is robust to noise. A fast global minimization method based on (Chan et al. in SIAM J. Appl. Math. 66(5):1632-1648, 2006; Bresson et al. in J. Math. Imaging Vis. 28(2):151-167, 2007) is employed to solve the proposed model. The advantages of using this method are two-fold. First, the computational time is less than that of the method by gradient descent of the associated Euler-Lagrange equation (Chan et al. in Proc. of SSVM, pp. 697-708, 2007). Second, it is able to find a global minimizer. Finally, we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changesShow more
Article, 2009
Publication:International Journal of Computer Vision, 84, 200908, 97
Publisher:2009

Local Histogram Based Segmentation Using the Wasserstein Distance

By: Ni, Kangyu; Bresson, Xavier; Chan, Tony; et al.

INTERNATIONAL JOURNAL OF COMPUTER VISION Volume: ‏ 84 Issue: ‏ 1 Pages: ‏ 97-111 Published: ‏ AUG 2009

Differential Forms on Wasserstein Space and Infinite-dimensionall Hamiltonian Systems Hamilopnian Systems

Peer-reviewed
The [unknown]-Wasserstein Distance: Local Solutions and Existence of Optimal Transport MapsAuthors:T. Champion, L. De Pascale, P. Juutinen
Article, 2009
Publication:SIAM JOURNAL ON MATHEMATICAL

<—–2009———2009———222— end 2009

start 2010 Wasserstein

Wilfrid Gangbo, ‎Hwa Kil Kim, ‎Tommaso Pacini - 2010 - ‎Preview - ‎More editions book

MR2731158 (2011h:53045) Kloeckner, Benoît A geometric study of Wasserstein spaces: Euclidean spaces. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010), no. 2, 297–323. (Reviewer: Nicolas Juillet), 53C23 (28A33 49Q05)

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

2010 see 2009

[pdf] Gradient flows in Wasserstein spaces and applications to crowd movement

Gradient ows in Wasserstein spaces and applications to crowd movement S eminaire X-EDP, October 19th, 2010 Filippo Santambrogio November 17, 2010

Gradient ows in Wasserstein spaces and applications to ...

cvgmt.sns.it/media/doc/paper/511/X-EDP.pdf · PDF file 2010

ideas from the theory of Gradient Flows in the space of ... we will give the step-by-step variational interpretation of gradient ...

2 Microscopic and Macroscopic ...

Santambrogio, Filippo. "Gradient flows in Wasserstein spaces and applications to crowd movement." Séminaire Équations aux dérivées partielles 2009-2010 (2010-2011): 1-16. <http://eudml.org/doc/116450>.

Gradient flows in Wasserstein spaces and applications to crowd movement

[PDF] from sns.itF Santambrogio - 2010 - cvgmt.sns.it

Abstract Starting from a motivation in the modeling of crowd movement, the paper presents the

topics of gradient flows, first in Rn, then in metric spaces, and finally in the space of prob- ability

measures endowed with the Wasserstein distance (induced by the quadratic trans- port ...

aarXiv:1104.4223 [pdf, ps, other]

Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions

Karl-Theodor Sturm

Subjects: Functional Analysis (math.FA); Probability (math.PR)

arXiv:1102.1842 [pdf, ps, other]

Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

Tomasz Komorowski, Anna Walczuk

Subjects: Probability (math.PR)

2010

MR2648273 Takatsu, Asuka On Wasserstein geometry of Gaussian measures. Probabilistic approach to geometry, 463–472, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, 2010. (Reviewer: Jonathan Henry Jordan), 60D05 (28A33). Zbl 1206.60016

Takatsu : On Wasserstein geometry of Gaussian measures

by A Takatsu - ‎2010 - ‎Cited by 69 - ‎Related articles

Pure Math. Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. ... . Asuka Takatsu ...

Advanced Studies in Pure Mathematics: Volume 57

Probabilistic Approach To Geometry

Edited by: Motoko Kotani (Tohoku University), Masanori Hino (Kyoto University), Takashi Kumagai (Kyoto University)

MR2752678 Granieri, Luca Metric currents and geometry of Wasserstein spaces. Rend. Semin. Mat. Univ. Padova 124 (2010), 91–125. ISBN: 978-88-7784-325-8, 37J50 (49Q20)

[PDF] Metric Currents and Geometry of Wasserstein Spaces

L Granieri - REND. SEM. MAT. UNIV. PADOVA, 2010 - archive.numdam.org

ABSTRACT-We investigate some geometric aspects of Wasserstein spaces through the

continuity equation as worked out in mass transportation theory. By defining a suitable

homology on the flat torus Tn, we prove that the space p (Tn) has nontrivial homology in a ...

Ordinary Least Squares for histogram data based on Wasserstein distance.

Irpino A., Verde R. (2010).

In: LECHEVALLIER YVES, SAPORTA GILBERT. Proceedings of COMPSTAT'2010. (pp. 581-589). ISBN: 978-3-7908-2603-6. HEIDELBERG: Physica Verlag (GERMANY).

Histogram data is a kind of symbolic representation which allows to describe an individual by an empirical frequency distribution. In this paper we introduce a linear regression model for histogram variables. We present a new Ordinary Least Squares approach for a linear model estimation, using the Wasserstein metric between histograms. In this paper we suppose that the regression coefficient are scalar values. After having illustrated the concurrent approaches, we corroborate the proposed estimation method by an application on a real dataset.

Ordinary least squares for histogram data based on wasserstein distance

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

in Proceedings of COMPSTAT'2010, 2010

MR2655156 Irpino, Antonio; Verde, Rosanna Clustering linear models using Wasserstein distance. Data analysis and classification, 41–48, Stud. Classification Data Anal. Knowledge Organ., Springer, Berlin, 2010, 62H30 (62J05)

Clustering Linear Models Using Wasserstein Distance,

IRPINO A., VERDE R. (2010)

In: Data Analysis and Classification,Proceedings of the 6th Conference of the Classification and Data Analysis Group of the Società Italiana di Statistica,

Series: Studies in Classification, Data Analysis, and Knowledge Organization , Palumbo, Francesco; Lauro, Carlo Natale; Greenacre, Michael J. (Eds.), 2010, ISBN: 978-3-642-03738-2, pages 41-48.

This paper deals with the clustering of complex data. The input elements to be clustered are linear models estimated on samples arising from several sub-populations (typologies of individuals). We review the main approaches to the computation of metrics between linear models. We propose to use a Wasserstein based metric for the first time in this field. We show the properties of the proposed metric and an application to real data using a dynamic clustering algorithm.

Approximating stochastic biochemical processes with Wasserstein pseudometrics

<——2010——2010—————— -10—

Author(s): Thorsley, D; Klavins, E

Source: IET SYSTEMS BIOLOGY Volume: 4 Issue: 3 Pages: 193-211 Published: 2010

Abstract: Modelling stochastic processes inside the cell is difficult due to the size and complexity

of the processes being investigated. As a result, new approaches are needed to address the

problems of model reduction, parameter estimation, model comparison and model ...

Approximating stochastic biochemical processes with wasserstein pseudometrics

D Thorsley, E Klavins - IET Systems Biology, 2010 - ieeexplore.ieee.org

Modelling stochastic processes inside the cell is difficult due to the size and complexity of

the processes being investigated. As a result, new approaches are needed to address the

problems of model reduction, parameter estimation, model comparison and model …

Texture segmentation based on the use of the structure tensor and the wasserstein distance

X XIE… - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of image

segmentation.The proposed new model which is based on the use of the structure tensor and

the Wasserstein distance belongs to this category.First,the classical tensor structure ...

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

Wasserstein distance based local energy model of segmentation

[PDF] Wasserstein Barycenter and its Application to Texture Mixing

J Delon, G Peyré, J Rabin… - 2010 - basepub.dauphine.fr

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Wasserstein space. Replacing the Wasserstein original metric by a sliced

approximation over 1D distributions allows us to use a fast stochastic gradient descent ...

All 14 versions

XH Qian, SX Guo… - Dianzi Xuebao(Acta Electronica Sinica), 2010 - ejournal.org.cn

Abstract A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between two

regions, we proposed to compare their respective histograms using the Wasserstein ...

A maximum principle for pointwise energies of quadratic Wasserstein minimal networks

[PDF] from arxiv.orgJ Dahl - Arxiv preprint arXiv:1011.0236, 2010 - arxiv.org

Given k points p1,...,pk in a geodesic space1 Y , one can ask for a minimal net- work spanning

p1,...,pk. For a complete, connected Riemannian manifold M, the space of Borel probability measure

P(M) may be metrized, allowing infinite dis- tances, by the Wasserstein distance W2 ...

2010

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

[PDF] from psu.eduN Gigli… - 2010 - Citeseer

The aim of this paper is twofold. On one side we give a simpler proof of a result found by the

second author ([4]). This amounts in proving that the minimizing movements scheme for the Energy

E(θ) = −∫ xθdx on a two-phase Wasserstein space produces the entropy solution of the ...

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

NGF Otto - 2010

Wasserstein space over Hadamard space

J Bertrand - Workshop on Geometric Probability and …, 2010 - atlas-conferences.com

In the talk, I will consider the quadratic Wasserstein space over a metric space of non-positive

curvature (globally). Despite the fact that the Wasserstein space does not inherit the curvature

property, I will show that some asymptotical properties extend to the Wasserstein space.

2010 see 2012

A geometric study of wasserstein spaces: Hadamard spaces

[PDF] from arxiv.orgJ Bertrand… - Arxiv preprint arXiv:1010.0590, 2010 - arxiv.org

Optimal transport enables one to construct a metric on the set

of (suciently small at in nity) probability measures on any (not too wild)

metric space

Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

[PDF] from casac-art.netC Selinger - casac-art.net

Definition 1.1. Let (M, 〈., .〉x) denote a complete simply connected Riemannian mani- fold without

boundary and T1 denote R mod Z equipped with the flat metric. • P(M) := P = {µ Borel probability

measure on M and ∫ dM (x, y)2µ(dx) < ∞} • Pac(M) := Pac = {µ ∈ P : µ ≪ volM } • P∞(M) ...

Zbl pre06056477

Duality on gradient estimates and Wasserstein controls

K Kuwada - 2009 - adsabs.harvard.edu

[PDF] from arxiv.orgK Kuwada - Journal of Functional Analysis, 2010 - Elsevier

We establish a duality between Lp-Wasserstein control and Lq-gradient estimate in a

general framework. Our result extends a known result for a heat flow on a Riemannian

manifold. Especially, we can derive a Wasserstein control of a heat flow directly from the ...

All 11 versions [PDF] arxiv.org

<——2010———2010————— -20—-

First variation formula in Wasserstein spaces over compact Alexandrov spaces

[PDF] from psu.eduN Gigli… - Preprint, 2010 - Citeseer

This paper should be considered as an addendum to [Oh] of the second author. In [Oh], it is studied

the quadratic Wasserstein space (P(X),W2) built over a compact Alexandrov space X with curvature

bounded below, and proven the existence of Euclidean tangent cones (see also [Gi]). ...

N Gigli, SI Ohta - Math. Bull, 2010

First variation formula in Wasserstein spaces over compact ...

by N Gigli - ‎2010 - ‎Cited by 16 - ‎Related articles

@MISC{Gigli10firstvariation, author = {Nicola Gigli and Shin-ichi Ohta}, title = {First variation formula in Wasserstein spaces over compact Alexandrov spaces},

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

[PDF] from arxiv.orgS Adams, N Dirr, M Peletier… - … online from http://arxiv. org/abs/ …, 2010 - arxiv.org

Abstract. We study the connection between a system of many independent Brownian particles

on one hand and the deterministic diffusion equation on the other. For a fixed time step h >

0, a large-deviations rate functional Jh characterizes the behaviour of the particle system ...

arXiv:1004.4076

Cited by 83 - ‎Related articles

基于结构张量和 Wasserstein 距离的纹理图像分割

谢晓振… - 中国图象图形学报 A, 2010 - 万方数据资源系统

Yezzi Jr,Tsai A,Willsky AA statistical approach to snakes for bimodal and trimodal

imagery[C]//Proceedings of International Conference on Computer Vision.Washington,DC,USA

:IEEE,1999:898-903. ... Rousson M,Brox T,Deriche R.Active unsupervised texture ...

Chan T;Esedoglu S;Ni K Histogram based segmentation using wasserstein distances [外文会议] 2007

基于结构张量和 Wasserstein 距离的纹理图像分割

谢晓振，吴纪桃 - 中国图象图形学报, 2010 - cqvip.com

基于区域的非参数活动轮廓模型被广泛地应用于图像分割领域. 在结构张量和图像灰度直方图

基础上建立的新模型就属于这个范畴, 它被用于灰度和彩色纹理图像的分割. 首先,

对经典的结构张量进行扩展, 使其能表达原始纹理图像的梯度信息和色彩信息 …

基于 Wasserstein 距离的局部能量分割模型

[PDF] from 210.29.99.10钱晓华，郭树旭… - 电子学报, 2010 - 210.29.99.10

Wasserstein distance based local energy model of segmentation

by Qian, Gio, and Li

[PDF] numdam.org Full View

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'Institut Henri Poincaré, Probabilités et …, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

2010

Approximating stochastic biochemical processes with Wasserstein pseudometrics

D Thorsley, E Klavins - IET Systems Biology, 2010 - ieeexplore.ieee.org

Modelling stochastic processes inside the cell is difficult due to the size and complexity of the processes being investigated. As a result, new approaches are needed to address the problems of model reduction, parameter estimation, model comparison and model …

2010 [PDF] uni.lu

Geometry and Stochastic Calculus on Wasserstein spaces

C Selinger - 2010 - orbilu.uni.lu

… measures with finite p-th moment- is called p-Wasserstein space. If not stated otherwise in this work we assume that M is a complete, simply connected Riemannian manifold without boundary. Additionnally we will restrict ourselves to the 2-Wasserstein distance and henceforth …

Wasserstein distance based local energy model of segmentation

2010

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

… A nonparametric Wasserstein distance-based active contour model that … Wasserstein

distance;Due to a Gaussian kernel introduced,intensity information in local regions is extracted

and embedded in model to guide the motion to overcome the difficulties in image segmentation …

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

2010

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

… of image segmentation.The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs … features of the texture can be extracted.Then,we

use the Wasserstein distance between each pixels' local distribution functions of the image …

A maximum principle for pointwise energies of quadratic Wasserstein minimal networks

2010 [PDF] arxiv.org

J Dahl - arXiv preprint arXiv:1011.0236, 2010 - arxiv.org

… We show that suitable convex energy functionals on a quadratic Wasserstein space

satisfy a maximum principle on minimal networks. We explore consequences of this

maximum principle for the structure of minimal networks. … We begin by defining …

<——2010—————2010———————— -30—

MR2574738 Andres, Shizan; Shao, Jinghai; Sturm, Karl-Theodor Wasserstein space over the Wiener space. Probab. Theory Related Fields 146 (2010), no. 3-4, 535–565. (Reviewer: Hélène Airault), 60J45 (58B20 60H07)

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

Particle approximation of the Wasserstein diffusion

S Andres, MK von Renesse - Journal of Functional Analysis, 2010 - Elsevier

We construct a system of interacting two-sided Bessel processes on the unit interval and

show that the associated empirical measure process converges to the Wasserstein diffusion

(von Renesse and Sturm (2009)[25]), assuming that Markov uniqueness holds for the …

MR2606878 (2011b:60224) Andres, Sebastian; von Renesse, Max-K. Particle approximation of the Wasserstein diffusion. J. Funct. Anal. 258 (2010), no. 11, 3879–3905. (Reviewer: Nikita Y. Ratanov), 60H10 (60J25 60J68 60K35)

Particle approximation of the Wasserstein diffusion - ScienceDirect

by S Andres - ‎2010 - ‎Cited by 29 - ‎Related articles

Jun 1, 2010 - We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process ...

Times Cited: 15

2010 eBook
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systemsAuthors:Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
eBook, 2010
English
Publisher:American Mathematical Society, Providence, R.I., 2010

Also available asPrint Book
View AllFormats & Editions

[BOOK] Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

W Gangbo, HK Kim, T Pacini - 2010 - books.google.com

Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $

endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely

continuous curves in $\mathcal {M} $ was introduced by Ambrosio, Gigli, and Savare. In this …

MR2593592 (2010k:60106) Wang, Ran; Wang, Xinyi; Wu, Liming Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition. Statist. Probab. Lett. 80 (2010), no. 5-6, 505–512, 60F10

[PDF] ustc.edu.cn

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & Probability Letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savar\'e and …

2010

MR2730652 Madras, Neal; Sezer, Deniz Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances. Bernoulli 16 (2010), no. 3, 882–908, 60J22

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to

equilibrium of a Markov chain on a general state space, with respect to both total variation

and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

Quantitative bounds for Markov chain convergence: Wasserstein

MR2672546 Lisini, Stefano; Marigonda, Antonio On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals. Manuscripta Math. 133 (2010), no. 1-2, 197–224, 49Q20 (49J27 49J40)

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

arXiv:0909.2512 [pdf, ps, other]

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

Stefano Lisini, Antonio Marigonda

Comments: 22 pages

Subjects: Functional Analysis (math.FA); Analysis of PDEs (math.AP)

MR2580956 (2011a:35237) Cavalli, Fausto; Naldi, Giovanni A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation. Kinet. Relat. Models 3 (2010), no. 1, 123–142, 35K55 (35B25 65M06)

[PDF] A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinet. Relat. Models, 2010 - researchgate.net

In this work we introduce a numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based of an alternative formulation of the problem using the pseudo …

[PDF] sissa.it

Estimates on path functionals over Wasserstein spaces

S Bianchini, A Brancolini - SIAM Journal on Mathematical Analysis, 2010 - SIAM

In this paper we consider the class a functionals (introduced in Brancolini, Buttazzo, and

Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 415–434 G_r,p defined on Lipschitz

curves γ valued in the p-Wasserstein space. The problem considered is the following: given …

Entropic Burgers' equation via a minimizing movement ...

2010 see 2013

http://citeseerx.ist.psu.edu › viewdoc › download

by N Gigli · 2010 · Cited by 18 — Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. Nicola Gigli. ∗. , Felix Otto.

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

NGF Otto - 201

<——2010—————2010——————— -40—

[PDF] A geometric study of Wasserstein spaces: embedding powers

B Kloeckner - 2010 - hal.archives-ouvertes.fr

The Wasserstein spaces# p (X) of a metric space X are sets of sufficiently concentrated

measures, endowed with a metric defined using optimal transportation. When X is compact,#

p (X) is a metrization of the set of probability measures on X endowed with the weak …

Geometry and Stochastic Calculus on Wasserstein spaces

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September

2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth

curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

[PDF] nii.ac.jp

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題

として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので,

最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

Well-posedness of a parabolic moving-boundary problem in the ...

MR2652014 Portegies, Jacobus W.; Peletier, Mark A. Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows. Interfaces Free Bound. 12 (2010), no. 2, 121–150, 35Rxx (80Axx 82Dxx)

by JW PORTEGIES - ‎2010 - ‎Cited by 18 - ‎Related articles

Interfaces and Free Boundaries 12 (2010), 121–150 ... JACOBUS W. PORTEGIES ... E-mail: m.a.peletier@tue.nl ... complete well-posedness setting for this parabolic moving-boundary problem. ... equations have been cast in the form of a Wasserstein gradient flow. ... by the requirement that no water traverses the boundary.

MR2644919 Bianchini, S.; Brancolini, A. Estimates on path functionals over Wasserstein spaces. SIAM J. Math. Anal. 42 (2010), no. 3, 1179–1217, 49Q20 (28A78 49K27 93B03)

Estimates on Path Functionals over Wasserstein Spaces - SIAM

by S Bianchini - ‎2010 - ‎Cited by 4 - ‎Related articles

tapping button above. Home Screen Newspaper. No matches found. No publications added. Journals. Books/Proceedings. Book Series. Working Papers.

2010

MR2641767 Erbar, Matthias The heat equation on manifolds as a gradient flow in the Wasserstein space. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 1, 1–23, 35A15 (58J35 58J65 60J60)

The heat equation on manifolds as a gradient flow in the Wasserstein ...

by M Erbar - ‎2010 - ‎Cited by 59 - ‎Related articles

Association des Publications de l'Institut Henri Poincaré, 2010 ... E-mail: matthias.erbar@web.de ... Keywords: Gradient flow; Wasserstein metric; Relative entropy; Heat ... We denote by P2(M) the Wasserstein space of probability measures on M ... to arbitrary initial measures and thus conclude the proof of Theorem 1. 2.

2010 zzz 25

[CITATION] Trotter's formula for Fokker-Planck equations in the Wasserstein space

P Clément, J Maas - preparation

A Trotter product formula for gradient flows in metric spaces

arxiv.org › mat

May 6, 2010 — This result is applied to establish convergence in the L^2-Wasserstein metric of the splitting method for some Fokker-Planck equations and ...

by P Clément · ‎2010 · ‎Cited by 8 · ‎Related articles

[CITATION] Trotter's formula for Fokker-Planck equations in the Wasserstein space

P Clément, J Maas - preparation

Duality on gradient estimates and Wasserstein controls

MR2606871 Kuwada, Kazumasa Duality on gradient estimates and Wasserstein controls. J. Funct. Anal. 258 (2010), no. 11, 3758–3774. (Reviewer: Po-Lam Yung), 35H20 (35R01 35R03 47D03 53C44 60J60)

by K Kuwada - ‎2009 - ‎Cited by 87 - ‎Related articles

Разложения типа Денниса–Васерштейна

НА Вавилов, СС Синчук - Записки научных семинаров ПОМИ, 2010 - mathnet.ru

В работе доказывается обобщение разложения Денниса–Васерштейна для произвольной пары максимальных параболических подгрупп $ P_r $ и $ P_s $ в полной линейной группе $\mathrm {GL}(n, R) $, в предположении $ rs\geq\mathrm {sr}(R) …

[Russian Dennis – Westerstein Type Expansions]

Geometry and Stochastic Calculus on Wasserstein spaces

PDF U du Luxembourg 2010 Ph.D.

by C Selinger - ‎2010 - ‎Related articles

The main object of interest in the present thesis is P(M) – the space of proba- bility measures on a Riemannian manifold (M,g) endowed with the Wasserstein.

Wasserstein Barycenter and its Application to Texture Mixing

<——2010—————2010———----50—

www-sop.inria.fr › Wasserstein-textures-peyret-ICCV10 PDF

Apr 23, 2010 - Wasserstein Barycenter and its Application to Texture. Mixing. Rabin Julien, Gabriel Peyré, Julie Delon, Bernot Marc. To cite this version:.

by R Julien - ‎Cited by 298 - ‎Related articles

ТРУДЫ МФТИ. 2016. Том 8, No 3 Информатика, вычисл. техника и управление5УДК 519.688А. В. Гасников1,2, П. Е. Двуреченский2,4, В. Г. Спокойный1,2,3,4, П. И. Стецюк5,А. Л. Суворикова1,2,61Московский физико-технический институт (государственный университет)2Институт проблем передачи информации РАН3Национальный исследовательский университет Высшая школа экономики4Weierstrass Institute for Applied Analysis and Stochastics, Berlin5Институт кибернетики им. В. М. Глушкова НАН Украины6The International Research Training Group 1792, Berlin

Суперпозиция метода балансировки и универсального градиентного метода для поиска энтропийно-регуляризованного барицентра Вассерштейна и равновесий в многостадийных моделях транспортных потоков
Russian Superposition of balance method and universal gradient method for search of entropy-regulated Vaserstein bariocenter and equilibria in multistage models of traffic flows]

2010

Particle approximation of the Wasserstein diffusion

S Andres, MK von Renesse - Journal of Functional Analysis, 2010 - Elsevier

We construct a system of interacting two-sided Bessel processes on the unit interval and

show that the associated empirical measure process converges to the Wasserstein diffusion

(von Renesse and Sturm (2009)[25]), assuming that Markov uniqueness holds for the …

Duality on gradient estimates and Wasserstein controls

By: Kuwada, Kazumasa

JOURNAL OF FUNCTIONAL ANALYSIS Volume: ‏ 258 Issue: ‏ 11 Pages: ‏ 3758-3774 Published: ‏ JUN 1 2010

Times Cited: 46

Wasserstein space over the Wiener space | SpringerLink

By: Fang, Shizan; Shao, Jinghai; Sturm, Karl-Theodor

PROBABILITY THEORY AND RELATED FIELDS Volume: ‏ 146 Issue: ‏ 3-4 Pages: ‏ 535-565 Published: ‏ MAR 2010

Times Cited: 19

link.springer.com/10.1007/s00440-009-0199-5

Wasserstein space over the Wiener space ... invaraint flows on the Wiener space. Bull. Sci. Math. (to appear) ... and Monge–Ampère equation on Wiener space. Probab ...

Author: Shizan Fang, Shizan Fang, Jinghai Shao, Jinghai Shao, Karl-Theodor Sturm

Cited by: 52

Publish Year: 2010

(PDF) Wasserstein space over the Wiener space

www.researchgate.net/publication/225547620...

The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy.

The heat equation on manifolds as a gradient flow in the Wasserstein space

By: Erbar, Matthias

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES Volume: ‏ 46 Issue: ‏ 1 Pages: ‏ 1-23 Published: ‏ FEB 2010

A geometric study of Wasserstein spaces: Euclidean spaces

Times Cited: 35

By: Kloeckner, Benoit

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE Volume: ‏ 9 Issue: ‏ 2 Pages: ‏ 297-323 Published: ‏ 2010

Times Cited: 12

Ordinary Least Squares for Histogram Data Based on Wasserstein Distance

By: Verde, Rosanna; Irpino, Antonio

Conference: 19th International Conference on Computational Statistics (COMPSTAT'2010) Location: ‏ Paris, FRANCE Date: ‏ AUG 22-27, 2010

Sponsor(s): ‏Conservatoire Natl Arts & Metiers; French Natl Inst Res Comp Sci & Control; Conseil Reg Ile France; Mairie Paris; Soc Francaise Stat; Assoc EGC; Soc Francophone Classificat; Electricite France; Inst Natl Rech Agronomique; Inst Natl Stat Etud Econ; IPSOS; Orange Labs; SAS Inst

COMPSTAT'2010: 19TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STATISTICS Pages: ‏ 581-588 Published: ‏ 2010

Times Cited: 7

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題

として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので,

最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

On Wasserstein geometry of Gaussian measures

By: Takatsu, Asuka

Conference: 1st Conference of the Seasonal-Institute-of-the-Mathematical-Society-of-Japan on Probabilistic Approach to Geometry Location: ‏ Kyoto Univ, Kyoto, JAPAN Date: ‏ JUL 28-AUG 08, 2008

PROBABILISTIC APPROACH TO GEOMETRY Book Series: ‏ Advanced Studies in Pure Mathematics Volume: ‏ 57 Pages: ‏ 463-472 Published: ‏ 2010

Times Cited: 3

[CITATION] On Wasserstein Geometry of Gaussian Measures

T Asuka - … ; Mathematical Society of Japan: Tokyo, Japan, 2010

Metric Currents and Geometry of Wasserstein Spaces

,<——2010———2010----- 60——

By: Granieri, Luca

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA Volume: ‏ 124 Pages: ‏ 91-125 Published: ‏ 2010

F] Wasserstein space over the Wiener space Shizan FANGa, b Jinghai SHAOb, c Karl-Theodor STURMc a: IMB, BP 47870, Université de Bourgogne, 21078 Dijon …

Times Cited: 1

(from Web of Scien

S FANG, J SHAO, KT STURM - fang.perso.math.cnrs.fr

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel-Ustünel. Carrying out the program of Ambrosio-Gigli-Savaré, we present a complete …

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to

equilibrium of a Markov chain on a general state space, with respect to both total variation

and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and

K KUWADA - Appl. Math, 2013 - core.ac.uk

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm-Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

2010

Duality on gradient estimates and Wasserstein controls

K Kuwada - Journal of Functional Analysis, 2010 - Elsevier

We establish a duality between L p-Wasserstein control and L q-gradient estimate in a

general framework. Our result extends a known result for a heat flow on a Riemannian

manifold. Especially, we can derive a Wasserstein control of a heat flow directly from the …

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

First variation formula in Wasserstein spaces over ... - cvgmt

2010

https://cvgmt.sns.it › paper

Feb 9, 2010 — Math. Bull. Year: 2010. Abstract: We extend results proven by the second author for nonnegatively curved Alexandrov spaces to general compact ...

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

Particle approximation of the Wasserstein diffusion

S Andres, MK von Renesse - Journal of Functional Analysis, 2010 - Elsevier

We construct a system of interacting two-sided Bessel processes on the unit interval and

show that the associated empirical measure process converges to the Wasserstein diffusion

(von Renesse and Sturm (2009)[25]), assuming that Markov uniqueness holds for the …

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

Cited by 45 Related articles All 15 versions
<——2010———2010----- 70 —

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

[BOOK] Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

W Gangbo, HK Kim, T Pacini - 2010 - books.google.com

Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $

endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely

continuous curves in $\mathcal {M} $ was introduced by Ambrosio, Gigli, and Savare. In this …

Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

Ordinary least squares for histogram data based on wasserstein distance

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savaré and …

Approximating stochastic biochemical processes with Wasserstein pseudometrics

D Thorsley, E Klavins - IET Systems Biology, 2010 - IET

Modelling stochastic processes inside the cell is difficult due to the size and complexity of

the processes being investigated. As a result, new approaches are needed to address the

problems of model reduction, parameter estimation, model comparison and model …

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

G Naldi, F Cavalli - 2010 - publicatt.unicatt.it

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

2010 [PDF] numdam.org

Gradient flows in Wasserstein spaces and applications to crowd movement

F Santambrogio - Séminaire Équations aux dérivées partielles …, 2010 - numdam.org

Starting from a motivation in the modeling of crowd movement, the paper presents the topics

of gradient flows, first in Rn, then in metric spaces, and finally in the space of probability

measures endowed with the Wasserstein distance (induced by the quadratic transport cost) …

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & Probability Letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation pri

nciple of L n from the weak convergence …

[PDF] sissa.it

Estimates on path functionals over Wasserstein spaces

S Bianchini, A Brancolini - SIAM journal on mathematical analysis, 2010 - SIAM

In this paper we consider the class a functionals (introduced in Brancolini, Buttazzo, and

Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 415–434 G_r,p defined on Lipschitz

curves γ valued in the p-Wasserstein space. The problem considered is the following: given …

Cited by 6 Related articles All 16 versions——2010———2010----- 80

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between

two regions, we proposed to compare their respective histograms using the Wasserstein …

[PDF] ejournal.org.cn

[PDF] 基于 Wasserstein 距离的局部能量分割模型

钱晓华， 郭树旭， 李雪妍 - 电子学报, 2010 - ejournal.org.cn

提出了一种基于Wasserstein 距离和图像局部区域直方图信息的非参数活动轮廓分割模型.

用该距离对图像中不同区域的直方图进行比较, 提高了相似性衡量的准确性;

引入高斯内核函数来获取图像局部区域直方图信息, 并将信息嵌入模型指导轮廓演化 …

[Chinese cal energy segmentation model based on Wasserstein distance]

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

[PDF] Metric currents and geometry of Wasserstein spaces

L Granieri - Rendiconti del Seminario Matematico della Università …, 2010 - numdam.org

We investigate some geometric aspects of Wasserstein spaces through the continuity

equation as worked out in mass transportation theory. By defining a suitable homology on

the flat torus Tn, we prove that the space p (Tn) has nontrivial homology in a metric sense …

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of

image segmentation. The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

A maximum principle for pointwise energies of quadratic Wasserstein minimal networks

J Dahl - arXiv preprint arXiv:1011.0236, 2010 - arxiv.org

Given k points p1,...,pk in a geodesic space1 Y , one can ask for a minimal net- work spanning

p1,...,pk. For a complete, connected Riemannian manifold M, the space of Borel probability measure

P(M) may be metrized, allowing infinite dis- tances, by the Wasserstein distance W2 associated …

Clustering linear models using Wasserstein distance

A Irpino, R Verde - Data Analysis and Classification, 2010 - Springer

This paper deals with the clustering of complex data. The input elements to be clustered are

linear models estimated on samples arising from several sub-populations (typologies of

individuals). We review the main approaches to the computation of metrics between linear …

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題

として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので,

最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

[PDF] A geometric study of Wasserstein spaces: embedding powers

B Kloeckner - 2010 - hal.archives-ouvertes.fr

The Wasserstein spaces# p (X) of a metric space X are sets of sufficiently concentrated

measures, endowed with a metric defined using optimal transportation. When X is compact,#

p (X) is a metrization of the set of probability measures on X endowed with the weak …

Geometry and Stochastic Calculus on Wasserstein spaces

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September

2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth

curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

[PDF] First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - 2010 - Citeseer

We extend results proven by the second author ([Oh]) for nonnegatively curved Alexandrov

spaces to general compact Alexandrov spaces X with curvature bounded below: the

gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P (X) …

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

Wasserstein space over the Wiener space

<——2010———2010----90—

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

… Page 7. Wasserstein space over the Wiener space 541 … An absolutely continuous curve {c(t); t ∈

[0, 1]} on a Riemannian manifold M admits tangent vectors c (t) ∈ Tc(t)M for almost everywhere

t ∈]0, 1[. In order to understand the tangent spaces of the Wasserstein space (P∗(X …

[CITATION] Wasserstein spaces over Wiener spaces

KT Sturm, S Fang, J Shao - Probab. Theory Related Fields, 2010

基于结构张量和 Wasserstein 距离的纹理图像分割

谢晓振，吴纪桃 - 中国图象图形学报, 2010 - cqvip.com

基于区域的非参数活动轮廓模型被广泛地应用于图像分割领域. 在结构张量和图像灰度直方图

基础上建立的新模型就属于这个范畴, 它被用于灰度和彩色纹理图像的分割. 首先,

对经典的结构张量进行扩展, 使其能表达原始纹理图像的梯度信息和色彩信息 …

[Chinese Texture image segmentation based on structure tensor and Wasserstein distance]

Entropic Burgers' equation via a minimizing movement ... - cvgmt

[PDF] Flussi gradiente in spazi metrici e nello spazio di Wasserstein delle misure di probabilita¡

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. created by gigli on 09 Feb 2010 modified on 02 Mar 2012. [BibTeX]. Accepted at Calc.Var and PDE Inserted: 9 feb 2010. Last Updated: 2 mar ...

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

NGF Otto - 2010

[Chinese Texture image segmentation based on structure tensor and Wasserstein distance]

[PDF] accademiaxl.it

L AMBROSIO - media.accademiaxl.it

In questo articolo riassumiamo i principali risultati del libro [4], dedicato ad una teoria dei

flussi gradiente in spazi metrici generali e nello spazio delle misure di probabilita¡ munito

della distanza di Wasserstein quadratica. La sintesi che faremo dei risultati (largamente …

Peer-reviewed
Authors:Neal Madras, Deniz

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distancesSezer
Summary:We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz’s convergence theorem for locally contractive random dynamical systems. We describe practical methods for finding Steinsaltz’s “drift functions” that prove local contractivity. We then use the idea of “one-shot coupling” to derive criteria that give bounds for total variation distances in terms of Wasserstein distances. Our methods are applied to two examples: a two-component Gibbs sampler for the Normal distribution and a random logistic dynamical systemShow more
Downloadable Article
Publication:https://projecteuclid.org/euclid.bj/1281099888Bernoulli, 16, 2010-08, 882

2010

2010 [PDF] arxiv.org

[BOOK] Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

W Gangbo, HK Kim, T Pacini - 2010 - books.google.com

Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $

endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely

continuous curves in $\mathcal {M} $ was introduced by Ambrosio, Gigli, and Savare. In this …

Logarithmic Sobolev inequality for diffusion semigroups

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

17, 2010 — Abstract: Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get ...

by I Gentil · ‎2010 · ‎Cited by 3 · ‎Related articles

2010

G Naldi, F Cavalli - 2010 - publicatt.unicatt.it

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

[CITATION] A geometric study of Wasserstein spaces: Euclidean spaces”, 2008, to appear in Ann

B Kloeckner - Sc. Norm. Super. Pisa Cl. Sci.(5)

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

Wasserstein space over the Wiener space

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

[PDF] Wasserstein space over the Wiener space Shizan FANGa, b Jinghai SHAOb, c Karl-Theodor STURMc a: IMB, BP 47870, Université de Bourgogne, 21078 Dijon …

S FANG, J SHAO, KT STURM - fang.perso.math.cnrs.fr

The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel-Ustünel. Carrying out the program of Ambrosio-Gigli-Savaré, we present a complete …

Related articles All 3 versions
<——2010———2010----- 100—

2010

Statistical learning in Wasserstein space

A Karimi, L Ripani, TT Georgiou - arXiv preprint arXiv:2004.07875, 2020 - arxiv.org

We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems. The particular formulation …

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので, 最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

Geometry and Stochastic Calculus on Wasserstein spaces

2010

[PDF] Metric currents and geometry of Wasserstein spaces

L Granieri - Rendiconti del Seminario Matematico della Università …, 2010 - numdam.org

We investigate some geometric aspects of Wasserstein spaces through the continuity equation as worked out in mass transportation theory. By defining a suitable homology on the flat torus Tn, we prove that the space p (Tn) has nontrivial homology in a metric sense …

2010

[PDF] uni.lu

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September 2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

Wasserstein geometry of porous medium equation ...

2010

www.sciencedirect.com › science › article › pii

by A Takatsu · ‎2012 · ‎Cited by 6 · ‎Related articles

Wasserstein geometry of porous medium equation☆ ... On the space of q-Gaussian measures, the porous medium equation is reduced to an ... A, 43 (2010), p.

[CITATION] Wasserstein geometry of porous medium equation, Preprint (2010)

A Takatsu

[CITATION] Wasserstein geometry of porous medium equation, to appear in Ann

A Takatsu - Inst. H. Poincaré Anal. Non Linéaire

Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine

J Li, C Chen, AMC So - arXiv preprint arXiv:2010.12865, 2020 - arxiv.org

Page 1. Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally

Robust Support Vector Machine Jiajin Li Department of Systems Engineering and Engineering

Management The Chinese University of Hong Kong jjli@se.cuhk.edu.hk …

Permutation invariant networks to learn Wasserstein metrics

A Sehanobish, N Ravindra, D van Dijk - arXiv preprint arXiv:2010.05820, 2020 - arxiv.org

Understanding the space of probability measures on a metric space equipped with a

Wasserstein distance is one of the fundamental questions in mathematical analysis. The

Wasserstein metric has received a lot of attention in the machine learning community …

Gradient flows in Wasserstein spaces and applications to crowd movement

F Santambrogio - Séminaire Équations aux dérivées partielles …, 2010 - numdam.org

Starting from a motivation in the modeling of crowd movement, the paper presents the topics

of gradient flows, first in Rn, then in metric spaces, and finally in the space of probability

measures endowed with the Wasserstein distance (induced by the quadratic transport cost) …

2010

[PDF] Metric currents and geometry of Wasserstein spaces

L Granieri - Rendiconti del Seminario Matematico della Università …, 2010 - numdam.org

We investigate some geometric aspects of Wasserstein spaces through the continuity

equation as worked out in mass transportation theory. By defining a suitable homology on

the flat torus Tn, we prove that the space p (Tn) has nontrivial homology in a metric sense …

2010

[PDF] A geometric study of Wasserstein spaces: embedding powers

B Kloeckner - 2010 - hal.archives-ouvertes.fr

The Wasserstein spaces# p (X) of a metric space X are sets of sufficiently concentrated

measures, endowed with a metric defined using optimal transportation. When X is compact,#

p (X) is a metrization of the set of probability measures on X endowed with the weak …

<——2010———2010----- 110—

2010

Geometry and Stochastic Calculus on Wasserstein spaces

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September

2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth

curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

t variation formula in Wasserstein spaces over compact ...

2010 PDF

www4.math.sci.osaka-u.ac.jp › ~sohta › papers

by N Gigli · ‎2010 · ‎Cited by 13 · ‎Related articles

First variation formula in Wasserstein spaces over compact Alexandrov spaces. Nicola Gigli. ∗ and Shin-ichi Ohta. †. July 29, 2010. Abstract. We extend results ...

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

2010

[CITATION] Wasserstein spaces over Wiener spaces

KT Sturm, S Fang, J Shao - Probab. Theory Related Fields, 2010

2010

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

[CITATION] A geometric study of Wasserstein spaces: Euclidean spaces”, 2008, to appear in Ann

B Kloeckner - Sc. Norm. Super. Pisa Cl. Sci.(5)

Estimates on path functionals over Wasserstein spaces

2010

[PDF] sissa.it

S Bianchini, A Brancolini - SIAM journal on mathematical analysis, 2010 - SIAM

In this paper we consider the class a functionals (introduced in Brancolini, Buttazzo, and

Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 415–434 G_r,p defined on Lipschitz

curves γ valued in the p-Wasserstein space. The problem considered is the following: given …

[CITATION] Estimates on path functionals over Wasserstein spaces, Preprint (2009)

S Bianchini, A Brancolini

ramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savaré and …

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

<——2010———2010——— ——

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & Probability Letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

Ordinary least squares for histogram data based on wasserstein distance

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between

two regions, we proposed to compare their respective histograms using the Wasserstein …

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

<——2010— - 2010————— 120—

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of

image segmentation. The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

Clustering linear models using Wasserstein distance

A Irpino, R Verde - Data Analysis and Classification, 2010 - Springer

This paper deals with the clustering of complex data. The input elements to be clustered are

linear models estimated on samples arising from several sub-populations (typologies of

individuals). We review the main approaches to the computation of metrics between linear …

[BOOK] Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

W Gangbo, HK Kim, T Pacini - 2010 - books.google.com

Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $

endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely

continuous curves in $\mathcal {M} $ was introduced by Ambrosio, Gigli, and Savare. In this …

Ordinary least squares for histogram data based on wasserstein distance

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

[PDF] uni.lu

Geometry and Stochastic Calculus on Wasserstein spaces

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September

2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth

curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

2010

2010 [PDF] projecteuclid.org

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

… For convenience, we shall sometimes talk about the Wasserstein or TV distance between

two random variables, which means the same thing as the Wasserstein or TV distance …

S Cited by 46 Related articles All 7 versio

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savaré and …

[PDF] Metric currents and geometry of Wasserstein spaces

L Granieri - Rendiconti del Seminario Matematico della Università …, 2010 - numdam.org

We investigate some geometric aspects of Wasserstein spaces through the continuity

equation as worked out in mass transportation theory. By defining a suitable homology on

the flat torus Tn, we prove that the space p (Tn) has nontrivial homology in a metric sense …

[PDF] A geometric study of Wasserstein spaces: embedding powers

B Kloeckner - 2010 - hal.archives-ouvertes.fr

The Wasserstein spaces# p (X) of a metric space X are sets of sufficiently concentrated

measures, endowed with a metric defined using optimal transportation. When X is compact,#

p (X) is a metrization of the set of probability measures on X endowed with the weak …

Entropic Burgers' equation via a minimizing movement ... - cvgmt

<——2010— - 2010————— 130—

Particle approximation of the Wasserstein diffusion

Cached

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. created by gigli on 09 Feb 2010 modified on 02 Mar 2012. [ BibTeX]. Accepted at Calc.Var and PDE Inserted: 9 feb 2010. Last

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

NGF Otto - 2010

S Andres, MK von Renesse - Journal of Functional Analysis, 2010 - Elsevier

We construct a system of interacting two-sided Bessel processes on the unit interval and

show that the associated empirical measure process converges to the Wasserstein diffusion

(von Renesse and Sturm (2009)[25]), assuming that Markov uniqueness holds for the …

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

[PDF] ustc.edu.cn

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & probability letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

2010

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

2010

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize image histogram information in local region is presented. To quantify the similarity between two regions, we proposed to compare their respective histograms using the Wasserstein …

The heat equation on manifolds as a gradient flow in the Wasserstein space

2010 [PDF] numdam.org

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

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<——2010— - 2010————— 140—

Duality on gradient estimates and Wasserstein controls

K Kuwada - Journal of Functional Analysis, 2010 - Elsevier

We establish a duality between L p-Wasserstein control and L q-gradient estimate in a general framework. Our result extends a known result for a heat flow on a Riemannian manifold. Especially, we can derive a Wasserstein control of a heat flow directly from the …

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a Riemannian manifold. To this aim we present a notion of a Riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

TION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

2010 see 2006 [PDF] sissa.it

Estimates on path functionals over Wasserstein spaces

S Bianchini, A Brancolini - SIAM journal on mathematical analysis, 2010 - SIAM

In this paper we consider the class a functionals (introduced in Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 415–434 G_r,p defined on Lipschitz curves γ valued in the p-Wasserstein space. The problem considered is the following: given …

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of image segmentation. The proposed new model which is based on the use of the structure tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

Entropic Burgers' equation via a minimizing movement ... - cvgmt

2010

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

Wasserstein space over the Wiener space

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

A geometric study of Wasserstein spaces: Euclidean spaces

B Kloeckner - Annali della Scuola Normale Superiore di Pisa-Classe …, 2010 - numdam.org

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic

metric spaces. We are interested in usual geometric properties: curvature, rank and isometry

group, mostly in the case of Euclidean spaces. Our most striking result is that the …

<——2010— - 2010————— 150—

2010 PDF

irst variation formula in Wasserstein spaces over compact ...

www4.math.sci.osaka-u.ac.jp › ~sohta › papers

by N Gigli · ‎2010 · ‎Cited by 13 · ‎Related articles

Jul 29, 2010 — J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces X with curvature bounded below: the gradient ...

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

Wasserstein space over the Wiener space

2010 published 2009

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

… Page 7. Wasserstein space over the Wiener space 541 … An absolutely continuous curve {c(t); t ∈

[0, 1]} on a Riemannian manifold M admits tangent vectors c (t) ∈ Tc(t)M for almost everywhere

t ∈]0, 1[. In order to understand the tangent spaces of the Wasserstein space (P∗(X …

[CITATION] Wasserstein spaces over Wiener spaces

KT Sturm, S Fang, J Shao - Probab. Theory Related Fields, 2010

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savaré and …

2010

Entropic Burgers' equation via a minimizing movement scheme ...

www.researchgate.net › publication › 257436649_Entrop...

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric ... of Burgers' equation can be recovered from a minimizing movement scheme ... December 2010 · European Journal of Risk Regulation.

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

Gradient flows in Wasserstein spaces and applications to crowd movement

F Santambrogio - Séminaire Équations aux dérivées partielles …, 2010 - numdam.org

Starting from a motivation in the modeling of crowd movement, the paper presents the topics

of gradient flows, first in Rn, then in metric spaces, and finally in the space of probability

measures endowed with the Wasserstein distance (induced by the quadratic transport cost) …

2010

Clustering linear models using Wasserstein distance

A Irpino, R Verde - Data Analysis and Classification, 2010 - Springer

This paper deals with the clustering of complex data. The input elements to be clustered are

linear models estimated on samples arising from several sub-populations (typologies of

individuals). We review the main approaches to the computation of metrics between linear …

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

2010

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of

image segmentation. The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

2010

Ordinary least squares for histogram data based on wasserstein distance

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

2010

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between

two regions, we proposed to compare their respective histograms using the Wasserstein …

[PDF] A geometric study of Wasserstein spaces: embedding powers

B Kloeckner - 2010 - hal.archives-ouvertes.fr

The Wasserstein spaces# p (X) of a metric space X are sets of sufficiently concentrated

measures, endowed with a metric defined using optimal transportation. When X is compact,#

p (X) is a metrization of the set of probability measures on X endowed with the weak …

<——2010— - 2010————— 160—

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

2010

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between

two regions, we proposed to compare their respective histograms using the Wasserstein …

Clustering linear models using Wasserstein distance

2010 [PDF] researchgate.net

A Irpino, R Verde - Data Analysis and Classification, 2010 - Springer

This paper deals with the clustering of complex data. The input elements to be clustered are

linear models estimated on samples arising from several sub-populations (typologies of

individuals). We review the main approaches to the computation of metrics between linear …

Dennis–Vaserstein type decompositions | SpringerLink

2010

https://link.springer.com › article

by NA Vavilov · 2010 · Cited by 5 — A generalization of the Dennis–Vaserstein decomposition is proved for an arbitrary pair of maximal parabolic subgroups P.

Dennis-Vaserstein type decompositions.

N Vavilov, S Sinchuk - Journal of Mathematical Sciences, 2010 - search.ebscohost.com

Abstract generalization of the Dennis-Vaserstein decomposition is proved for an arbitrary

pair of maximal parabolic subgroups P and P in the general linear group GL (n, R), provided

that r− s≥ sr (R). The usual Dennis-Vaserstein decomposition is the special case where r …

[CITATION] Decompositions of Dennis–Vaserstein type

NA Vavilov, SS Sinchuk - Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst …, 2010

Dennis–Vaserstein type decompositions

Nov 10, 2010 — A generalization of the Dennis–Vaserstein decomposition is proved for an arbitrary pair of maximal parabolic subgroups P.

Journal of Mathematical Sciences (2010) 171: 331-337 , November 17, 2010

By Vavilov, N. A.; Sinchuk, S. S.. Zbl 1215.20049

2010

MR2749274 Vavilov, N. A.; Sinchuk, S. S. Decompositions of Dennis-Vaserstein type. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 375 (2010), Voprosy Teorii Predstavleniĭ Algebr i Grupp. 19, 48--60, 210; translation in J. Math. Sci. (N.Y.) 171 (2010), no. 3, 331–337 (Reviewer: Mikhail V. Belolipetsky) 20G35

6 Citations

Dennis-Vaserstein type decompositions.

N Vavilov, S Sinchuk - Journal of Mathematical Sciences, 2010 - search.ebscohost.com

Abstract generalization of the Dennis-Vaserstein decomposition is proved for an arbitrary

pair of maximal parabolic subgroups P and P in the general linear group GL (n, R), provided

that r− s≥ sr (R). The usual Dennis-Vaserstein decomposition is the special case where r …

Zbl 1215.20049

2010

2010 [PDF] aimsciences.org

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

2010 see 2009 [PDF] numdam.org

Gradient flows in Wasserstein spaces and applications to crowd movement

F Santambrogio - … aux dérivées partielles (Polytechnique) dit aussi" …, 2010 - numdam.org

… in the last years, that the concept of gradient flow in metric spaces, applied to the case of

probability measures endowed with the Wasserstein distance (ie the distance induced by the …

2010 [PDF] numdam.org

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

… of the gradient flow using a discrete approximation scheme. Furthermore we show that its …

We denote by P2(M) the Wasserstein space of probability measures on M equipped with the …

[BOOK] Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

W Gangbo, HK Kim, T Pacini - 2010 - books.google.com

Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $

endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely

continuous curves in $\mathcal {M} $ was introduced by Ambrosio, Gigli, and Savare. In this …

2010

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between

two regions, we proposed to compare their respective histograms using the Wasserstein …

On Wasserstein geometry of Gaussian measures

<——2010— - 2010————— 170—

A Takatsu - Probabilistic approach to geometry, 2010 - projecteuclid.org

The space of Gaussian measures on a Euclidean space is geodesically convex in the $ L^

2$-Wasserstein space. This is a finite dimensional manifold since Gaussian measures are

parameterized by means and covariance matrices. By restricting to the space of Gaussian …

Particle approximation of the Wasserstein diffusion

S Andres, MK von Renesse - Journal of Functional Analysis, 2010 - Elsevier

We construct a system of interacting two-sided Bessel processes on the unit interval and

show that the associated empirical measure process converges to the Wasserstein diffusion

(von Renesse and Sturm (2009)[25]), assuming that Markov uniqueness holds for the …

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

Wasserstein distance based local energy model of segmentation

XH Qian, SX Guo, XY Li - Dianzi Xuebao(Acta Electronica Sinica), 2010 - en.cnki.com.cn

A nonparametric Wasserstein distance-based active contour model that is able to utilize

image histogram information in local region is presented. To quantify the similarity between

two regions, we proposed to compare their respective histograms using the Wasserstein …

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient ﬂows

[PDF] ems.press

JW Portegies, MA Peletier - Interfaces and Free Boundaries, 2010 - ems.press

We develop a gradient-ﬂow framework based on the Wasserstein metric for a parabolic

moving boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

<——2010— - 2010————— 180—

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of

image segmentation. The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

A maximum principle for pointwise energies of quadratic Wasserstein minimal networks

J Dahl - arXiv preprint arXiv:1011.0236, 2010 - arxiv.org

Given k points p1,...,pk in a geodesic space1 Y , one can ask for a minimal net- work spanning

p1,...,pk. For a complete, connected Riemannian manifold M, the space of Borel probability measure

P(M) may be metrized, allowing infinite dis- tances, by the Wasserstein distance W2 associated …

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to

equilibrium of a Markov chain on a general state space, with respect to both total variation

and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

Duality on gradient estimates and Wasserstein controls

K Kuwada - Journal of Functional Analysis, 2010 - Elsevier

We establish a duality between L p-Wasserstein control and L q-gradient estimate in a

general framework. Our result extends a known result for a heat flow on a Riemannian

manifold. Especially, we can derive a Wasserstein control of a heat flow directly from the …

[BOOK] Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

W Gangbo, HK Kim, T Pacini - 2010 - books.google.com

Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $

endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely

continuous curves in $\mathcal {M} $ was introduced by Ambrosio, Gigli, and Savare. In this …

2010

Gradient flows in Wasserstein spaces and applications to crowd movement

F Santambrogio - Séminaire Équations aux dérivées partielles …, 2010 - numdam.org

Starting from a motivation in the modeling of crowd movement, the paper presents the topics

of gradient flows, first in Rn, then in metric spaces, and finally in the space of probability

measures endowed with the Wasserstein distance (induced by the quadratic transport cost) …

[CITATION] Gradient flows in Wasserstein spaces and applications to crowd movement, Séminaire XEDP, 2009-2010

F Santambrogio - Exp. No. XXVII, 2012

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & probability letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題

として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので,

最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

Geometry and Stochastic Calculus on Wasserstein spaces

[PDF] uni.lu

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September

2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth

curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

The heat equation on manifolds as a gradient flow in the Wasserstein space

2010

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

<——2010— - 2010————— 190—

2010

Wasserstein space over the Wiener space

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & probability letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

Entropic Burgers' equation via a minimizing movement ... - cvgmt

http://cvgmt.sns.it › paper

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. created by gigli on 09 Feb 2010 modified on 02 Mar 2012.

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

NGF Otto - 2010

2010 [PDF] inria.fr

Ordinary least squares for histogram data based on wasserstein distance

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

2010 [PDF] numdam.org

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

2010 [PDF] ustc.edu.cn

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & probability letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

M Herrmann, B Niethammer - arXiv preprint arXiv:1008.3658, 2010 - arxiv.org

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well

potential. The convergence proof is based on the Rayleigh principle of the underlying

Wasserstein gradient structure and complements a recent result by Peletier, Savaré and …

A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

F Cavalli, G Naldi - Kinetic & Related Models, 2010 - aimsciences.org

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with

Neumann boundary conditions involving recent mass transportation methods. The

numerical scheme is based on an alternative formulation of the problem using the so called …

Gradient flows in Wasserstein spaces and applications to crowd movement

F Santambrogio - Séminaire Équations aux dérivées partielles …, 2010 - numdam.org

Starting from a motivation in the modeling of crowd movement, the paper presents the topics

of gradient flows, first in Rn, then in metric spaces, and finally in the space of probability

measures endowed with the Wasserstein distance (induced by the quadratic transport cost) …

<——2010— - 2010————— 200—

Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition

R Wang, X Wang, L Wu - Statistics & probability letters, 2010 - Elsevier

Let (X n) n≥ 1 be a sequence of iidrv's with values in a Polish space (E, d) of law μ.

Consider the empirical measures L n= 1 n∑ k= 1 n δ X k, n≥ 1. Our purpose is to generalize

Sanov's theorem about the large deviation principle of L n from the weak convergence …

[PDF] ems.press

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient ﬂows

JW Portegies, MA Peletier - Interfaces and Free Boundaries, 2010 - ems.press

We develop a gradient-ﬂow framework based on the Wasserstein metric for a parabolic

moving boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題

として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので,

最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

[PDF] Flussi gradiente in spazi metrici e nello spazio di Wasserstein delle misure di probabilita¡

YEAR 2010 [PDF] accademiaxl.it

L AMBROSIO - media.accademiaxl.it

In questo articolo riassumiamo i principali risultati del libro [4], dedicato ad una teoria dei

flussi gradiente in spazi metrici generali e nello spazio delle misure di probabilita¡ munito

della distanza di Wasserstein quadratica. La sintesi che faremo dei risultati (largamente …

Italian Gradient flows in metric spaces and in the Wasserstein space of probability measurements\

[PDF] accademiaxl.it

[PDF] Flussi gradiente in spazi metrici e nello spazio di Wasserstein delle misure di probabilita¡

L AMBROSIO - media.accademiaxl.it

In questo articolo riassumiamo i principali risultati del libro [4], dedicato ad una teoria dei

flussi gradiente in spazi metrici generali e nello spazio delle misure di probabilita¡ munito

della distanza di Wasserstein quadratica. La sintesi che faremo dei risultati (largamente …

2010

First variation formula in Wasserstein spaces over compact ...

https://webusers.imj-prg.fr › Site › GO-CMB

PDF

by N GIGLI · Cited by 13 — Math.,. 2009) for nonnegatively curved Alexandrov spaces to general compact Alexan- drov spaces X with curvature bounded below: the gradient flow of a geodesi ...

Missing: 2011 ‎| Must include: 2011

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

Entropic Burgers' equation via a minimizing movement ... - cvgmt

A [CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

http://cvgmt.sns.it › paper

Feb 9, 2010 — Accepted at Calc.Var and PDE Inserted: 9 feb 2010. Last Updated: 2 mar 2012. Year: 2010. Abstract: As noted by the second author in the ...

[CITATION] Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

NGF Otto - 2010

2010

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

Estimates on path functionals over Wasserstein spaces

2010 [PDF] sissa.it

S Bianchini, A Brancolini - SIAM journal on mathematical analysis, 2010 - SIAM

In this paper we consider the class a functionals (introduced in Brancolini, Buttazzo, and

Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 415–434 G_r,p defined on Lipschitz

curves γ valued in the p-Wasserstein space. The problem considered is the following: given …

Existence and Uniqueness of GEXIT curves via

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

<——2010— - 2010————— 210—

A maximum principle for pointwise energies of quadratic Wasserstein minimal networks

J Dahl - arXiv preprint arXiv:1011.0236, 2010 - arxiv.org

Given k points p1,...,pk in a geodesic space1 Y , one can ask for a minimal net- work spanning

p1,...,pk. For a complete, connected Riemannian manifold M, the space of Borel probability measure

P(M) may be metrized, allowing infinite dis- tances, by the Wasserstein distance W2 associated …

2010 [PDF] numdam.org

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

Geometry and Stochastic Calculus on Wasserstein spaces

C Selinger - 2010 - orbilu.uni.lu

PhD Thesis under the supervision of Prof. Anton Thalmaier at Université du Luxembourg, September

2010 … 1.1 Weak topology and optimal transport distance . . . . . . . . . . 12 1.2 Topology of smooth

curves . . . . . . . . . . . . . . . . . . . . . 19 … 2.1 Wasserstein geodesics . . . . . . . . . . . . . . . . . . . . . . . . 25 …

Particle approximation of the Wasserstein diffusion

S Andres, MK von Renesse - Journal of Functional Analysis, 2010 - Elsevier

We construct a system of interacting two-sided Bessel processes on the unit interval and

show that the associated empirical measure process converges to the Wasserstein diffusion

(von Renesse and Sturm (2009)[25]), assuming that Markov uniqueness holds for the …

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of

image segmentation. The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

2010

2010 [PDF] nii.ac.jp

[PDF] Some linear and non-linear structures in Wasserstein geometry

高津飛鳥 - 2010 - tohoku.repo.nii.ac.jp

論である. 彼らは砂山の質量を正規化し確率測度とみなし, 問題を確率測度空間上の変分問題

として定式化した. もし二つの山が同位置にあり同形状であれば動かす必要はないので,

最小総輸送費用は 0 である. 逆にこっの砂山の間に隔たりがあればある程, 最小総費用は高くなると …

The heat equation on manifolds as a gradient flow in the Wasserstein space

M Erbar - Annales de l'IHP Probabilités et statistiques, 2010 - numdam.org

We study the gradient flow for the relative entropy functional on probability measures over a

Riemannian manifold. To this aim we present a notion of a Riemannian structure on the

Wasserstein space. If the Ricci curvature is bounded below we establish existence and …

[CITATION] The heat equation on manifolds as a gradient flow in the Wasserstein space Ann

M Erbar - Inst. H. Poincare Probab. Statist, 2010

[PDF] A geometric study of Wasserstein spaces: embedding powers

B Kloeckner - 2010 - hal.archives-ouvertes.fr

The Wasserstein spaces# p (X) of a metric space X are sets of sufficiently concentrated

measures, endowed with a metric defined using optimal transportation. When X is compact,#

p (X) is a metrization of the set of probability measures on X endowed with the weak …

Ordinary least squares for histogram data based on wasserstein distance

2010 [PDF] ethernet.edu.et

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

2010 [PDF] sciencedirect.com

Duality on gradient estimates and Wasserstein controls

K Kuwada - Journal of Functional Analysis, 2010 - Elsevier

… For the proof, we show basic properties of Wasserstein … In Section 4, we consider a heat

flow on a sub-Riemannian … two probability measures μ and ν on X, we denote the space …

<——2010— - 2010————— 220—

2010

Texture segmentation based on the use of the structure tensor and the wasserstein distance [J]

X XIE, J WU - Journal of Image and Graphics, 2010 - en.cnki.com.cn

Nonparametric region-based active contour models have been widely used in the field of

image segmentation. The proposed new model which is based on the use of the structure

tensor and the Wasserstein distance belongs to this category. First, the classical tensor …

Ordinary least squares for histogram data based on wasserstein distance

2010 [PDF] ethernet.edu.et

R Verde, A Irpino - Proceedings of COMPSTAT'2010, 2010 - Springer

Histogram data is a kind of symbolic representation which allows to describe an individual

by an empirical frequency distribution. In this paper we introduce a linear regression model

for histogram variables. We present a new Ordinary Least Squares approach for a linear …

2010 [PDF] arxiv.org

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient ﬂows

JW Portegies, MA Peletier - Interfaces and Free Boundaries, 2010 - ems.press

We develop a gradient-ﬂow framework based on the Wasserstein metric for a parabolic

moving boundary problem that models crystal dissolution and precipitation. In doing so we

derive a new weak formulation for this moving-boundary problem and we show that this …

2010 [PDF] projecteuclid.org

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to

equilibrium of a Markov chain on a general state space, with respect to both total variation

and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

2010 [PDF] psu.edu

Wasserstein space over the Wiener space

S Fang, J Shao, KT Sturm - Probability theory and related fields, 2010 - Springer

The goal of this paper is to study optimal transportation problems and gradient flows of

probability measures on the Wiener space, based on and extending fundamental results of

Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete …

[CITATION] Wasserstein spaces over Wiener spaces

KT Sturm, S Fang, J Shao - Probab. Theory Related Fields, 2010

Estimates on path functionals over Wasserstein spaces

2010

2010 [PDF] sissa.it

S Bianchini, A Brancolini - SIAM journal on mathematical analysis, 2010 - SIAM

In this paper we consider the class a functionals (introduced in Brancolini, Buttazzo, and

Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 415–434 G_r,p defined on Lipschitz

curves γ valued in the p-Wasserstein space. The problem considered is the following: given …

2010

A geometric study of Wasserstein spaces: Hadamard spaces

2010 ARXIV: METRIC GEOMETRY

Liver and skin histopathology in adults with acid sphingomyelinase deficiency (Niemann-Pick disease type B).

58 citations*

2012 THE AMERICAN JOURNAL OF SURGICAL PATHOLOGY

Beth L. Thurberg ¹,Melissa P. Wasserstein ²,Thomas Schiano ²,Fanny O’Brien ¹,Susan Richards ¹ see all 7 authors

¹ Genzyme ,² Icahn School of Medicine at Mount Sinai

Liver biopsy

Cirrhosis

View More (26+)

Acid sphingomyelinase deficiency (ASMD) is a lysosomal storage disorder characterized by the pathologic accumulation of sphingomyelin (SM) in multiple cell types, and occurs most prominently within the liver, spleen, and lungs, leading to significant clinical disease. Seventeen ASMD patients underwe... View Full Abstract

2010 see 2011

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

2010 ARXIV: PROBABILITY

2011 OSAKA JOURNAL OF MATHEMATICS

190 citations*

Fundamental theorem of Riemannian geometry

SCI - Mathematics

Information geometry

View More (9+)

This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the L 2 -Wasserstein geometry. The space of Gaussian measures is of finite dimension, which allows to write down the ex plicit Riemannian metric which in turn induces the L 2 -Wasserstein distance. Mo... View Full Abstract

2010

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence

2010 ARXIV: PROBABILITY

10 citations* for all

2020 NEURAL INFORMATION PROCESSING SYSTEMS

Sinho Chewi ,Thibaut Le Gouic ,Chen Lu ,Tyler Maunu ,Philippe Rigollet

Massachusetts Institute of Technology

Gradient descent

Laplace operator

View More (8+)

Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport. We introduce a new perspective on SVGD that instead views SVGD as the (kernelized) gradient flow of th... View Full Abstract

2010

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

58 citations* for all

57 citations*

2010 BERNOULLI

Neal Madras ,Deniz Sezer

Markov chain

Random dynamical system

View More (8+)

<——2010— - 2010————— 230—

2010 [PDF] projecteuclid.org

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

N Madras, D Sezer - Bernoulli, 2010 - projecteuclid.org

We present a framework for obtaining explicit bounds on the rate of convergence to

equilibrium of a Markov chain on a general state space, with respect to both total variation

and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's …

2010

Approximating stochastic biochemical processes with Wasserstein pseudometrics

D Thorsley, E Klavins - IET Systems Biology, 2010 - ieeexplore.ieee.org

Modelling stochastic processes inside the cell is difficult due to the size and complexity of

the processes being investigated. As a result, new approaches are needed to address the …

2010 [PDF] arxiv.org

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient ﬂows

JW Portegies, MA Peletier - Interfaces and Free Boundaries, 2010 - ems.press

We develop a gradient-ﬂow framework based on the Wasserstein metric for a parabolic

moving boundary problem that models crystal dissolution and precipitation. In doing so we …

2010 [PDF] arxiv.org

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

S Lisini, A Marigonda - manuscripta mathematica, 2010 - Springer

We study a new class of distances between Radon measures similar to those studied in

Dolbeault et al.(Calc Var Partial Differ Equ 34: 193–231, 2009). These distances (more

correctly pseudo-distances because can assume the value+∞) are defined generalizing the …

2010 Short communication
Sanov’s theorem in the Wasserstein distance: A necessary and sufficient condition
Statistics & Probability Letters1–15 March 2010...

Ran WangXinyu WangLiming Wu

2010

2010 Computer Program,

Heat equation on manifolds as a gradient flow in the Wasserstein spaceAuthor:Erbar, Matthias (Creator)
Summary:We study the gradient flow for the relative entropy functional on probability measures over a Riemannian manifold. To this aim we present a notion of a Riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equationShow more
Computer Program, 2010-02
English
Publisher:Institut Henri Poincaré, 2010-02
Access Free

2010 comp file

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distancesAuthors:Madras, Neal (Creator), Sezer, Deniz (Creator)
Summary:We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz’s convergence theorem for locally contractive random dynamical systems. We describe practical methods for finding Steinsaltz’s “drift functions” that prove local contractivity. We then use the idea of “one-shot coupling” to derive criteria that give bounds for total variation distances in terms of Wasserstein distances. Our methods are applied to two examples: a two-component Gibbs sampler for the Normal distribution and a random logistic dynamical systemShow more
Computer File, 2010-08
English
Publisher:Bernoulli Society for Mathematical Statistics and Probability, 2010-08

Peer-reviewed
Duality on gradient estimates and Wasserstein controlsAuthor:Kazumasa Kuwada
Summary:We establish a duality between L p -Wasserstein control and L q -gradient estimate in a general framework. Our result extends a known result for a heat flow on a Riemannian manifold. Especially, we can derive a Wasserstein control of a heat flow directly from the corresponding gradient estimate of the heat semigroup without using any other notion of lower curvature bound. By applying our result to a subelliptic heat flow on a Lie group, we obtain a coupling of heat distributions which carries a good control of their relative distanceShow more
Article, 2010
Publication:Journal of Functional Analysis, 258, 20100601, 3758
Publisher:2010

Peer-reviewed
The heat equation on manifolds as a gradient flow in the Wasserstein spaceAuthor:Matthias Erbar
Summary:We study the gradient flow for the relative entropy functional on probability measures over a Riemannian manifold. To this aim we present a notion of a Riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equationShow more
Downloadable Article
Publication:Ann. Inst. H. Poincaré Probab. Statist., 46, 2010-02, 1

Peer-reviewed
Particle approximation of the Wasserstein diffusionAuthors:Sebastian Andres, Max-K. von Renesse
Summary:We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process converges to the Wasserstein diffusion (von Renesse and Sturm (2009) [25]), assuming that Markov uniqueness holds for the generating Wasserstein Dirichlet form. The proof is based on the variational convergence of an associated sequence of Dirichlet forms in the generalized Mosco sense of Kuwae and Shioya (2003) [19]Show more
Article
Publication:Journal of Functional Analysis, 258, 2010, 3879
<—–2010—–– 2010——— 240—

Peer-reviewed
Sanov’s theorem in the Wasserstein distance: A necessary and sufficient conditionAuthors:Ran Wang, Xinyu Wang, Liming Wu
Summary:Let ( X n ) n ≥ 1 be a sequence of i.i.d.r.v.’s with values in a Polish space ( E , d ) of law μ . Consider the empirical measures L n = 1 n ∑ k = 1 n δ X k , n ≥ 1 . Our purpose is to generalize Sanov’s theorem about the large deviation principle of L n from the weak convergence topology to the stronger Wasserstein metric W p . We show that L n satisfies the large deviation principle in the Wasserstein metric W p ( p ∈ [ 1 , + ∞ ) ) if and only if ∫ E e λ d p ( x 0 , x ) d μ ( x ) < + ∞ for all λ > 0 , and for some x 0 ∈ EShow more
Article, 2010
Publication:Statistics and Probability Letters, 80, 20100301, 505
Publisher:2010

2010 see 2009 Peer-reviewed
A Wasserstein Approach to the One-Dimensional Sticky Particle SystemAuthors:L. Natile, G. Savare
Article, 2010
Publication:SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 41, 2010, 1340
Publisher:2010

Skorohod representation theorem via disintegrations

P Berti, L Pratelli, P Rigo - Sankhya A, 2010 - Springer

… In checking W is a metric, and even more in proving Theorem … just a little bit more than a

Skorohod representation. In addition, … of Wasserstein distance to a large class of metric spaces (…

2010 book

From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage
Authors:S. Adams, N. Dirr, M.A. Peletier, J. Zimmer
Summary:We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional Jh characterizes the behaviour of the particle system at t = h in terms of the initial distribution at t = 0. For the diffusion equation, a single step in the time-discretized entropy-Wasserstein gradient fl ow is characterized by the minimization of a functional Kh. We establish a new connection between these systems by proving that Jh and Kh are equal up to second order in h as h --> 0. This result gives a microscopic explanation of the origin of the entropy-Wasserstein gradient fl ow formulation of the diffusion equation. Simultaneously, the limit passage presented here gives a physically natural description of the underlying particle system by describing it as an entropic gradient flowShow more
Book, 2010
Publication:2010
Publisher:Technische Universiteit Eindhoven, 2010

代数的K群に関するWassersteinの仕事 (Analytic Varieties及びStratified Spaces上の諸問題)
Authors:AOMOTO, KAZUHIKO (Contributor), アオモト, カズヒコ (Contributor), 青本, 和彦 (Creator)
Downloadable Archival Material, 2010-03-08T01:54:39Z
Japanese
Publisher:京都大学数理解析研究所, 2010-03-08T01:54:39Z
[Japanese Wasserstein's work on algebraic K groups (problems on Analytic Varieties and Stratified Spaces)]

Peer-reviewed
On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals
Authors:Stefano Lisini, Antonio Marigonda, SpringerLink (Online service)
Downloadable Article, 2010
English
Publication:Manuscripta mathematica
Publisher:2010

2010. [PDF] sonycsl.co.jp

On Wasserstein geometry of Gaussian measures

A Takatsu - Probabilistic approach to geometry, 2010 - projecteuclid.org

… This is a finite dimensional manifold since Gaussian … of Gaussian measures inside the

£ 2- Wasserstein space, we manage to provide detailed descriptions of the £ 2- Wasserstein …

[CITATION] On Wasserstein Geometry of Gaussian Measures

T Asuka - … Approach to Geometry; Mathematical Society of Japan …, 2010

Takatsu : Wasserstein geometry of Gaussian measures - Project Euclid

<—–2010—–– 2010——— 247— end 2010

including 5 titles with Vaserstein

start 2011 Wasserstein

MR2871291 Takatsu, Asuka Wasserstein geometry of Gaussian measures. Osaka J. Math. 48 (2011), no. 4, 1005–1026. 53Cxx (60D05 60G15). Zbl pre06006848. Published: DEC 2011. pdf

by A Takatsu - ‎2011 - ‎Cited by 69 - ‎Related articles

The space of Gaussian measures is of finite dimension, which allows to write down the explicit Riemannian metric which in turn induces the -Wasserstein distance. Moreover, its completion as a metric space provides a complete picture of the singular behavior of the -Wasserstein geometry.

MR2812740 Kreitmeier, Wolfgang Optimal vector quantization in terms of Wasserstein distance. J. Multivariate Anal. 102 (2011), no. 8, 1225–1239. 60E05 (60B05 62E17 68P30 94A17 94A29). Zbl 05918992. Zbl 05918992 . Published: SEP 2011

Optimal Vector Quantization in Terms of Wasserstein Distance

Wolfgang Kreitmeier - 2011

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a

quantization error which is equal to a Wasserstein distortion. However, for the optimal

(Shannon-) entropy constrained quantization error a proof for a similar identity is still

missing. Relying on principal results of the optimal mass transportation theory, we will prove

that the optimal quantization error is equal to a Wasserstein distance. Since we will state the

[PDF] arxiv.org Comparison between distance and norm, and localisation of Wasserstein distance

R Peyre - arXiv preprint arXiv:1104.4631, 2011 - arxiv.org

Abstract: It is well known that the quadratic Wasserstein distance $ W_2 (\mathord

{\boldsymbol {\cdot}},\mathord {\boldsymbol {\cdot}}) $ is formally equivalent, for

infinitesimally small perturbations, to some weighted $ H^{-1} $ homogeneous Sobolev

2011 zzz 26 online

[CITATION] Second order analysis over the Wasserstein space

N Gigli - Memoirs of the American Mathematical Society, 2011 - iris.sissa.it

We develop a rigorous second order analysis on the space of probability measures on a

Riemannian manifold endowed with the quadratic optimal transport distance $ W_2 $. Our

discussion comprehends: definition of covariant derivative, discussion of the problem of

arXiv:1104.4631 [pdf, ps, other]

Comparison between W₂ distance and H˙^-1 1norm, and localisation of Wasserstein distance

Rémi Peyre

Comments: Added a new section about application to the localisation of Wasserstein distance

Subjects: Functional Analysis (math.FA)

MR2815689 Herrmann, Michael; Niethammer, Barbara Kramers' formula for chemical reactions in the context of Wasserstein gradient flows. Commun. Math. Sci. 9 (2011), no. 2, 623–635, 35Q84 (35B25 49S05 80Axx). Zbl 1219.35315

arXiv:1008.3658 [pdf, ps, other]

Kramers' formula for chemical reactions in the context of Wasserstein gradient flows

Michael Herrmann, Barbara Niethammer

Comments: revised proofs, 12 pages, 1 figure

Journal-ref: Commun. Math. Sci., vol. 9, no. 2, pp.623-635, 2011

Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)

Problèmes d'interaction discret-continu et distances de Wasserstein

E Boissard - 2011 - thesesups.ups-tlse.fr

On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la

théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur

pour l'approximation particulaire des solutions de certaines équations aux dérivées ...

Dissertation

Régularisation de Wasserstein. Application au Transfert de Couleur

G Peyré, R Julien - 2011 - basepub.dauphine.fr

Résumé en français: Ce papier introduit une nouvelle approche méthodologique pour la

résolution de problèmes variationnels sous contraintes statistiques en grande dimension.

Nous nous plaçons dans le cadre de la théorie du transport optimal de Monge- ...

Large Deviations for a matching problem related to the $\ infty $-Wasserstein distance

J Trashorras - 2011 - hal.archives-ouvertes.fr

Abstract: Let (E, d) be a compact metric space, X=(X1,..., Xn,...) and Y=(Y1,..., Yn,...) two

independent sequences of independent E-valued random variables and (LX n) n≥ 1 and

(LY n) n≥ 1 the associated sequences of empirical measures. We establish a Large ... 2011

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - arXiv preprint arXiv:1111.0058, 2011 - arxiv.org

Abstract: This is a condensed form of the author's essay, which can be found at [arXiv:

1105.2883]. We prove that the entropic measure constructed by von Renesse-Sturm over

Wasserstein space on the unit interval (probability measures on the unit interval equipped ...

[CITATION] A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - 2011

<——2011—————2011—————— -10—

Well-posedness of Wasserstein Gradient Flow Solutions of Higher Order Evolution Equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

Abstract: A relaxed notion of displacement convexity is defined and used to establish short

time existence and uniqueness of Wasserstein gradient flows for higher order energy

functionals. As an application, local and global well-posedness of different higher order ...

Existence and uniqueness of GEXIT curves via the Wasserstein metric

S Kudekar, T Richardson… -Information Theory Workshop (ITW), 2011 IEEE - ieeexplore.ieee.org

Abstract In the analysis of iterative coding systems it is often necessary to compare two

densities and to measure how close they are. Sometimes it is convenient to compare their

entropy or their Battacharyya parameter. But sometimes a more powerful measure is ...

Metric): In the following, a, b, c, and d denote L-distributions. Given …

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability}, 2011 - emis.ams.org

Abstract We study the problem of non-asymptotic deviations between a reference measure µ

and its empirical version Ln, in the 1-Wasserstein metric, under the standing assumption that

µ satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin ...

arXiv:1103.3188 [pdf, ps, other] math.PR math.ST

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - arXiv preprint arXiv:1105.0360, 2011 - arxiv.org

Abstract: A Wasserstein spaces is a metric space of sufficiently concentrated probability

measures over a general metric space. The main goal of this paper is to estimate the

largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize ...

published

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of Computational Mathematics, 2011 - Springer

Abstract This paper discusses certain modifications of the ideas concerning the Gromov–

Hausdorff distance which have the goal of modeling and tackling the practical problems of

object matching and comparison. Objects are viewed as metric measure spaces, and ...

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are ...

All 9 versions [PDF] arxiv.org

Regularisation de Wasserstein et Application au Transfert de Couleur (J. Rabin, G. Peyré), Gretsi'11, 2011. [bib] [pdf]

““Exact” Deviations in Wasserstein Distance for Empirical and Occupation Measures”,

E. Boissard, and T. le Gouic,

Preprint, arXiv:1103.3188v1, 2011.

We study the problem of so-called "exact" or non-asymptotic deviations between a reference measure $μ$ and its empirical version $L_n$, in the $p$-Wasserstein metric, $1 ≤ p ≤ 2$, under the standing assumption that $μ$ satisfies a transport-entropy inequality. This work is a generalization of an article by F.Bolley, A.Guillin and C.Villani, where the case of measures with support in $\R^d$ was studied. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting Markov chain in $W_1$ distance are also given. Throughout the text, several examples are worked out, including the cases of Gaussian measures on separable Banach spaces, and laws of diffusion processes.

Wasserstein distances for discrete measures and convergence in nonparametric mixture models

[PDF] from arxiv.orgXL Nguyen - Arxiv preprint arXiv:1109.3250, 2011 - arxiv.org

Abstract: We consider Wasserstein distance functionals for comparing between and

assessing the convergence of latent discrete measures, which serve as mixing distributions

in hierarchical and nonparametric mixture models. We explore the space of discrete ...

A Monotone Approximation to the Wasserstein Diffusion

[PDF] from arxiv.orgKT Sturm - Arxiv preprint arXiv:1105.3963, 2011 - arxiv.org

Abstract: Von Renesse and the author (Ann. Prob.'09) developed a second order calculus

on the Wasserstein space P ([0, 1]) of probability measures on the unit interval. The basic

objects of interest had been Dirichlet form, semigroup and continuous Markov process, ...

MR3205035

<——2011—————2011————————— -20—

Transport equation with nonlocal velocity in Wasserstein spaces: existence, uniqueness and numerical schemes

PDF] from arxiv.orgB Piccoli… - Arxiv preprint arXiv:1106.2555, 2011 - arxiv.org

Abstract: Motivated by pedestrian modelling, we study evolution of measures in the

Wasserstein space. In particular, we consider the Cauchy problem for a transport equation,

where the velocity field depends on the measure itself. We prove existence and ...

Functional inequalities for the Wasserstein Dirichlet Form

MR 2013

MR2857030 Stannat, Wilhelm Functional inequalities for the Wasserstein Dirichlet form. Seminar on Stochastic Analysis, Random Fields and Applications VI, 245–260, Progr. Probab., 63, Birkhäuser/Springer Basel AG, Basel, 2011. (Reviewer: Ren Ming Song) 60J60 (28A33 35A23 35P15 47D07 58J65 60J35)

[PDF] from tu-darmstadt.deW Stannat - Seminar on Stochastic Analysis, Random Fields and …, Progress in Probability, 2011,

Volume 63, Part 1, 245-260, Springer

Abstract. We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and generalize

the Poincaré and loga- rithmic Sobolev inequality obtained for the Wasserstein Dirichlet ...
Functional Inequalities for the Wasserstein Dirichlet Form

Author:W. Stannat
Article, 2011
Publication:PROGRESS IN PROBABILITY, 63, 2011, 245
Publisher:2011

2011 see 2910

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

R Grübel - 2011 - citeulike.org

... wasserstein statistics pearson mcmc coupling. Search all the public and authenticated

articles in CiteULike. ... Tags. Quantitative bounds for Markov chain convergence:

Wasserstein and total variation distances. by: Rudolf Grübel. ...

Wasserstein Regularization of Imaging Problems

[PDF] from archives-ouvertes.frJ Rabin…G Peyré - 2011 - hal.archives-ouvertes.fr Proc. ICIP'11, pp. 1541-1544, 2011. [bib] [pdf]

ABSTRACT This paper introduces a novel and generic framework embedding statistical constraints

for variational problems. We resort to the the- ory of Monge-Kantorovich optimal mass transport

to define penalty terms depending on statistics from images. To cope with the com- ...

Wasserstein Active Contours

J Rabin, J Fadili… - 2011 - basepub.dauphine.fr

[PDF] from archives-ouvertes.frG Peyré, J Fadili, J Rabin - 2011 - hal.archives-ouvertes.fr

In this paper, we propose a novel and rigorous framework for region-based active contours that

combines the Wasserstein distance between statistical distributions in arbitrary dimension and

shape derivative tools. To the best of our knowledge, this is the first variational image ...

Behaviors of $\ phi $-exponential distributions in Wasserstein geometry and an evolution equation

[PDF] from arxiv.orgA Takatsu - Arxiv preprint arXiv:1109.6776, 2011 - arxiv.org

Abstract: A $\ phi $-exponential distribution is a generalization of an exponential distribution

associated to functions $\ phi $ in an appropriate class, and the space of $\ phi $-

exponential distributions has a dually flat structure. We study features of the space of $\ ...

SIAM Journal on Mathematical Analysis, 2013

Stability of the global attractor under Markov-Wasserstein noise

[PDF] from arxiv.orgM Kell - Arxiv preprint arXiv:1103.3401, 2011 - arxiv.org

Abstract. We develop a “weak Ważewski principle” for discrete and contin- uous time dynamical

systems on metric spaces having a weaker topology to show that attractors can be continued

in a weak sense. After showing that the Wasserstein space of a proper metric space is ...

Optimal Transport and Ricci Curvature: Wasserstein Space Over the Interval

[PDF] from arxiv.orgO Chodosh - Arxiv preprint arXiv:1105.2883, 2011 - arxiv.org

Abstract. In this essay, we discuss the notion of optimal transport on (geodesic) metric

spaces, and the associated (2-)Wasserstein distance. We then examine displacement convexity

of the en- tropy functional on P(X) and associated synthetic Ricci lower bounds. In ...

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

[PDF] from arxiv.orgE Boissard… - Arxiv preprint arXiv:1105.5263, 2011 - arxiv.org

Abstract. In this work, we provide non-asymptotic bounds for the average speed of convergence

of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider

occupation measures of ergodic Markov chains. One motivation is the approximation of a ...

" Exact" deviations in Wasserstein distance for empirical and occupation measures

[PDF] from arxiv.orgE Boissard… - Arxiv preprint arXiv:1103.3188, 2011 - arxiv.org

Abstract. We study the problem of so-called “exact” or non-asymptotic de- viations between a

reference measure µ and its empirical version Ln, in the p-Wasserstein metric, 1 ≤ p ≤ 2, under

the standing assumption that µ satis- fies a transport-entropy inequality. This work is a ...

<——2011————2011———— -30——

Dynamic Clustering of Histogram Data Based on Adaptive Squared Wasserstein Distances

[PDF] from arxiv.orgA Irpino, R Verde… - Arxiv preprint arXiv:1110.1462, 2011 - arxiv.org

Abstract: This paper deals with clustering methods based on adaptive distances for

histogram data using a dynamic clustering algorithm. Histogram data describes individuals

in terms of empirical distributions. These kind of data can be considered as complex ...

Expert Systems with Applications, 2014 - Elsevier

MR2851684 Caillerie, Claire; Chazal, Frédéric; Dedecker, Jérôme; Michel, Bertrand Deconvolution for the Wasserstein metric and geometric inference. Electron. J. Stat. 5 (2011), 1394–1423. (Reviewer: Vera Pawlowsky-Glahn) 62H12 (28A33 60B10 60D99 62G07 62G99)

Deconvolution for the Wasserstein Metric and Geometric Inference

[PDF] from archives-ouvertes.frC Caillerie, F Chazal, J Dedecker… - 2011 - hal.archives-ouvertes.fr

Claire Caillerie — Frédéric Chazal — Jérôme Dedecker — Bertrand Michel

- Electronic Journal of …, 2011

Abstract: Recently,[4] have defined a distance function to measures to answer geometric

inference problems in a probabilistic setting. According to their result, the topological

properties of a shape can be recovered by using the distance to a known measure ν, if ν is ...

Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

Kantorovich-Rubinstein-Wasserstein Lp-距离 (p> 2) 沈银芳 - 科技信息, 2011 - cqvip.com

SHEN Yin Fong

Kantorovich-Rubinstein-Wasserstein Lp-distance (p> 2) [Chinese]

Zhejiang Finance and Economics College of Mathematics and Statistics , Zhejiang Hangzhou 310018,

Abstract: This article get Euclidean plane bounded region's diverse Kantorovich-Rubinstein-Wasserstein Lp-distance (abbreviated as an accurate representation of: KRW-Lp distance),

a given from the point of view of the theory of probability prove

[PDF] from tum.deS Lisini, D Matthes… - Preprint, 2011 - www-m8.ma.tum.de

Abstract. In this paper, we establish an approach to the existence theory of certain

degenerate fourth-order evolution equations which arise in applications in mathematical

physics; particular examples are the Cahn-Hilliard and the (destabilized) thin film equation ...

Zbl pre06052907

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein Lp-distance

[PDF] from ccsenet.orgY Shen - Journal of Mathematics Research, Vol. 3, No. 4; November 2011 - journal.ccsenet.org

Yinfang Shen (Corresponding author) Institute of Mathematics and

Statistics, Zhejiang University of Finance and Economics PO ...

Zbl 1270.35232 Shen, Yinfang

Optimal couplings of Kantorovich-Rubinstein-Wasserstein

Lp-distance. (English) J. Math. Res. 3, No. 4, 3-7 (2011).

Conformal Wasserstein Distance: Comparing disk and sphere-type surfaces in polynomial time II, computational aspects

Yaron Lipman, Jesus Puente, Ingrid Daubechies- Arxiv preprint arXiv:1103.4681, 2011.published in 2013

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete approximation to the arising mass-transportation problems. We furthermore generalize the framework to support sphere-type surfaces, and prove a result connecting this distance to local geodesic distortion. Lastly, we provide numerical experiments on several surfaces' datasets and compare to state of the art method.

Conformal Wasserstein distances: comparing surfaces in polynomial time

by Y Lipman - 2011 - Cited by 5 - Related articles arXiv Yaron Lipman, Ingrid Daubechies

Mar 22, 2011 – We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass ...

published 2011

Conformal Wasserstein distance: II. Computational aspects and extensions

Y Lipman, J Puente, I Daubechies - arXiv preprint arXiv:1103.4681, 2011 - arxiv.org

Abstract: This paper is a companion paper to [Lipman and Daubechies 2011]. We provide

numerical procedures and algorithms for computing the alignment of and distance between

two disk type surfaces. We provide a convergence analysis of the discrete approximation ...

2011? 2015?

Large Deviations for a matching problem related to the∞-Wasserstein distance

[PDF] from archives-ouvertes.frJ Trashorras - Arxiv preprint math.PR/0000000 - hal.archives-ouvertes.fr

Résumé en anglais: Let $(E, d) $ be a compact metric space, $ X=(X_1,\ dots, X_n,\ dots) $

and $ Y=(Y_1,\ dots, Y_n,\ dots) $ two independent sequences of independent $ E $-valued

random variables and $(L^ X_n) _ {n\ geq 1} $ and $(L^ Y_n) _ {n\ geq 1} $ the associated ...

Gromov–Wasserstein Distances and the Metric Approach to Object ...

MR2811584 Mémoli, Facundo Gromov-Wasserstein distances and the metric approach to object matching. Found. Comput. Math. 11 (2011), no. 4, 417–487. 68T10 (49Q15 54E35 60B05 60B10 68U10)

by F Mémoli - ‎2011 - ‎Cited by 98 - ‎Related articles

Apr 30, 2011 - The representation of objects as metric measure spaces is natural and flexible and permits modeling problems that originate in different disciplines. ... Without this probability measure one could directly try to use the Gromov–Hausdorff distance [80, 81] for measuring dissimilarity between two objects.

MR2740101 Muskulus, Michael; Verduyn-Lunel, Sjoerd Wasserstein distances in the analysis of time series and dynamical systems. Phys. D 240 (2011), no. 1, 45–58, 37M10 (60G35 62M10). Zbl 1214.37054

Wasserstein distances in the analysis of time series ... - Science Direct

by M Muskulus - ‎2011 - ‎Cited by 28 - ‎Related articles

Jan 1, 2011 - A new approach based on Wasserstein distances, which are numerical costs of an optimal transportation problem, allows us to analyze ...

<——2011—————2011————— —— -50 —

MR2861675 Boissard, Emmanuel Simple bounds for convergence of empirical and occupation measures in 1-Wasserstein distance. Electron. J. Probab. 16 (2011), no. 83, 2296–2333. 60B10 (39B72). Zbl pre06049139. Published: NOV 15 2011

Simple Bounds for the Convergence of Empirical and Occupation ...

by E Boissard - ‎2011 - ‎Cited by 38 - ‎Related articles

Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting Markov chain in 1-Wasserstein distance are also given.

MR2843007 Eberle, Andreas Reflection coupling and Wasserstein contractivity without convexity. C. R. Math. Acad. Sci. Paris 349 (2011), no. 19-20, 1101–1104. 60J60. Zbl 05966335 . Published: OCT 2011

Reflection coupling and Wasserstein contractivity ... - Probability Theory

by A Eberle - ‎Cited by 34 - ‎Related articles

Sep 4, 2011 - Reflection coupling and Wasserstein contractivity without convexity. Andreas Eberle. University of Bonn, Institute for Applied Mathematics, ...

Cited by 60 Related articles

MR2842966 Adams, Stefan; Dirr, Nicolas; Peletier, Mark A.; Zimmer, Johannes From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage. Comm. Math. Phys. 307 (2011), no. 3, 791–815. (Reviewer: Boualem Djehiche) 60K35 (60F10). Zbl 05977587 . Published: NOV 2011

From a Large-Deviations Principle to the Wasserstein Gradient Flow: A ...

by S Adams - ‎2011 - ‎Cited by 71 - ‎Related articles

Sep 24, 2011 - Abstract: We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion ...

MR2838101 Sturm, Karl-Theodor Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions. Bull. Sci. Math. 135 (2011), no. 6-7, 795–802. 60B05 (46E30). Zbl 05970569 . Published: SEP-NOV 2011

Generalized Orlicz spaces and Wasserstein distances ... - Science Direct

by KT Sturm - ‎2011 - ‎Cited by 11 - ‎Related articles

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale ... For such functions ϑ we extend the concept of Orlicz spaces, defining the ...

A Lack of Ricci Bounds for the Entropic Measure on Wasserstein ...

by O Chodosh - ‎2011 - ‎Cited by 5 - ‎Related articles

Oct 31, 2011 - We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein space on the unit interval (probability measures on ...

A generalization of Hausdorff dimension applied to Hilbert cubes and ...

by B Kloeckner - ‎2011 - ‎Cited by 2 - ‎Related articles

May 2, 2011 - In a first part, we generalize the Hausdorff dimension by defining a ... as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 ...

2011 PDF

Wasserstein Regularization of Imaging Problems - Archive ouverte HAL

by J Rabin - ‎2011 - ‎Cited by 40 - ‎Related articles

May 8, 2011 - Wasserstein Regularization of Imaging Problems. ICIP 2011: 2011 IEEE ..... some other applications in image processing and computer vision.

Distribution's template estimate with Wasserstein metrics arXiv ...

by E Boissard - ‎2011 - ‎Cited by 9 - ‎Related articles

Dec 11, 2013 - Distribution's template estimate with Wasserstein metrics. Emmanuel Boissard, Thibaut Le Gouic, Jean-Michel Loubes. Institut de ...

Quasineutral Limit of the Vlasov-Poisson System with Massless ...

by D Han-Kwan - ‎2011 - ‎

In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the ...

Cited by 47 Related articles

Conformal Wasserstein Distance: II. Computational Aspects and ... arXiv

by Y Lipman - ‎2011 - ‎Cited by 31 - ‎Related articles

Mar 24, 2011 - Computational Aspects and Extensions ... and algorithms for computing the alignment of and distance between two disk type surfaces.

Conformal Wasserstein Distance: II. Computational Aspects and ...

Request PDF on ResearchGate | Conformal Wasserstein Distance: II. Computational Aspects and Extensions | This paper is a companion paper to [Lipman and ...

<——2011———2011—————60—

Convergence to equilibrium in Wasserstein distance for Fokker-Planck ...

by F Bolley - ‎2011 - ‎Cited by 62 - ‎Related articles

Oct 17, 2011 - Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations. We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

by Bolley, François; Gentil, Ivan; Guillin, Arnaud

Journal of Functional Analysis, 10/2011, Volume 263, Issue 8

Journal of Functional Analysis 263, 8 (2012) 2430-2457 We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to...

Journal Article: Full Text Online

[PDF] Non-asymptotic equivalence between W2 distance and H− 1 norm

R Peyre - Preprint, 2011 - Citeseer

… In this article I show that this equivalence can be integrated to get non-asymptotic comparison results between these distances. Notation … Let us give a few standard definitions which will be at the core of this work: • For fa (bounded) C1 real function on M, one denotes …

Cited by 4 Related articles dated 2013 modified 3030

www.i2m.univ-amu.fr › Nov2011 › exposes › marseille_jti_rabin

Approximate Wasserstein Metric and its Application to Image ...

PDF

Nov 24, 2011 - Approximate Wasserstein Metric and its Application to Image Processing. Julien Rabin ♢, with Gabriel Peyré ♤, Julie Delon ♥ and Marc Bernot ...

Comparison between $ W_2 $ distance and $\dot {H}^{-1 norm, and localisation of Wasserstein distance

arxiv.org › math

by R Peyre - ‎2011 - ‎Related articles

Apr 24, 2011 - Comparison between W_2 distance and \dot{H}^{-1} norm, and localisation of Wasserstein distance. Authors:Rémi Peyre. (Submitted on 24 Apr ...

It is well known that the quadratic Wasserstein distance W2(⋅,⋅) is formally equivalent, for infinitesimally small perturbations, to some weighted H−1 homogeneous Sobolev norm. In this article I show that this equivalence can be integrated to get non-asymptotic comparison results between these distances. Then I give an application of these results to prove that the W2 distance exhibits some localisation phenomenon: if μ and ν are measures on Rn and φ:Rn→R+ is some bump function with compact support, then under mild hypotheses, you can bound above the Wasserstein distance between φ⋅μ and φ⋅ν by an explicit multiple of W2(μ,ν).

Stability of the global attractor under Markov-Wasserstein noise

M Kell - arXiv preprint arXiv:1103.3401, 2011 - arxiv.org

We develop a" weak Ważewski principle" for discrete and continuous time dynamical

systems on metric spaces having a weaker topology to show that attractors can be continued

in a weak sense. After showing that the Wasserstein space of a proper metric space is …

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

A Takatsu - Osaka Journal of Mathematics, 2011 - projecteuclid.org

This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the

view point of the $ L^{2} $-Wasserstein geometry. The space of Gaussian measures is of

finite dimension, which allows to write down the explicit Riemannian metric which in turn …

[CITATION] Wasserstein geometry of Gaussian measures, to appear in Osaka J A Takatsu - 2011 - Math

Cited by 177 Related a0

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein L^

sub p^-distance (p> 2)(abbreviation: KRW L^ sub p^-distance) in a bounded region of

Euclidean plane satisfy a partial differential equation. We can also obtain the similar results …

Kantorovich-Rubinstein-Wasserstein Lp-距离 (p> 2)

沈银芳 - 科技信息, 2011 - cqvip.com

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Lp-距离（p〉2）. 《科技信息》2011年第15期 | 沈银芳浙江财经学院数学与统计学院浙江杭州310018

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Kantorovich-Rubinstein-Wasserstein Lp-距离（简记为：KRW-Lp距离）的一个精确表示 …

[Chinese Kantorovich-Rubinstein-Wasserstein Lp-distance (p> 2)\

A Trotter product formula for gradient flows in metric spaces ...

Entropic Burgers' equation via a minimizing movement ...

21, 2011 — This result is applied to establish convergence in the L ²-Wasserstein metric of the splitting method for some Fokker-Planck equations and ...

<——2011———2011——— — - 70———

webusers.imj-prg.fr › Publications_files › Gigli-Otto

PDF 2011

by N Gigli · 2011 · Cited by 14 — Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. Nicola Gigli∗, Felix Otto†. January 25, 2011. Abstract.

Wasserstein barycenter and its application to texture mixing

J Rabin, G Peyré, J Delon, M Bernot - International Conference on Scale …, 2011 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein …

Barycenters in the Wasserstein space

M Agueh, G Carlier - SIAM Journal on Mathematical Analysis, 2011 - SIAM

In this paper, we introduce a notion of barycenter in the Wasserstein space which

generalizes McCann's interpolation to the case of more than two measures. We provide

existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the …

Gromov–Wasserstein distances and the metric approach to object matching

A Takatsu - Osaka Journal of Mathematics, 2011 - projecteuclid.org

This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the

view point of the $ L^{2} $-Wasserstein geometry. The space of Gaussian measures is of

finite dimension, which allows to write down the explicit Riemannian metric which in turn …

[PDF] ucdavis.edu

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

Wasserstein regularization of imaging problem

J Rabin, G Peyré - 2011 18th IEEE International Conference on …, 2011 - ieeexplore.ieee.org

This paper introduces a novel and generic framework embedding statistical constraints for

variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport

to define penalty terms depending on statistics from images. To cope with the computation …

Reflection coupling and Wasserstein contractivity without convexity

A Eberle - Comptes Rendus Mathematique, 2011 - Elsevier

We note that even if convexity of the potential U fails locally, overdamped Langevin

diffusions in R d are contractions wrt the Kantorovich–Rubinstein-Wasserstein distance

based on an appropriately chosen concave distance function equivalent to the Euclidean …

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are isometric …

Conformal Wasserstein distances: Comparing surfaces in polynomial time

Y Lipman, I Daubechies - Advances in Mathematics, 2011 - Elsevier

We present a constructive approach to surface comparison realizable by a polynomial-time

algorithm. We determine the “similarity” of two given surfaces by solving a mass-

transportation problem between their conformal densities. This mass transportation problem …

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

<——2011———2011———— - 80—

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a

quantization error which is equal to a Wasserstein distortion. However, for the optimal

(Shannon-) entropy constrained quantization error a proof for a similar identity is still …

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its

empirical version, in the 1-Wasserstein metric, under the standing assumption that the

reference measure satisfies a transport-entropy inequality. We extend some results of F …

Comparison between distance and norm, and localisation of Wasserstein distance

R Peyre - arXiv preprint arXiv:1104.4631, 2011 - arxiv.org

It is well known that the quadratic Wasserstein distance $ W_2 (\mathord {\boldsymbol

{\cdot}},\mathord {\boldsymbol {\cdot}}) $ is formally equivalent, for infinitesimally small

perturbations, to some weighted $ H^{-1} $ homogeneous Sobolev norm. In this article I …

Distribution's template estimate with Wasserstein metrics

E Boissard, TL Gouic, JM Loubes - arXiv preprint arXiv:1111.5927, 2011 - arxiv.org

In this paper we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale functions

KT Sturm - Bulletin des sciences mathématiques, 2011 - Elsevier

Given a strictly increasing, continuous function ϑ: R+→ R+, based on the cost functional∫

X× X ϑ (d (x, y)) dq (x, y), we define the L ϑ-Wasserstein distance W ϑ (μ, ν) between

probability measures μ, ν on some metric space (X, d). The function ϑ will be assumed to …

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

[PDF] ups-tlse.fr

Problèmes D'interaction Discret-continu et Distances de Wasserstein

E Boissard - 2011 - thesesups.ups-tlse.fr

On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la

théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur

pour l'approximation particulaire des solutions de certaines équations aux dérivées …

Functional inequalities for the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer

We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and

generalize the Poincaré and logarithmic Sobolev inequality obtained for the Wasserstein …

Stability of the global attractor under Markov-Wasserstein noise

M Kell - arXiv preprint arXiv:1103.3401, 2011 - arxiv.org

We develop a" weak Ważewski principle" for discrete and continuous time dynamical

systems on metric spaces having a weaker topology to show that attractors can be continued

in a weak sense. After showing that the Wasserstein space of a proper metric space is …

<——2011———2011————— — - 90—

[PDF] Wasserstein distances for discrete measures and convergence in nonparametric mixture models

XL Nguyen - 2011 - Citeseer

We consider Wasserstein distance functionals for comparing between and assessing the

convergence of latent discrete measures, which serve as mixing distributions in hierarchical

and nonparametric mixture models. We explore the space of discrete probability measures …

" Exact" deviations in Wasserstein distance for empirical and occupation measures

E Boissard, T Gouic - 2011 - cds.cern.ch

We study the problem of so-called" exact" or non-asymptotic deviations between a reference

measure $\mu $ and its empirical version $ L_n $, in the $ p $-Wasserstein metric, $1\leq

p\leq 2$, under the standing assumption that $\mu $ satisfies a transport-entropy inequality …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals.

As an application, local and global well-posedness of different higher order non-linear …

Transportation cost inequalities for Wasserstein diffusions

J Shao - Bulletin des sciences mathematiques, 2011 - Elsevier

In this work we establish some types of transportation cost inequalities for two kinds of

probability measure-valued processes: Wasserstein diffusions and Fleming–Viot processes.

Besides, we prove that the Fleming–Viot processes generally donʼt satisfy the super …

Existence and Uniqueness of GEXIT curves via the Wasserstein Metric

S Kudekar, T Richardson… - 2011 IEEE Information …, 2011 - ieeexplore.ieee.org

In the analysis of iterative coding systems it is often necessary to compare two densities and

to measure how close they are. Sometimes it is convenient to compare their entropy or their

Battacharyya parameter. But sometimes a more powerful measure is required. The …

2011

flection coupling and Wasserstein contractivity without convexity

A Eberle - Comptes Rendus Mathematique, 2011 - Elsevier

We note that even if convexity of the potential U fails locally, overdamped Langevin

diffusions in R d are contractions wrt the Kantorovich–Rubinstein-Wasserstein distance

based on an appropriately chosen concave distance function equivalent to the Euclidean …

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Journal of Differential Equations, 2013 - Elsevier

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein

space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the

Moreau–Yosida approximation and denote it by H τ. We show that solutions of the …

[PDF] Deconvolution for the Wasserstein Metric and Geometric Inference

CCFCJ Dedecker, B Michel - 2011 - hal.inria.fr

Recently,[4] have defined a distance function to measures to answer geometric inference

problems in a probabilistic setting. According to their result, the topological properties of a

shape can be recovered by using the distance to a known measure ν, if ν is close enough to …

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein L^

sub p^-distance (p> 2)(abbreviation: KRW L^ sub p^-distance) in a bounded region of

Euclidean plane satisfy a partial differential equation. We can also obtain the similar results …

[PDF] Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

C Selinger - Theory of Stochastic Processes, 2011 - imath.kiev.ua

Via elements of second order differential geometry on smooth Wasserstein spaces of

probability measures we give an explicit formula for a Laplacian in the case that the

Wasserstein space is based on the unit circle. The Laplacian on this infinite dimensional …

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

<——2011———2011————100—-

O Chodosh - 2011 - cds.cern.ch

This is a condensed form of the author's essay, which can be found at [arXiv: 1105.2883].

We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein

space on the unit interval (probability measures on the unit interval equipped with the 2 …

2011 see 2010

Wasserstein geometry of Gaussian measures - Project Euclid

https://projecteuclid.org › volume-48 › issue-4 › ojm

by A Takatsu · 2011 · Cited by 162 — This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the L2 L 2 -Wasserstein geometry. The space of Gaussian ...

[CITATION] Wasserstein geometry of Gaussian measures, to appear in Osaka J

A Takatsu - 2011 - Math

Takatsu : Wasserstein geometry of Gaussian measures

projecteuclid.org › euclid.ojm by A Takatsu · 2011 · Cited by 124 — The space of Gaussian measures is of finite dimension, which allows to write down the explicit Riemannian metric which in turn induces the L2-Wasserstein ...

[CITATION] Wasserstein geometry of Gaussian measures, to appear in Osaka J

A Takatsu - 2011 - Math

advances made by Brenier [4] and McCann [16] in the 90's, and also implicit in …

2011 [PDF] core.ac.uk

[PDF] Deconvolution for the Wasserstein Metric and Geometric Inference

CCFCJ Dedecker, B Michel - 2011 - core.ac.uk

Recently,[4] have defined a distance function to measures to answer geometric inference problems in a probabilistic setting. According to their result, the topological properties of a shape can be recovered by using the distance to a known measure ν, if ν is close enough to …

Barycentre de Wasserstein

J RABIN, G PEYRÉ, J DELON - smai.emath.fr

Contexte De nombreuses applications en vision par ordinateur ou en traitement d'images

requierent une étape préliminaire d'apprentissage des statistiques “moyennes” des

caractéristiques d'une classe d'objets. Cette problématique a été principalement étudié dans …

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the

solution concentrates onto the two wells, resulting into a limiting system that is a pair of

ordinary differential equations for the density at the two wells. This convergence has been

proved in Peletier et al.(SIAM J Math Anal, 42 (4): 1805–1825, 2010), using the linear …

Régularisation de Wasserstein. Application au Transfert de Couleur

R Julien, G Peyré - 2011 - hal.archives-ouvertes.fr

Ce papier introduit une nouvelle approche méthodologique pour la résolution de problèmes

variationnels sous contraintes statistiques en grande dimension. Nous nous plaçons dans le

cadre de la théorie du transport optimal de Monge-Kantorovich pour définir des termes de …

]French Regularization of Wasserstein. Application to Color Transfer]

[CITATION] Régularisation de Wasserstein. application au transfert de couleur

J Rabin, G Peyré - 2011 - Gretsi

Functional inequalities for the Wasserstein Dirichlet form

[PDF] nozdr.ru

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer

We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and

generalize the Poincaré and logarithmic Sobolev inequality obtained for the Wasserstein …

2011

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - 2011 - cds.cern.ch

This is a condensed form of the author's essay, which can be found at [arXiv: 1105.2883].

We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein

space on the unit interval (probability measures on the unit interval equipped with the 2 …

2011

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

2011

[PDF] imath.kiev.ua

[PDF] Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

C Selinger - Theory of Stochastic Processes, 2011 - imath.kiev.ua

Via elements of second order differential geometry on smooth Wasserstein spaces of

probability measures we give an explicit formula for a Laplacian in the case that the

Wasserstein space is based on the unit circle. The Laplacian on this infinite dimensional …

Wasserstein distances in the analysis of time series and dynamical systems

<——2011———2011—————110—-

M Muskulus, S Verduyn-Lunel - Physica D: Nonlinear Phenomena, 2011 - Elsevier

A new appr

2011 [PDF] archives-ouvertes.fr

Wasserstein barycenter and its application to texture mixing

J Rabin, G Peyré, J Delon, M Bernot - International Conference on Scale …, 2011 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein …

Barycenters in the Wasserstein space

hal.archives-ouvertes.fr › hal-00637399 › document

PDF

Nov 1, 2011 — Wasserstein space by simply replacing the squared euclidean distance with the squared ... The properties of barycenters in the Wasserstein space ... In the previous L∞ estimate, it is actually not necessary to require that all ...

by M Agueh · ‎2011 · ‎Cited by 480 · ‎Related articles

2011 [PDF] archives-ouvertes.fr

Barycenters in the Wasserstein space

M Agueh, G Carlier - SIAM Journal on Mathematical Analysis, 2011 - SIAM

In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann's interpolation to the case of more than two measures. We provide existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the …

2011 [PDF] arxiv.org

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-) Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In particular, we give a detailed …

2011

Wasserstein geometry of Gaussian measures

A Takatsu - Osaka Journal of Mathematics, 2011 - projecteuclid.org

This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the $ L^{2} $-Wasserstein geometry. The space of Gaussian measures is of finite dimension, which allows to write down the explicit Riemannian metric which in turn …

Wasserstein geometry of Gaussian measures - Project Euclid

projecteuclid.org › euclid.ojm

by A Takatsu · 2011 · Cited by 127 — "Wasserstein geometry of Gaussian measures." Osaka J. Math. 48 (4) 1005 - 1026, December 2011. Information.

[CITATION] Wasserstein geometry of Gaussian measures, to appear in Osaka J

A Takatsu - 2011 - Math

Behaviors of ϕ-exponential distributions in Wasserstein ... - arXiv

2011 see 2013

by A Takatsu · 2011 · Cited by 11 — Title:Behaviors of ϕ-exponential distributions in Wasserstein geometry and an evolution equation ; MSC classes: 60D05, 94A17 ; Cite as: arXiv: ...

[CITATION] Behaviors of ϕ-exponential distributions in Wasserstein geometry and an evolution equation, Preprint (2011)

A Takatsu - Available at arXiv

Distribution's template estimate with Wasserstein metrics

E Boissard, TL Gouic, JM Loubes - arXiv preprint arXiv:1111.5927, 2011 - arxiv.org

In this paper we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

[CITATION] Distribution's template estimate with Wasserstein metrics, ArXiv e-prints(2011)

E Boissard, T Le Gouic, JM Loubes

Generalized Wasserstein Dice Score, Distributionally Robust Deep Learning, and Ranger for brain tumor segmentation: BraTS 2020 challenge

L Fidon, S Ourselin, T Vercauteren - arXiv preprint arXiv:2011.01614, 2020 - arxiv.org

Training a deep neural network is an optimization problem with four main ingredients: the

design of the deep neural network, the per-sample loss function, the population loss

function, and the opt

imizer. However, methods developed to compete in recent BraTS …

<——2011———2011————— — - 120—-

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are isometric …

2011

Passing to the Limit in a Wasserstein Gradient Flow: From ...

by S Arnrich · 2011 · Cited by 61 — Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction. ... This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells.

[CITATION] Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

Distribution's template estimate with Wasserstein metrics

E Boissard, TL Gouic, JM Loubes - arXiv preprint arXiv:1111.5927, 2011 - arxiv.org

In this paper we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals.

As an application, local and global well-posedness of different higher order non-linear …

2011

Passing to the Limit in a Wasserstein Gradient Flow: From ...

by S Arnrich · 2011 · Cited by 60 — [Submitted on 6 Feb 2011 (v1), last revised 16 Apr 2011 (this version, v2)]. Title:Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction.

[CITATION] Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

SAAMM Peletier, GSM Veneroni - 20

2011 [PDF] imath.kiev.ua

[PDF] Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

C Selinger - Theory of Stochastic Processes, 2011 - imath.kiev.ua

Via elements of second order differential geometry on smooth Wasserstein spaces of

probability measures we give an explicit formula for a Laplacian in the case that the

Wasserstein space is based on the unit circle. The Laplacian on this infinite dimensional

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

Conformal Wasserstein distances: Comparing surfaces in polynomial time

Y Lipman, I Daubechies - Advances in Mathematics, 2011 - Elsevier

We present a constructive approach to surface comparison realizable by a polynomial-time

algorithm. We determine the “similarity” of two given surfaces by solving a mass-

transportation problem between their conformal densities. This mass transportation problem …

Wasserstein distances in the analysis of time series and dynamical systems

M Muskulus, S Verduyn-Lunel - Physica D: Nonlinear Phenomena, 2011 - Elsevier

A new approach based on Wasserstein distances, which are numerical costs of an optimal

transportation problem, allows us to analyze nonlinear phenomena in a robust manner. The

long-term behavior is reconstructed from time series, resulting in a probability distribution …

Cited by 44 Related articles All 6 versions
<——2011———2011————— — - 130—-

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale functions

KT Sturm - Bulletin des sciences mathématiques, 2011 - Elsevier

Given a strictly increasing, continuous function ϑ: R+→ R+, based on the cost functional∫

X× X ϑ (d (x, y)) dq (x, y), we define the L ϑ-Wasserstein distance W ϑ (μ, ν) between

probability measures μ, ν on some metric space (X, d). The function ϑ will be assumed to …

[PDF] Wasserstein distances for discrete measures and convergence in nonparametric mixture models

XL Nguyen - 2011 - Citeseer

We consider Wasserstein distance functionals for comparing between and assessing the

convergence of latent discrete measures, which serve as mixing distributions in hierarchical

and nonparametric mixture models. We explore the space of discrete probability measures …

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are isometric …

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a

quantization error which is equal to a Wasserstein distortion. However, for the optimal

(Shannon-) entropy constrained quantization error a proof for a similar identity is still …

" Exact" deviations in Wasserstein distance for empirical and occupation measures

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a

quantization error which is equal to a Wasserstein distortion. However, for the optimal

(Shannon-) entropy constrained quantization error a proof for a similar identity is still …

E Boissard, T Gouic - 2011 - cds.cern.ch

We study the problem of so-called" exact" or non-asymptotic deviations between a reference

measure $\mu $ and its empirical version $ L_n $, in the $ p $-Wasserstein metric, $1\leq

p\leq 2$, under the standing assumption that $\mu $ satisfies a transport-entropy inequality …

Conformal Wasserstein Distance: Comparing disk and sphere-type surfaces in polynomial time II, computational aspects

Y Lipman, J Puente, I Daubechies - 2011 - cds.cern.ch

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical

procedures and algorithms for computing the alignment of and distance between two disk

type surfaces. We furthermore generalize the framework to support sphere-type surfaces …

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

Page 1. www.ccsenet.org/jmr Journal of Mathematics Research Vol. 3, No. 4;

November 2011 Optimal Couplings of Kantorovich-Rubinstein-Wasserstein Lp-distance

Yinfang Shen (Corresponding author) Institute of Mathematics …

Existence and Uniqueness of GEXIT curves via the Wasserstein Metric

S Kudekar, T Richardson… - 2011 IEEE Information …, 2011 - ieeexplore.ieee.org

In the analysis of iterative coding systems it is often necessary to compare two densities and

to measure how close they are. Sometimes it is convenient to compare their entropy or their

Battacharyya parameter. But sometimes a more powerful measure is required. The …

[PDF] Deconvolution for the Wasserstein Metric and Geometric Inference

CCFCJ Dedecker, B Michel - 2011 - hal.inria.fr

Recently,[4] have defined a distance function to measures to answer geometric inference

problems in a probabilistic setting. According to their result, the topological properties of a

shape can be recovered by using the distance to a known measure ν, if ν is close enough to …

<——2011———2011————— — - 140—

Comparison between distance and norm, and localisation of Wasserstein distance

R Peyre - arXiv preprint arXiv:1104.4631, 2011 - arxiv.org

It is well known that the quadratic Wasserstein distance $ W_2 (\mathord {\boldsymbol

{\cdot}},\mathord {\boldsymbol {\cdot}}) $ is formally equivalent, for infinitesimally small

perturbations, to some weighted $ H^{-1} $ homogeneous Sobolev norm. In this article I …

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a

quantization error which is equal to a Wasserstein distortion. However, for the optimal

(Shannon-) entropy constrained quantization error a proof for a similar identity is still …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals.

As an application, local and global well-posedness of different higher order non-linear …

2011

A Trotter product formula for gradient flows in metric spaces

Jan 21, 2011 — This result is applied to establish convergence in the L ²-Wasserstein metric of the splitting method for some Fokker-Planck equations and ..

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are isometric …

2011

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - 2011 - cds.cern.ch

This is a condensed form of the author's essay, which can be found at [arXiv: 1105.2883].

We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein

space on the unit interval (probability measures on the unit interval equipped with the 2 …

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals.

As an application, local and global well-posedness of different higher order non-linear …

Simple bounds for convergence of empirical and occupation measures in 1- Wasserstein distance

Author:Boissard E.
Article, 2011
Publication:Electronic Journal of Probability, 16, 2011 12 15, 2296
Publisher:2011

2011 see 2012

https://www.semanticscholar.org › paper › Passing-to-the-...

[PDF] Passing to the limit in a Wasserstein gradient flow

Feb 6, 2011 — We study a singular-limit problem arising in the modelling of chemical reactions. At finite $${\varepsilon\, > \,0,}$$ the system is ...

[CITATION] Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

SAAMM Peletier, GSM Veneroni - 2011
<——2011———2011———150-

Wasserstein regularization of imaging problem

J Rabin, G Peyré - 2011 18th IEEE International Conference on …, 2011 - ieeexplore.ieee.org

This paper introduces a novel and generic framework embedding statistical constraints for

variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport

to define penalty terms depending on statistics from images. To cope with the computation …

2011

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - 2011 - cds.cern.ch

This is a condensed form of the author's essay, which can be found at [arXiv: 1105.2883].

We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein

space on the unit interval (probability measures on the unit interval equipped with the 2 …

2011

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its

empirical version, in the 1-Wasserstein metric, under the standing assumption that the

reference measure satisfies a transport-entropy inequality. We extend some results of F …

2011

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein L^

sub p^-distance (p> 2)(abbreviation: KRW L^ sub p^-distance) in a bounded region of

Euclidean plane satisfy a partial differential equation. We can also obtain the similar results …

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F …

2011

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time existence and uniqueness of Wasserstein gradient flows for higher order energy functionals. As an application, local and global well-posedness of different higher order non-linear …

2011

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - 2011 - cds.cern.ch

This is a condensed form of the author's essay, which can be found at [arXiv: 1105.2883]. We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein space on the unit interval (probability measures on the unit interval equipped with the 2 …

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

… We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein Lp−distance (p > 2) (abbrevia- tion: KRW Lp−distance) in a … Keywords: Monge-Kantorovich Problem, KRW Lp−distance, Optimal coupling, Partial differential equation 1. Introduction …

Wasserstein regularization of imaging problem

J Rabin, G Peyré - 2011 18th IEEE International Conference on …, 2011 - ieeexplore.ieee.org

This paper introduces a novel and generic framework embedding statistical constraints for

variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport

to define penalty terms depending on statistics from images. To cope with the computation …

<——2011———2011—— — - 160—

[PDF] Cadlág stability and approximation of reversible coalescing-fragmentating Wasserstein dynamics

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - researchgate.net

We construct coalescing-fragmentating Wasserstein dynamics [27] for any initial condition

and interacting potential by a finite particle approximation. We show that such a model

admits a description by a family of continuous semimartingales, where every semimartingale …

[PDF] Transport equation with nonlocal velocity in wasserstein spaces: existence, uniqueness and numerical schemes

B Piccoli, F Rossi - Preprint, 2011 - researchgate.net

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We prove existence and uniqueness of the …

2011 [PDF] projecteuclid.org

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F …

2011

[PDF] Wasserstein distances for discrete measures and convergence in nonparametric mixture models

XL Nguyen - 2011 - Citeseer

We consider Wasserstein distance functionals for comparing between and assessing the convergence of latent discrete measures, which serve as mixing distributions in hierarchical and nonparametric mixture models. We explore the space of discrete probability measures …

Stability of the global attractor under Markov-Wasserstein noise

M Kell - arXiv preprint arXiv:1103.3401, 2011 - arxiv.org

We develop a" weak Ważewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a proper metric space is …

[PDF] mathnet.ru

Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

C Selinger - Theory of Stochastic Processes, 2011 - mathnet.ru

Via elements of second order differential geometry on smooth Wasserstein spaces of probability measures we give an explicit formula for a Laplacian in the case that the Wasserstein space is based on the unit circle. The Laplacian on this infinite dimensional …

A spectral notion of Gromov-Wasserstein distances and ...

22011

https://hekyll.services.adelaide.edu.au › dspace › handle

by F Memoli · 2011 · Cited by 53 — Keywords: Shape and data analysis; Spectral methods; Gromov–Wasserstein distance; Gromov–Hausdorff distance; Heat kernel; Spectral invariants; Diffusion ...

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a quantization error which is equal to a Wasserstein distortion. However, for the optimal (Shannon-) entropy constrained quantization error a proof for a similar identity is still …

2011

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-) Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In particular, we give a detailed …

2011

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance (p> 2)(abbreviation: KRW L^ sub p^-distance) in a bounded region of Euclidean plane satisfy a partial differential equation. We can also obtain the similar results …

<——2011———2011—— — - 170—

Comparison between distance and norm, and localisation of Wasserstein distance

R Peyre - arXiv preprint arXiv:1104.4631, 2011 - arxiv.org

It is well known that the quadratic Wasserstein distance $ W_2 (\mathord {\boldsymbol {\cdot}},\mathord {\boldsymbol {\cdot}}) $ is formally equivalent, for infinitesimally small perturbations, to some weighted $ H^{-1} $ homogeneous Sobolev norm. In this article I …

Reflection coupling and Wasserstein contractivity without convexity

A Eberle - Comptes Rendus Mathematique, 2011 - Elsevier

We note that even if convexity of the potential U fails locally, overdamped Langevin diffusions in R d are contractions wrt the Kantorovich–Rubinstein-Wasserstein distance based on an appropriately chosen concave distance function equivalent to the Euclidean …

2011

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale functions

KT Sturm - Bulletin des sciences mathématiques, 2011 - Elsevier

Given a strictly increasing, continuous function ϑ: R+→ R+, based on the cost functional∫ X× X ϑ (d (x, y)) dq (x, y), we define the L ϑ-Wasserstein distance W ϑ (μ, ν) between probability measures μ, ν on some metric space (X, d). The function ϑ will be assumed to …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time existence and uniqueness of Wasserstein gradient flows for higher order energy functionals. As an application, local and global well-posedness of different higher order non-linear …

2011

Wasserstein distances in the analysis of time series and dynamical systems

M Muskulus, S Verduyn-Lunel - Physica D: Nonlinear Phenomena, 2011 - Elsevier

A new approach based on Wasserstein distances, which are numerical costs of an optimal transportation problem, allows us to analyze nonlinear phenomena in a robust manner. The long-term behavior is reconstructed from time series, resulting in a probability distribution …

2011

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale functions

KT Sturm - Bulletin des sciences mathématiques, 2011 - Elsevier

Given a strictly increasing, continuous function ϑ: R+→ R+, based on the cost functional∫

X× X ϑ (d (x, y)) dq (x, y), we define the L ϑ-Wasserstein distance W ϑ (μ, ν) between

probability measures μ, ν on some metric space (X, d). The function ϑ will be assumed to …

2011

Barycenters in the Wasserstein space

M Agueh, G Carlier - SIAM Journal on Mathematical Analysis, 2011 - SIAM

In this paper, we introduce a notion of barycenter in the Wasserstein space which

generalizes McCann's interpolation to the case of more than two measures. We provide

existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the …

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

Problèmes d'interaction discret-continu et distances de Wasserstein

E Boissard - 2011 - thesesups.ups-tlse.fr

On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la

théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur

pour l'approximation particulaire des solutions de certaines équations aux dérivées …

<——2011———2011—— — - 180-—

2011

Régularisation de Wasserstein. application au transfert de couleur

R Julien, G Peyré - GRETSI'11, 2011 - hal.archives-ouvertes.fr

Ce papier introduit une nouvelle approche méthodologique pour la résolution de problèmes

variationnels sous contraintes statistiques en grande dimension. Nous nous plaçons dans le

cadre de la théorie du transport optimal de Monge-Kantorovich pour définir des termes de …

2011

Barycentre de Wasserstein

J RABIN, G PEYRÉ, J DELON - smai.emath.fr

Contexte De nombreuses applications en vision par ordinateur ou en traitement d'images

requierent une étape préliminaire d'apprentissage des statistiques “moyennes” des

caractéristiques d'une classe d'objets. Cette problématique a été principalement étudié dans …

2011 [PDF] nozdr.ru

Functional inequalities for the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer

We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and

generalize the Poincaré and logarithmic Sobolev inequality obtained for the Wasserstein …

2011

Reflection coupling and Wasserstein contractivity without convexity

A Eberle - Comptes Rendus Mathematique, 2011 - Elsevier

We note that even if convexity of the potential U fails locally, overdamped Langevin

diffusions in R d are contractions wrt the Kantorovich–Rubinstein-Wasserstein distance

based on an appropriately chosen concave distance function equivalent to the Euclidean …

Wasserstein barycenter and its application to texture mixing

J Rabin, G Peyré, J Delon, M Bernot - International Conference on Scale …, 2011 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein …

2011

Wasserstein barycenter and its application to texture mixing

J Rabin, G Peyré, J Delon, M Bernot - International Conference on Scale …, 2011 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein …

2011

Régularisation de Wasserstein. application au transfert de couleur

R Julien, G Peyré - GRETSI'11, 2011 - hal.archives-ouvertes.fr

Ce papier introduit une nouvelle approche méthodologique pour la résolution de problèmes

variationnels sous contraintes statistiques en grande dimension. Nous nous plaçons dans le

cadre de la théorie du transport optimal de Monge-Kantorovich pour définir des termes de …

2011 Research article
Wasserstein distances in the analysis of time series and dynamical systems
Physica D: Nonlinear Phenomena1 January 2011...

Michael MuskulusSjoerd Verduyn-Lunel

2011 [PDF] projecteuclid.org

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its

empirical version, in the 1-Wasserstein metric, under the standing assumption that the

reference measure satisfies a transport-entropy inequality. We extend some results of F …

2011

" Exact" deviations in Wasserstein distance for empirical and occupation measures

E Boissard, T Gouic - 2011 - cds.cern.ch

We study the problem of so-called" exact" or non-asymptotic deviations between a reference

measure $\mu $ and its empirical version $ L_n $, in the $ p $-Wasserstein metric, $1\leq

p\leq 2$, under the standing assumption that $\mu $ satisfies a transport-entropy inequality …

<——2011———2011—— — - 190—

2011

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

2011

Transportation cost inequalities for Wasserstein diffusions

J Shao - Bulletin des sciences mathematiques, 2011 - Elsevier

In this work we establish some types of transportation cost inequalities for two kinds of

probability measure-valued processes: Wasserstein diffusions and Fleming–Viot processes.

Besides, we prove that the Fleming–Viot processes generally donʼt satisfy the super …

2011

[PDF] Transport equation with nonlocal velocity in wasserstein spaces: existence, uniqueness and numerical schemes

B Piccoli, F Rossi - Preprint, 2011 - researchgate.net

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We prove existence and uniqueness of the …

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

2011 [PDF] psu.edu

[PDF] Wasserstein distances for discrete measures and convergence in nonparametric mixture models

XL Nguyen - 2011 - Citeseer

We consider Wasserstein distance functionals for comparing between and assessing the

convergence of latent discrete measures, which serve as mixing distributions in hierarchical

and nonparametric mixture models. We explore the space of discrete probability measures …

2011

Passing to the limit in a Wasserstein gradient flow: from ...

link.springer.com › article › 10

Aug 30, 2011 · We study a singular-limit problem arising in the modelling of chemical reactions. At finite $${\\varepsilon\\, > \\,0,}$$ the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by $${1 / \\varepsilon,}$$ and in the limit $${\\varepsilon\\to0,}$$ the solution concentrates onto the two wells, resulting into a ...

Author: Steffen Arnrich, Alexander Mielke, Mark A. Peletier, Giuseppe Savaré, Marco Veneroni

Cited by: 63

[CITATION] Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its

empirical version, in the 1-Wasserstein metric, under the standing assumption that the

reference measure satisfies a transport-entropy inequality. We extend some results of F …

Transportation cost inequalities for Wasserstein diffusions

J Shao - Bulletin des sciences mathematiques, 2011 - Elsevier

In this work we establish some types of transportation cost inequalities for two kinds of

probability measure-valued processes: Wasserstein diffusions and Fleming–Viot processes.

Besides, we prove that the Fleming–Viot processes generally donʼt satisfy the super …

Wasserstein regularization of imaging problem

J Rabin, G Peyré - 2011 18th IEEE International Conference on …, 2011 - ieeexplore.ieee.org

This paper introduces a novel and generic framework embedding statistical constraints for

variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport

to define penalty terms depending on statistics from images. To cope with the computation …

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

Cited by 89 Related articles All 33 versions
<——2011———2011—— — - 200—

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale functions

KT Sturm - Bulletin des sciences mathématiques, 2011 - Elsevier

Given a strictly increasing, continuous function ϑ: R+→ R+, based on the cost functional∫

X× X ϑ (d (x, y)) dq (x, y), we define the L ϑ-Wasserstein distance W ϑ (μ, ν) between

probability measures μ, ν on some metric space (X, d). The function ϑ will be assumed to …

2011

Conformal Wasserstein Distance: Comparing disk and sphere-type surfaces in polynomial time II, computational aspects

Y Lipman, J Puente, I Daubechies - 2011 - cds.cern.ch

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical

procedures and algorithms for computing the alignment of and distance between two disk

type surfaces. We furthermore generalize the framework to support sphere-type surfaces …

2011

[HTML] Optimal vector quantization in terms of Wasserstein distance

W Kreitmeier - Journal of multivariate analysis, 2011 - Elsevier

The optimal quantizer in memory-size constrained vector quantization induces a

quantization error which is equal to a Wasserstein distortion. However, for the optimal

(Shannon-) entropy constrained quantization error a proof for a similar identity is still …

2011

[PDF] On asymptotics for Vaserstein coupling of a Markov chain

OA Butkovsky, AY Veretennikov - 2011 - newton.ac.uk

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

2011

[PDF] newton.ac.uk

[PDF] On asymptotics for Vaserstein coupling of a Markov chain

OA Butkovsky, AY Veretennikov - 2011 - newton.ac.uk

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

2011

[PDF] On asymptotics for Vaserstein coupling of a Markov chain

OA Butkovsky, AY Veretennikov - 2011 - pdfs.semanticscholar.org

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

[PDF] On asymptotics for Vaserstein coupling of a Markov chain

OA Butkovsky, AY Veretennikov - 2011 - Citeseer

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

On asymptotics of Vaserstein's coupling for a. Markov chain. O.A.Butkovsky. ∗. & A.Yu.Veretennikov. †. Abstract. In this paper rate of convergence to stationary ...

July 25-29 2011

STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume: 123 Issue: 9 Pages: 3518-3541 DOI: 10.1016/j.spa.2013.04.016 Published: SEP 2013

2011

Functional inequalities for the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer

We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and

generalize the Poincaré and logarithmic Sobolev inequality obtained for the Wasserstein …

2011

Stability of the global attractor under Markov-Wasserstein noise

M Kell - arXiv preprint arXiv:1103.3401, 2011 - arxiv.org

We develop a" weak Ważewski principle" for discrete and continuous time dynamical

systems on metric spaces having a weaker topology to show that attractors can be continued

in a weak sense. After showing that the Wasserstein space of a proper metric space is …

2011

Stability of the global attractor under Markov-Wasserstein noise

M Kell - arXiv preprint arXiv:1103.3401, 2011 - arxiv.org

We develop a" weak Ważewski principle" for discrete and continuous time dynamical

systems on metric spaces having a weaker topology to show that attractors can be continued

in a weak sense. After showing that the Wasserstein space of a proper metric space is …

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

<——2011———2011—— — - 210—

2011 [PDF] arxiv.org

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

2011

Existence and Uniqueness of GEXIT curves via the Wasserstein Metric

S Kudekar, T Richardson… - 2011 IEEE Information …, 2011 - ieeexplore.ieee.org

In the analysis of iterative coding systems it is often necessary to compare two densities and

to measure how close they are. Sometimes it is convenient to compare their entropy or their

Battacharyya parameter. But sometimes a more powerful measure is required. The …

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are isometric …

2011

Wasserstein distances in the analysis of time series and dynamical systems

M Muskulus, S Verduyn-Lunel - Physica D: Nonlinear Phenomena, 2011 - Elsevier

A new approach based on Wasserstein distances, which are numerical costs of an optimal

transportation problem, allows us to analyze nonlinear phenomena in a robust manner. The

long-term behavior is reconstructed from time series, resulting in a probability distribution …

Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance

E Boissard - Electronic Journal of Probability, 2011 - projecteuclid.org

We study the problem of non-asymptotic deviations between a reference measure and its

empirical version, in the 1-Wasserstein metric, under the standing assumption that the

reference measure satisfies a transport-entropy inequality. We extend some results of F …

2011

Stability of the global attractor under Markov-Wasserstein noise

M Kell - arXiv preprint arXiv:1103.3401, 2011 - arxiv.org

We develop a" weak Ważewski principle" for discrete and continuous time dynamical

systems on metric spaces having a weaker topology to show that attractors can be continued

in a weak sense. After showing that the Wasserstein space of a proper metric space is …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals.

As an application, local and global well-posedness of different higher order non-linear …

2011

Existence and Uniqueness of GEXIT curves via the Wasserstein Metric

S Kudekar, T Richardson… - 2011 IEEE Information …, 2011 - ieeexplore.ieee.org

In the analysis of iterative coding systems it is often necessary to compare two densities and

to measure how close they are. Sometimes it is convenient to compare their entropy or their

Battacharyya parameter. But sometimes a more powerful measure is required. The …

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - search.proquest.com

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein L^

sub p^-distance (p> 2)(abbreviation: KRW L^ sub p^-distance) in a bounded region of

Euclidean plane satisfy a partial differential equation. We can also obtain the similar results …

A Lack of Ricci Bounds for the Entropic Measure constructed by von Renesse-Sturm on Wasserstein space over the Interval

O Chodosh - 2011 - cds.cern.ch

This is a condensed form of the author's essay, which can be found at [arXiv: 1105.2883].

We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein

space on the unit interval (probability measures on the unit interval equipped with the 2 …

<——2011———2011——— 220—

2011 ebook
Optimal vector quantization in terms of Wasserstein distance

Author:Wolfgang Kreitmeier
eBook, 2011
English
Publisher:Universität Passau, Passau, 2011

Wasserstein barycenter and its application to texture mixing

J Rabin, G Peyré, J Delon, M Bernot - … Conference on Scale Space and …, 2011 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein …

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

Reflection coupling and Wasserstein contractivity without convexity

A Eberle - Comptes Rendus Mathematique, 2011 - Elsevier

We note that even if convexity of the potential U fails locally, overdamped Langevin

diffusions in R d are contractions wrt the Kantorovich–Rubinstein-Wasserstein distance

based on an appropriately chosen concave distance function equivalent to the Euclidean …

Generalized Orlicz spaces and Wasserstein distances for convex–concave scale functions

KT Sturm - Bulletin des sciences mathématiques, 2011 - Elsevier

Given a strictly increasing, continuous function ϑ: R+→ R+, based on the cost functional∫

X× X ϑ (d (x, y)) dq (x, y), we define the L ϑ-Wasserstein distance W ϑ (μ, ν) between

probability measures μ, ν on some metric space (X, d). The function ϑ will be assumed to …

2011

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

[PDF] Wasserstein distances for discrete measures and convergence in nonparametric mixture models

XL Nguyen - 2011 - Citeseer

We consider Wasserstein distance functionals for comparing between and assessing the

convergence of latent discrete measures, which serve as mixing distributions in hierarchical

and nonparametric mixture models. We explore the space of discrete probability measures …

" Exact" deviations in Wasserstein distance for empirical and occupation measures

E Boissard, T Gouic - 2011 - cds.cern.ch

We study the problem of so-called" exact" or non-asymptotic deviations between a reference

measure $\mu $ and its empirical version $ L_n $, in the $ p $-Wasserstein metric, $1\leq

p\leq 2$, under the standing assumption that $\mu $ satisfies a transport-entropy inequality …

[PDF] Transport equation with nonlocal velocity in wasserstein spaces: existence, uniqueness and numerical schemes

B Piccoli, F Rossi - Preprint, 2011 - researchgate.net

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We prove existence and uniqueness of the …

Conformal Wasserstein Distance: Comparing disk and sphere-type surfaces in polynomial time II, computational aspects

Y Lipman, J Puente, I Daubechies - 2011 - cds.cern.ch

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical

procedures and algorithms for computing the alignment of and distance between two disk

type surfaces. We furthermore generalize the framework to support sphere-type surfaces …

<——2011———2011—— — - 230—

[PDF] Deconvolution for the Wasserstein Metric and Geometric Inference

CCFCJ Dedecker, B Michel - 2011 - core.ac.uk

Recently,[4] have defined a distance function to measures to answer geometric inference

problems in a probabilistic setting. According to their result, the topological properties of a

shape can be recovered by using the distance to a known measure ν, if ν is close enough to …

McInerney argues that Greece did not operate in a bovine idiom, as did some of the

historical African herding cultures, but worked as a settled, agricultural, manufacturing,

trading society that retained a “bovine register.” For the Greeks, keeping cattle engendered …

Cahn–Hilliard and thin film equations with nonlinear mobility ...

https://www.sciencedirect.com › science › article › pii › pdf

by S Lisini · 2012 · Cited by 45 — mobility as gradient flows in weighted-Wasserstein metrics ... Thin film equation ... of fourth order, like the Cahn–Hilliard and certain thin film ... supported by the INDAM-GNAMPA project 2011 “Measure solution of differential ...

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

Cited by 1 Related articlesƒ

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

Cited by 1 Related articles see 2012

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

Cited by 1 Related articles see 2012

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

Barycenters in the Wasserstein space

2011

M Agueh, G Carlier - SIAM Journal on Mathematical Analysis, 2011 - SIAM

In this paper, we introduce a notion of barycenter in the Wasserstein space which

generalizes McCann's interpolation to the case of more than two measures. We provide

existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the …

Gromov–Wasserstein distances and the metric approach to object matching

F Mémoli - Foundations of computational mathematics, 2011 - Springer

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff

distance which have the goal of modeling and tackling the practical problems of object

matching and comparison. Objects are viewed as metric measure spaces, and based on …

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

S Adams, N Dirr, MA Peletier, J Zimmer - … in Mathematical Physics, 2011 - Springer

We study the connection between a system of many independent Brownian particles on one

hand and the deterministic diffusion equation on the other. For a fixed time step h> 0, a large-

deviations rate functional J h characterizes the behaviour of the particle system at t= h in …

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

Functional inequalities for the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer

We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and

generalize the Poincaré and logarithmic Sobolev inequality obtained for the Wasserstein …

[PDF] Deconvolution for the Wasserstein Metric and Geometric Inference

CCFCJ Dedecker, B Michel - 2011 - core.ac.uk

Recently,[4] have defined a distance function to measures to answer geometric inference

problems in a probabilistic setting. According to their result, the topological properties of a

shape can be recovered by using the distance to a known measure ν, if ν is close enough to …

Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

[PDF] mathnet.ru

C Selinger - Theory of Stochastic Processes, 2011 - mathnet.ru

Via elements of second order differential geometry on smooth Wasserstein spaces of

probability measures we give an explicit formula for a Laplacian in the case that the

Wasserstein space is based on the unit circle. The Laplacian on this infinite dimensional …

Wasserstein distances in the analysis of time series and dynamical systems

2011

M Muskulus, S Verduyn-Lunel - Physica D: Nonlinear Phenomena, 2011 - Elsevier

… and its natural measure with arbitrary precision [21]; in the case of finite time series this … In the

following we assume that the reconstruction process has been performed, so let x … the long-term

behavior of dynamical systems quantitatively, we employ the Wasserstein distances of …

2011

[PDF] ups-tlse.fr

Problèmes d'interaction discret-continu et distances de Wasserstein

E Boissard - 2011 - thesesups.ups-tlse.fr

On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la

théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur

pour l'approximation particulaire des solutions de certaines équations aux dérivées …

2011

A spectral notion of Gromov–Wasserstein distance and related methods

F Mémoli - Applied and Computational Harmonic Analysis, 2011 - Elsevier

We introduce a spectral notion of distance between objects and study its theoretical

properties. Our distance satisfies the properties of a metric on the class of isometric shapes,

which means, in particular, that two shapes are at 0 distance if and only if they are isometric …

2011 see 2012

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

<——2011———2011—— — - 260—

[CITATION] Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

S Lisini, D Matthes, G Savaré - Preprint, 2011

Comparison between distance and norm, and localisation of Wasserstein distance

R Peyre - arXiv preprint arXiv:1104.4631, 2011 - arxiv.org

It is well known that the quadratic Wasserstein distance $ W_2 (\mathord {\boldsymbol

{\cdot}},\mathord {\boldsymbol {\cdot}}) $ is formally equivalent, for infinitesimally small

perturbations, to some weighted $ H^{-1} $ homogeneous Sobolev norm. In this article I …

2011 see 2013

[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

Functional inequalities for the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer

We give an alternative representation of the Wasserstein Dirichlet form that was introduced

by von Renesse and Sturm in [7]. Based on this alternative representation we improve and

generalize the Poincaré and logarithmic Sobolev inequality obtained for the Wasserstein …

2011

Transportation cost inequalities for Wasserstein diffusions

J Shao - Bulletin des sciences mathematiques, 2011 - Elsevier

In this work we establish some types of transportation cost inequalities for two kinds of

probability measure-valued processes: Wasserstein diffusions and Fleming–Viot processes.

Besides, we prove that the Fleming–Viot processes generally donʼt satisfy the super …

2011

Wasserstein distances in the analysis of time series and dynamical systems

M Muskulus, S Verduyn-Lunel - Physica D: Nonlinear Phenomena, 2011 - Elsevier

A new approach based on Wasserstein distances, which are numerical costs of an optimal

transportation problem, allows us to analyze nonlinear phenomena in a robust manner. The

long-term behavior is reconstructed from time series, resulting in a probability distribution …

[PDF] leidenuniv.nl

2011

Transportation cost inequalities for Wasserstein diffusions

J Shao - Bulletin des sciences mathematiques, 2011 - Elsevier

In this work we establish some types of transportation cost inequalities for two kinds of

probability measure-valued processes: Wasserstein diffusions and Fleming–Viot processes.

Besides, we prove that the Fleming–Viot processes generally donʼt satisfy the super …

2011

Existence and Uniqueness of GEXIT curves via the Wasserstein Metric

S Kudekar, T Richardson… - 2011 IEEE Information …, 2011 - ieeexplore.ieee.org

In the analysis of iterative coding systems it is often necessary to compare two densities and

to measure how close they are. Sometimes it is convenient to compare their entropy or their

Battacharyya parameter. But sometimes a more powerful measure is required. The …

2011 many 2013

[PDF] Transport equation with nonlocal velocity in wasserstein spaces: existence, uniqueness and numerical schemes

B Piccoli, F Rossi - Preprint, 2011 - researchgate.net

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We prove existence and uniqueness of the …

Wasserstein barycenter and its application to texture mixing

2011 [PDF] archives-ouvertes.fr

J Rabin, G Peyré, J Delon, M Bernot - International Conference on Scale …, 2011 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein …

<——2011———2011—— — - 270—

2011 [PDF] arxiv.org

Optimal transport and Ricci curvature: Wasserstein space over the interval

O Chodosh - arXiv preprint arXiv:1105.2883, 2011 - arxiv.org

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and

the associated (2-) Wasserstein distance. We then examine displacement convexity of the

entropy functional on the space of probability measures. In particular, we give a detailed …

2011

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

2011 BEHAVIOURAL BRAIN RESEARCH

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

56 citations* for all

56 citations*

2014 ANNALS OF APPLIED PROBABILITY

Oleg Butkovsky

Conformal Wasserstein Distance: II. Computational Aspects and Extensions

Rate of convergence

View More (8+)

We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a “good” $d$-small set imply subgeometric convergence to the invariant measure. In the continuous t... View Full Abstract

2011 see 2012

2011 ARXIV: NUMERICAL ANALYSIS

An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy

69 citations* for all

69 citations*

2014 COMMUNICATIONS IN MATHEMATICAL PHYSICS

Eric A. Carlen ¹,Jan Maas ²

¹ Rutgers University ,² University of Bonn

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

Von Neumann algebra

View More (9+)

Let ${\mathfrak{C}}$ denote the Clifford algebra over ${\mathbb{R}^n}$, which is the von Neumann algebra generated by n self-adjoint operators Qj, j = 1,…,n satisfying the canonical anticommutation relations, QiQj + QjQi = 2δijI, and let τ denote the normalized trace on ${\mathfrak{C}}$. This ... View Full Abstract

EXCERPTS (20)

2011

2011 ARXIV: ANALYSIS OF PDES

Limiting disclosure of sensitive data in sequential releases of databases

51 citations*

2012 INFORMATION SCIENCES

Erez Shmueli ¹,Tamir Tassa ²,Raz Wasserstein ¹,Bracha Shapira ¹,Lior Rokach ¹

¹ Ben-Gurion University of the Negev ,² Open University

Data publishing

Privacy laws of the United States

View More (7+)

Privacy Preserving Data Publishing (PPDP) is a research field that deals with the development of methods to enable publishing of data while minimizing distortion, for maintaining usability on one hand, and respecting privacy on the other hand. Sequential release is a scenario of data publishing wher... View Full Abstract

2011

Barycenters in the Wasserstein Space

701 citations*

2011 SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Martial Agueh ¹,Guillaume Carlier ²

¹ Department of Mathematics and Statistics,² Centre de Recherches Mathématiques

Convexity

Uniqueness

View More (6+)

In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann's interpolation to the case of more than two measures. We provide existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the multimarginal optimal transport probl... View Full Abstract

2011

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

2011 ARXIV: STATISTICS THEORY

View Less

Neal Madras ,Deniz Sezer

Coupling (probability)

Markov chain

View More (9+)

2011

Barycenters in the Wasserstein Space

701 citations*

2011 SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Martial Agueh ¹,Guillaume Carlier ²

¹ Department of Mathematics and Statistics,² Centre de Recherches Mathématiques

Convexity

Uniqueness

View More (6+)

2014

2014 INTERNATIONAL CONFERENCE ON MACHINE LEARNING

482 citations* for all

456 citations*

Marco Cuturi ¹,Arnaud Doucet ²

¹ Kyoto University ,² University of Oxford

Subgradient method

Distribution's template estimate with Wasserstein metrics

View More (8+)

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances to each element in that set. We propose two original algorit... View Full Abstract

2011 [PDF] arxiv.org

E Boissard, TL Gouic, JM Loubes - arXiv preprint arXiv:1111.5927, 2011 - arxiv.org

In this paper we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

2011 [PDF] sciencedirect.com

Conformal Wasserstein distances: Comparing surfaces in polynomial time

Y Lipman, I Daubechies - Advances in Mathematics, 2011 - Elsevier

We present a constructive approach to surface comparison realizable by a polynomial-time

algorithm. We determine the “similarity” of two given surfaces by solving a mass-

transportation problem between their conformal densities. This mass transportation problem …

22011 [PDF] arxiv.org

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals.

As an application, local and global well-posedness of different higher order non-linear …

<——2011———2011——— 280—

2011 see 2012

[1102.1202] Passing to the Limit in a Wasserstein Gradient Flow

by S Arnrich · 2011 · Cited by 65 — Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology.

[CITATION] Passing to the limit in a wasserstein gradient flow: From diffusion to reaction, To appear on Calc

S Arnrich, A Mielke, MA Peletier, G Savaré, M Veneroni - Var. Partial Differential …, 2011

[CITATION] Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

2011 OSAKA JOURNAL OF MATHEMATICS

190 citations*

Fundamental theorem of Riemannian geometry

SCI - Mathematics

Information geometry

View More (9+)

2011 [PDF] mathnet.ru

Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle

C Selinger - Theory of Stochastic Processes, 2011 - mathnet.ru

Via elements of second order differential geometry on smooth Wasserstein spaces of

probability measures we give an explicit formula for a Laplacian in the case that the …

Cite Related articles All 5 versions

2011

Reflection coupling and Wasserstein contractivity without convexity

A Eberle - Comptes Rendus Mathematique, 2011 - Elsevier

We note that even if convexity of the potential U fails locally, overdamped Langevin

diffusions in R d are contractions wrt the Kantorovich–Rubinstein-Wasserstein distance …

Cite Cited by 57 Related articles All 5 versions

2011 [PDF] semanticscholar.org

[PDF] Optimal Couplings of Kantorovich-Rubinstein-Wasserstein L^ sub p^-distance

Y Shen - Journal of Mathematics Research, 2011 - pdfs.semanticscholar.org

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein Lp−

distance (p> 2)(abbreviation: KRW Lp− distance) in a bounded region of Euclidean plane …

Well-posedness of Wasserstein gradient flow solutions of higher order evolution equations

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Preprint, 2018

2011

2011 [PDF] arxiv.org

E Kamalinejad - arXiv preprint arXiv:1112.4407, 2011 - arxiv.org

A relaxed notion of displacement convexity is defined and used to establish short time

existence and uniqueness of Wasserstein gradient flows for higher order energy functionals …

2011 comp f9le
Deconvolution for the Wasserstein metric and geometric inferenceAuthors:Caillerie, Claire (Creator), Chazal, Frédéric (Creator), Dedecker, Jérôme (Creator), Michel, Bertrand (Creator)
Summary:Recently, Chazal, Cohen-Steiner and Mérigot have defined a distance function to measures to answer geometric inference problems in a probabilistic setting. According to their result, the topological properties of a shape can be recovered by using the distance to a known measure ν, if ν is close enough to a measure μ concentrated on this shape. Here, close enough means that the Wasserstein distance W2 between μ and ν is sufficiently small. Given a point cloud, a natural candidate for ν is the empirical measure μn. Nevertheless, in many situations the data points are not located on the geometric shape but in the neighborhood of it, and μn can be too far from μ. In a deconvolution framework, we consider a slight modification of the classical kernel deconvolution estimator, and we give a consistency result and rates of convergence for this estimator. Some simulated experiments illustrate the deconvolution method and its application to geometric inference on various shapes and with various noise distributionsShow more
Computer File, 2011
English
Publisher:The Institute of Mathematical Statistics and the Bernoulli Society, 2011

2011 Computer Program,
Wasserstein geometry of Gaussian measuresAuthor:Takatsu, Asuka (Creator)
Summary:This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the $L^{2}$-Wasserstein geometry. The space of Gaussian measures is of finite dimension, which allows to write down the explicit Riemannian metric which in turn induces the $L^{2}$-Wasserstein distance. Moreover, its completion as a metric space provides a complete picture of the singular behavior of the $L^{2}$-Wasserstein geometry. In particular, the singular set is stratified according to the dimension of the support of the Gaussian measures, providing an explicit nontrivial example of Alexandrov space with extremal setsShow more
Computer Program, 2011-12
English
Publisher:Osaka University and Osaka City University, Departments of Mathematics, 2011-12
Access Free

Behaviors of $\phi$-exponential distributions in Wasserstein geometry and an evolution equationAuthor:Takatsu, Asuka (Creator)
Summary:A $\phi$-exponential distribution is a generalization of an exponential distribution associated to functions $\phi$ in an appropriate class, and the space of $\phi$-exponential distributions has a dually flat structure. We study features of the space of $\phi$-exponential distributions, such as the convexity in Wasserstein geometry and the stability under an evolution equation. From this study, we provide the new characterizations to the space of Gaussian measures and the space of $q$-Gaussian measuresShow more
Downloadable Archival Material, 2011-09-30
Undefined
Publisher:2011-09-30

Behaviors of $\phi$-exponential distributions in Wasserstein geometry and an evolution equation

Author:Takatsu, Asuka (Creator)
Summary:A $\phi$-exponential distribution is a generalization of an exponential distribution associated to functions $\phi$ in an appropriate class, and the space of $\phi$-exponential distributions has a dually flat structure. We study features of the space of $\phi$-exponential distributions, such as the convexity in Wasserstein geometry and the stability under an evolution equation. From this study, we provide the new characterizations to the space of Gaussian measures and the space of $q$-Gaussian measuresShow more
Downloadable Archival Material, 2011-09-30
Undefined
Publisher:2011-09-30

<——2011———2011———290—

2011 see 2014
Dynamic Clustering of Histogram Data Based on Adaptive Squared Wasserstein Distances

Authors:Irpino, Antonio (Creator), Verde, Rosanna (Creator), De Carvalho, Francisco de AT (Creator)
Summary:This paper deals with clustering methods based on adaptive distances for histogram data using a dynamic clustering algorithm. Histogram data describes individuals in terms of empirical distributions. These kind of data can be considered as complex descriptions of phenomena observed on complex objects: images, groups of individuals, spatial or temporal variant data, results of queries, environmental data, and so on. The Wasserstein distance is used to compare two histograms. The Wasserstein distance between histograms is constituted by two components: the first based on the means, and the second, to internal dispersions (standard deviation, skewness, kurtosis, and so on) of the histograms. To cluster sets of histogram data, we propose to use Dynamic Clustering Algorithm, (based on adaptive squared Wasserstein distances) that is a k-means-like algorithm for clustering a set of individuals into $K$ classes that are apriori fixed. The main aim of this research is to provide a tool for clustering histograms, emphasizing the different contributions of the histogram variables, and their components, to the definition of the clusters. We demonstrate that this can be achieved using adaptive distances. Two kind of adaptive distances are considered: the first takes into account the variability of each component of each descriptor for the whole set of individuals; the second takes into account the variability of each component of each descriptor in each cluster. We furnish interpretative tools of the obtained partition based on an extension of the classical measures (indexes) to the use of adaptive distances in the clustering criterion function. Applications on synthetic and real-world data corroborate the proposed procedureShow more
Downloadable Archival Material, 2011-10-07
Undefined
Publisher:2011-10-07

2011 see 2010Peer-reviewed
From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage

Authors:S. Adams, N. Dirr, M.A. Peletier, J. Zimmer
Summary:We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional J h characterizes the behaviour of the particle system at t = h in terms of the initial distribution at t = 0. For the diffusion equation, a single step in the time-discretized entropy-Wasserstein gradient flow is characterized by the minimization of a functional K h . We establish a new connection between these systems by proving that J h and K h are equal up to second order in h as h ¿ 0. This result gives a microscopic explanation of the origin of the entropy-Wasserstein gradient flow formulation of the diffusion equation. Simultaneously, the limit passage presented here gives a physically natural description of the underlying particle system by describing it as an entropic gradient flowShow more
Article
Publication:Communications in Mathematical Physics, 307, 2011, 791

2011 see 2010 Peer-reviewed
Estimates on Path Functionals over Wasserstein Spaces

Authors:S. Bianchini, A. Brancolini
Article, 2011
Publication:SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 42, 2011, 1179
Publisher:2011

2011 ebook
Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

Authors:S. Arnrich, Arnrich, S. (Creator), Mielke, A. (Creator), Peletier, M.A. (Creator), Savaré, G. (Creator), Veneroni, M. (Creator)
Summary:We study a singular-limit problem arising in the modelling of chemical reactions. At finite $\epsilon > 0$, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by $1/\epsilon$, and in the limit $\epsilon \rightarrow 0$, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savaré, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the $\epsilon$-problem converge to a solution of the limiting problemShow more
eBook, 2011
English
Publication:Eindhoven : Technische Universiteit Eindhoven, CASA-report, (2011), 28 pp.
Publisher:Technische Universiteit Eindhoven, 2011

Barycenters in the Wasserstein Space - SIAM Journals

https://epubs.siam.org › doi

by M Agueh · 2011 · Cited by 759 — In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann's interpolation to the case of more than two measures.

<——2011———2011———295—end 2011

including 3 titles with Vaserstein

start 2012 Wasserstein

Perelman's W-entropy and Wasserstein distance for the Witten-Laplacian and the Fokker-Planck diffusions on Riemannian manifolds

University of Kansas

Jan 22, 2012 - Perelman's W-entropy and Wasserstein distance for the. Witten-Laplacian and the Fokker-Planck diffusions on. Riemannian manifolds.

MR3021775 Bertrand, Jérôme; Kloeckner, Benoît A geometric study of Wasserstein spaces: Hadamard spaces. J. Topol. Anal. 4 (2012), no. 4, 515–542. 53C21 (28A33 49Q20)

A GEOMETRIC STUDY OF WASSERSTEIN SPACES : EMBEDDING POWERS… - HAL

File Format: Adobe PostScript - View as HTML 2012 by. Benoˆıt Kloeckner.

Abstract. — The Wasserstein spaces #p(X) of a metric ... pdf

Optimality of the triangular lattice for a particle system with Wasserstein interaction

DP Bourne, MA Peletier, F Theil - arXiv preprint arXiv:1212.6973, 2012 - arxiv.org

Abstract: We prove strong crystallization results in two dimensions for an energy that arises

in the theory of block copolymers. The energy is defined on sets of points and their weights,

or equivalently on the set of atomic measures. It consists of two terms; the first term is the ...

An extension of the Weak KAM theory to the Wasserstein torus

[PDF] from wvu.edu W Gangbo… - math.wvu.edu

Abstract The study of asymptotic behavior of minimizing trajectories on the Wasserstein

space P (Td) has so far been limited to the case d= 1 as all prior studies heavily relied on the

isometric identification of P (T) with a subset of the Hilbert space L2 (0, 1). There is no ...

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

Wasserstein barycenter and its application to texture mixing

J Rabin, G Peyré, J Delon… - Scale Space and Variational …, 2012 - Springer

This paper proposes a new definition of the averaging of discrete probability distributions as

a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time

complexity involved by the numerical solving of such problem, the original Wasserstein ...

Cited by 18 - Related articles - All 3 versions [PDF] from arxiv.org [bib] [pdf] [doi]

Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Arxiv preprint arXiv:1206.2673, 2012 - arxiv.org

Abstract: In this paper, we study the stability property of Hamiltonian systems on the

Wasserstein space. Let $ H $ be a given Hamiltonian satisfying certain properties. We

regularize $ H $ using the Moreau-Yosida approximation and denote it by $ H_\ tau. $ We ...

[PDF] Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions

V Omelchenko - Bulletin of the Czech Econometric Society, 2012 - library.utia.cas.cz

In this paper, we aim to explore the speed of convergence of the Wasserstein distance

between stable cumulative distribution functions and their empirical counterparts. The

theoretical results are compared with the results provided by simulations. The need to use …

Wasserstein decay of one dimensional jump-diffusions

B Cloez - Arxiv preprint arXiv:1202.1259, 2012 - arxiv.org

Abstract: We are interested by a one dimensional Markov process which moves following a

diffusion for some random time and then jumps. It can represent some natural phenomena

like size of cell or data transmission over the Internet. The paper begin with some results ...

Frequency Domain Model Validation in Wasserstein Metric

File Format: PDF/Adobe Acrobat

by A Halder - Related articles [PDF] from arxiv.org - Tamu.edu A. Halder and R. Bhattacharya submitted 2013

Abstract:This paper connects the time-domain uncertainty propagation approach for model validation in Wasserstein distance 2W2, introduced by the authors in ...

American Control Conference (ACC …, 2013 - ieeexplore.ieee.org

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos… - Arxiv preprint arXiv:1203.0676, 2012 - arxiv.org

Abstract: We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic

particle system on one hand and as a Wasserstein gradient flow on the other. We write the

rate functional, that characterizes the large deviations from the hydrodynamic limit, in a ...

[PDF] from uvic.ca Cited by 3 Related articles All 7 versions

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

<——2012—————2012—————— -10—

[PDF] One-dimensional numerical algorithms for gradient flows in the p-Wasserstein spaces

M Agueh… - math.uvic.ca

Abstract We numerically approximate, on the real line, solutions to a large class of parabolic

partial differential equations which are “gradient flows” of some energy functionals with

respect to the Lp-Wasserstein metrics for all p> 1. Our method relies on variational ...

Acta applicandae mathematicae, 2013 - Springer

Contraction of the proximal map and generalized convexity of the Moreau-Yosida regularization in the 2-Wasserstein metric

EA Carlen… - Arxiv preprint arXiv:1205.6565, 2012 - arxiv.org

Abstract: We investigate the Moreau-Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and a restricted convexity result for the ...

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli… - Arxiv preprint arXiv:1206.3219, 2012 - arxiv.org

We use this generalized Wasserstein distance to study a transport equation with source, in which

both the vector field and the source depend on the measure itself. We prove existence and uniqueness

of the solution to the Cauchy problem when the vector field and the source are ...

Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

Archive for Rational Mechanics and Analysis, 2014

MR2921215 Lisini, Stefano; Matthes, Daniel; Savaré, Giuseppe Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. J. Differential Equations 253 (2012), no. 2, 814–850. 35K35 (35A15)

Published: JUL 15 2012

S Lisini, D Matthes… - Arxiv preprint arXiv:1201.2367, 2012 - arxiv.org

Abstract: In this paper, we establish a novel approach to proving existence of non-negative

weak solutions for degenerate parabolic equations of fourth order, like the Cahn-Hilliard and

certain thin film equations. The considered evolution equations are in the form of a ...

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint, 2012

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367

Cahn-Hilliard and Thin Film equations with nonlinear mobility ...

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint, 2012

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367

Jan 11, 2012 — Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn-Hilliard and certain thin film equations.

by S Lisini · ‎2012 · ‎Cited by 45 · ‎Related articles

Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance

A Irpino… - Arxiv preprint arXiv:1202.1436, 2012 - arxiv.org

Abstract: In this paper we present a linear regression model for modal symbolic data. The

observed variables are histogram variables according to the definition given in the

framework of Symbolic Data Analysis and the parameters of the model are estimated ...

Adv. Data Anal. Classif. 9 (2015), no. 1, 81–106. 62J05

Classification of periodic activities using the Wasserstein distance

L Oudre, J Jakubowicz, P Bianchi… - … , IEEE Transactions on, 2012 - ieeexplore.ieee.org

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Volume: 59 Issue: 6 Pages: 1610-1619

Abstract In this paper, we introduce a novel nonparametric classification technique based on

the use of the Wasserstein distance. The proposed scheme is applied in a biomedical

context for the analysis of recorded accelerometer data: the aim is to retrieve three types of ...

All 13 versions [PDF] arxiv.org Cited by 15 Related articles

Volume: 59 Issue: 6 Pages: 1610-1619

[PDF] WEAK KAM ON THE WASSERSTEIN TORUS WITH MULTI-DIMENSIONAL UNDERLYING SPACE

W GANGBO… - people.math.gatech.edu

Abstract. The study of asymptotic behavior of minimizing trajectories on the Wasserstein

space P (Td) has so far been limited to the case d= 1 as all prior studies heavily relied on the

isometric identification of P (T) with a subset of the Hilbert space L2 (0, 1). There is no ...

Transport Equation with Nonlocal Velocity in Wasserstein Spaces: Convergence of Numerical Schemes

B Piccoli… - Acta Applicandae Mathematicae, 2012 - Springer

Abstract Motivated by pedestrian modelling, we study evolution of measures in the

Wasserstein space. In particular, we consider the Cauchy problem for a transport equation,

where the velocity field depends on the measure itself. We deal with numerical schemes ...

An Analog of the 2-Wasserstein Metric in Non-commutative Probability under which the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy

EA Carlen… - Arxiv preprint arXiv:1203.5377, 2012 - arxiv.org

Abstract: Let $\ Cl $ denote the Clifford algebra over $\ R^ n $, which is the von Neumann

algebra generated by $ n $ self-adjoint operators $ Q_j $, $ j= 1,..., n $ satisfying the

canonical anticommutation relations, $ Q_iQ_j+ Q_jQ_i= 2\ delta_ {ij} I $, and let $\ tau $ ...

MR3248053

数据挖掘中区间数据模糊聚类研究——基于 Wasserstein 测度 [Study on Fuzzy Clustering of Interval Data in Data Mining - Based on Wasserstein Measurements]

李红… - 计算机工程与应用, 2012 - cqvip.com

针对目前区间数据模糊聚类研究中区间距离定义存在的局限性, 引入能够考虑区间数值分布特征

的Wasserstein 距离测度, 提出基于Wasserstein 距离测度的单指标和双指标自适应模糊聚类

算法及迭代模型. 通过仿真实验和CR 指数, 证实了该类模型的优势. 该算法在海量, 堆积如山 ...

[Li Hong , Sun Qiu Bi Data Mining the interval fuzzy clustering - based Wasserstein measure]

[School of Management Department of Statistics, Fuzhou 350108]

Abstract:

The Wasserstein distance measure introduced to be able to consider the limitations of fuzzy clustering interval data interval distance defined interval value distribution characteristics, proposed based on the Wasserstein distance measure single indicators and indicators adaptive fuzzy clustering algorithm and iterative model. confirmed the advantages of this kind of model simulation and CR Index, the algorithm has important practical significance in the massive mountains of data mining.

<——2012—————2012————— -20—

MR2915328 Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. Calc. Var. Partial Differential Equations 44 (2012), no. 3-4, 419–454. 35Q84 (35B25 49S05 70F40 70G75). Published: JUL 2012

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

Abstract We study a singular-limit problem arising in the modelling of chemical reactions. At

finite ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with

a double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\ to0, ...

arXiv:1102.1202 [pdf, other]

Cited by 42 Related articles All 29 versions

MR2949241 Takatsu, Asuka; Yokota, Takumi Cone structure of L2-Wasserstein spaces. J. Topol. Anal. 4 (2012), no. 2, 237–253. 58Bxx (28A33 53Cxx)

Cone structure of L2-Wasserstein spaces

A TAKATSU, T YOKOTA - Journal of Topology and Analysis, 2012 - World Scientific

The aim of this paper is to obtain a better understanding of the geometric structure of

quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on

their cone and product structures, and prove that the quadratic Wasserstein space over ...

CONE STRUCTURE OF L2-WASSERSTEIN SPACES | Journal of ...

by A TAKATSU - ‎2012 - ‎Cited by 4 - ‎Related articles

The aim of this paper is to obtain a better understanding of the geometric structure of quadratic Wasserstein spaces over separable Hilbert spaces. For this sake ...

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - arXiv preprint arXiv:1211.4273, 2012 - arxiv.org

Abstract: We establish subgeometric bounds on convergence rate of general Markov

processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov

drift condition and the existence of a" good" d-small set imply subgeometric convergence ...

Subgeometric rates of convergence of Markov processes in the ...

by O Butkovsky - ‎2012 - ‎Cited by 26 - ‎Related articles

Nov 18, 2012 - ... rate of general Markov processes in the Wasserstein metric. ... a "good" -small set imply subgeometric convergence to the invariant measure.

[PDF] WEAK KAM THEORY ON THE WASSERSTEIN TORUS WITH MULTI-DIMENSIONAL UNDERLYING SPACE

W GANGBO, A TUDORASCU - math.wvu.edu

Abstract. The study of asymptotic behavior of minimizing trajectories on the Wasserstein

space P (Td) has so far been limited to the case d= 1 as all prior studies heavily relied on the

isometric identification of P (T) with a subset of the Hilbert space L2 (0, 1). There is no ...

MR3158572

Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance

A Irpino, R Verde - arXiv preprint arXiv:1202.1436, 2012 - arxiv.org

Abstract: In this paper we present a linear regression model for modal symbolic data. The

observed variables are histogram variables according to the definition given in the

framework of Symbolic Data Analysis and the parameters of the model are estimated ...

2012

Speed of convergence to equilibrium in Wasserstein metrics for Kac's like kinetic equations

F Bassetti, E Perversi - arXiv preprint arXiv:1205.3690, 2012 - arxiv.org

Abstract: This work deals with a class of one-dimensional measure-valued kinetic equations,

which constitute extensions of the Kac caricature. It is known that if the initial datum belongs

to the domain of normal attraction of an\ alpha-stable law, the solution of the equation ...

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

Decomposition of geodesics in the Wasserstein space ... - arXiv

s://arxiv.org › math

by F Cavalletti · 2012 · Cited by 38 — Abstract: We will prove a decomposition for Wasserstein geodesics in the following sense: let (X,d,m) be a non-branching metric measure ...

Missing: GA ‎| Must include: GA

Decomposition of geodesics in the Wasserstein space and the globalization property

F Cavalletti - arXiv preprint arXiv:1209.5909, 2012 - arxiv.org

Abstract: Let $(X, d, m) $ be a non-branching metric measure space verifying $\ mathsf {CD}

_ {loc}(K, N) $ or equivalently $\ mathsf {CD}^{*}(K, N) $. In this note we show that given a

geodesic $\ mu_ {t} $ in the $ L^{2} $-Wasserstein space, it is always possible to write the ...

MR3192034 P

Estimation of deformations between distributions by minimal Wasserstein distance.

H Lescornel, JM Loubes - 2012 - hal.archives-ouvertes.fr

Abstract We consider the issue of estimating a measure observed in a deformation

framework. For this we consider a parametric deformation model on an empirical sample

and provide a new matching criterion for cloud points based on a generalization of the ...

[PDF] Estimation of deformations between distributions by minimal Wasserstein distance

L Hélène, L Jean-Michel - hal.archives-ouvertes.fr

AN EXTENSION OF WASSERSTEIN CONTRACTION ASSOCIATED WITH THE CURVATURE-DIMENSION CONDITION

K KUWADA - bcc.impan.pl

We obtain a new characterization of complete Riemannian manifolds with lower Ricci

curvature bound and upper dimension bound in terms of the Wasserstein distance between

heat distributions. It is formulated as a local space-time Lipschitz estimate of the ...

[PDF] tohoku.ac.jp

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - math.tohoku.ac.jp

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

二元离散antorovich-Rubinstein-Wasserstein L2-距离的精确表示在线 ...

<——2012———201—— -30—

lib.cqvip.com/read/detail.aspx?ID... - Translate this page [accurate representation of the binary the discrete Kantorovich-Rubinstein-Wasserstein L2-distance]

本文得到二元离散Kantorovich-Rubinstein-WassersteinL2-距离的一个精确表示。

SHEN Yin Fong

An accurate representation of the binary discrete antorovich-Rubinstein-Wasserstein L2-distance

Hangzhou 310018, Zhejiang Finance and Economics College of Mathematics and Statistics 2012

'Burenruzie in het Jodendom' [Review of: B. Wasserstein. Aan de vooravond]

Author:Houwink Ten Cate, J.T.M. (Creator)
Downloadable Archival Material, 2012
Undefined
Publication:Historisch Nieuwsblad vol.12 (2012) p.81-82 [ISSN 0927-2690]
Publisher:2012

2012 book
Burenruzie in het Jodendom' [Review of: B. Wasserstein. Aan de vooravond]

Author:J.T.M. Houwink Ten Cate
Book
Publication:2012

Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012 - arxiv.org

Abstract: We define a notion of barycenter for random probability measures in the

Wasserstein space. We give a characterization of the population barycenter in terms of

existence and uniqueness for compactly supported measures. Then, the problem of ...

Cited by 42 Related articles All 12 versions

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

Consistent estimation of a population barycenter in the Wasserstein space

CITATION] Consistent estimation of a population barycenter in the Wasserstein space. eprint

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012
Cited by 60 Related articles All 7 versions

Wasserstein Active Contours

G Peyré, J Fadili, J Rabin - Proc. ICIP'12, 2012 - hal.archives-ouvertes.fr [bib] [pdf]

Abstract. In this paper, we propose a novel and rigorous framework for region-based active

contours that combines the Wasserstein distance between statistical distributions in arbitrary

dimension and shape derivative tools. To the best of our knowledge, this is the first ...

Cited by 46 Related articles All 7 versions

WASSERSTEIN ACTIVE CONTOURS

By: Peyre, Gabriel; Fadili, Jalal; Rabin, Julien

Conference: 19th IEEE International Conference on Image Processing (ICIP) Location: ‏ Lake Buena Vista, FL Date: ‏ SEP 30-OCT 03, 2012

Sponsor(s): ‏Inst Elect & Elect Engineers (IEEE); IEEE Signal Proc Soc

2012 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP 2012) Book Series: ‏ IEEE International Conference on Image Processing ICIP Pages: ‏ 2541-2544 Published: ‏ 2012

Times Cited: 17

2012 see 2010

MR3098634 Santambrogio, Filippo Gradient flows in Wasserstein spaces and applications to crowd movement. Seminaire: Equations aux Dérivées Partielles. 2009–2010, Exp. No. XXVII, 16 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 2012. 49Q20 (35F15 35Q84)

[CITATION] Gradient flows in Wasserstein spaces and applications to crowd movement, Séminaire

XEDP, 200-210

F Santambrogio - Exp. No. XXVII, 2012

First variation formula in Wasserstein spaces over compact ...

2012

MR2994677 Gigli, Nicola; Ohta, Shin-Ichi; First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces. Canad. Math. Bull. 55 (2012), no. 4, 723–735.

by N Gigli - ‎2012 - ‎Cited by 15 - ‎Related articles

Titolo: First variation formula in Wasserstein spaces over compact Alexandrov spaces. Autori: Gigli, N.; Ohta, Shin-ichi. Rivista: CANADIAN MATHEMATICAL

MR2964689 Bolley, François; Gentil, Ivan; Guillin, Arnaud; Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations. J. Funct. Anal. 263 (2012), no. 8, 2430–2457. Arxiv preprint arXiv:1110.3606, 2011 - arxiv.org

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with …

MR2921976 Komorowski, Tomasz; Walczuk, Anna Central limit theorem for Markov processes with spectral gap in the Wasserstein metric. Stochastic Process. Appl. 122 (2012), no. 5, 2155–2184. 60J25 (60B12 60F05 60J35). Published: MAY 2012

Central limit theorem for Markov processes with spectral gap in the ...

by T Komorowski - ‎2012 - ‎Cited by 31 - ‎Related article

Central limit theorem for Markov processes with spectral gap in the .... in the Wasserstein metric for the transfer operator semigroup associated with the process ...

MR2901195 Takatsu, Asuka Wasserstein geometry of porous medium equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 2, 217–232. 35K57 (28A75 35C06 46E27 60D05). Published: MAR-APR 2012

Wasserstein geometry of porous medium equation - ScienceDirect

by A Takatsu - ‎2012 - ‎Cited by 5 - ‎Related articles

We study the porous medium equation with emphasis on q-Gaussian measures, which are generalizations of Gaussian measures by using power-law ...

MR2900478 Chodosh, Otis A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval. J. Funct. Anal. 262 (2012), no. 10, 4570–4581. 53Cxx (58Dxx 60B05)

A lack of Ricci bounds for the entropic measure on Wasserstein space ...

by O Chodosh - ‎2012 - ‎Cited by 5 - ‎Related articles

May 15, 2012 - We examine the entropic measure, recently constructed by von Renesse and Sturm, a measure over the metric space of probability measures ...

<——2012———2012————— ———— -40—

MR2887832 Agueh, Martial Finsler structure in the p-Wasserstein space and gradient flows. C. R. Math. Acad. Sci. Paris 350 (2012), no. 1-2, 35–40. (Reviewer: Benoît Kloeckner) 49Q20 (53C60 58B20)/ Published: JAN 2012

Finsler structure in the p-Wasserstein space and gradient flows ...

by M Agueh - ‎2012 - ‎Cited by 5 - ‎Related articles

It is known from the work of F. Otto (2001) [9], that the space of probability measures equipped with the quadratic Wasserstein distance, i.e., the 2-Wasserstein ...

MR2949240 Kloeckner, Benoît A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces. J. Topol. Anal. 4 (2012), no. 2, 203–235. 58Dxx (28A78 60B05)

a generalization of hausdorff dimension applied to hilbert cubes and ...

A Wasserstein space is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate ...

Approximate Wasserstein Metric and its Applications to Image ...

Jul 11, 2012 - Approximate Wasserstein Metric for Imaging Problems .... Applica

Passing to the limit in a Wasserstein gradient flow: from ...

Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it …

Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

by Arnrich, S Steffen; Mielke, A; Peletier, MA Mark; More...

Calculus of Variations and Partial Differential Equations Calculus of Variations and Partial Differential Equations Calculus of Variations and Partial Differential Equations, 2012, Volume 44, Issue 3-4

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $${\varepsilon\, > \,0,}$$ the system is described by a...

Journal Article: Full Text Online

Conformal Wasserstein distance: II. computational aspects and ...

Jul 16, 2012 - Conformal Wasserstein distance: II. computational aspects and extensions.

2012

Moreau-Yosida approximation and convergence of Hamiltonian ...

by HK Kim - ‎2012 - ‎Cited by 1 - ‎Related articles

Jun 12, 2012 - We regularize using the Moreau-Yosida approximation and denote it by We show that solutions of the Hamiltonian system for converge to a ...

[PDF]

Moreau-Yosida approximation and convergence of Hamiltonian ...

by HK Kim - ‎2012 - ‎Cited by 1 - ‎Related articles

Jun 12, 2012 - arXiv:1206.2673v1 [math.AP] 12 Jun 2012. Moreau-Yosida approximation and convergence of. Hamiltonian systems on Wasserstein space.

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

by Kim, Hwa Kil

Journal of Differential Equations, 04/2013, Volume 254, Issue 7

Journal Article: Full Text Online 2013

Convergence to equilibrium in Wasserstein distance for Fokker –Planck equations

by F Bolley - ‎2012 - ‎Cited by 62 - ‎Related articles

Oct 15, 2012 - We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its solutions to converge to equilibrium with a uniform ...

Cited by 62 Related articles All 27 versions

Characterization of barycenters in the Wasserstein space by ...

by J Bigot - ‎2012 - ‎Cited by 12 - ‎Related articles

Dec 11, 2012 - ... in the Wasserstein space by averaging optimal transport maps ... we give a precise characterization of the population barycenter for various ...

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

by Bigot, Jérémie; Klein, Thierry 12/2012

This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise...

Journal Article: Full Text Online 1915, 1918

Speed of convergence to equilibrium in Wasserstein metrics for Kac-s ...

by F Bassetti - ‎2012 - ‎Cited by 8 - ‎Related articles

May 16, 2012 - ... to equilibrium in Wasserstein metrics for Kac-s like kinetic equations ... the solution of the equation converges weakly to a suitable scale ...

Speed of convergence to equilibrium in Wasserstein metrics for Kac-s like kinetic equations

by Bassetti, Federico; Perversi, Eleonora 05/2012

This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the...

Journal Article:Full Text Onlinetions to many image processing and computer vision tasks: • Color transfer;.

2012

An Analog of the 2-Wasserstein Metric in Non-commutative Probability under which the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy

2012 ARXIV: FUNCTIONAL ANALYSIS

Further results on probabilistic model validation in Wasserstein metric

20 citations*

2012 CONFERENCE ON DECISION AND CONTROL

Abhishek Halder ,Raktim Bhattacharya

Texas A&M University

[PF] Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions

Probabilistic logic

View More (8+)

In a recent work [1], we have introduced a probabilistic formulation for the model validation problem to provide a unifying framework for (in)validating nonlinear deterministic and stochastic models, in both discrete and continuous time. As an extension to that work, this paper provides rigorous per... View Full Abstract

<——2012————2012——————— 50—

V Omelchenko - Bulletin of the Czech Econometric Society, 2012 - library.utia.cas.cz

In this paper, we aim to explore the speed of convergence of the Wasserstein distance

between stable cumulative distribution functions and their empirical counterparts. The

theoretical results are compared with the results provided by simulations. The need to use …

Finsler structure in the p-Wasserstein space and gradient flows

https://www.researchgate.net › publication › 257674151_...

Using this Finsler structure of the p-Wasserstein space, we give definitions of the differential and gradient of functionals defined on this space, and then ...

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

Video: Benoît Kloeckner, "The size of Wasserstein spaces"

.. at BIRS workshop, Optimal Transportation and Differential Geometry, on Thursday, May 24, 2012 on the topic ...

Banff International Research Station · Banff International Research Station · May 24, 2012

[CITATION] The size of Wasserstein spaces

B Kloeckner - 2012 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search;

General (Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; …

[PDF] unc.edu

[PDF] Lattice Fokker-Planck Method Based on Wasserstein Gradient Flows

S Mitran - 2012 - mitran.web.unc.edu

A lattice Fokker-Planck method is introduced based upon a variational formulation of the

time evolution as a Wasserstein gradient flow within the space of probability densities of the

system. Gradient descent directions are efficiently generated by exploiting the link to …

[CITATION] Lattice Fokker-Planck Method Based on Wasserstein Gradient Flows

S Mitran - 2012

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

二元离散 antorovich-Rubinstein-Wasserstein L2-距离的精确表示

2012

2012 zzz 27 see q0q0

[CITATION] Differential forms and symplectic geometry on Wasserstein space

T Pacini - 2012 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search;

General (Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; …

沈银芳 - 科技信息, 2012 - cqvip.com

. 我的维普: 帐户余额; 充值记录; 下载记录; 我的收藏. 购物车; 充值; 客服. 首页 | 期刊大全 |

《中文科技期刊数据库》 > 工程技术 > 机械仪表 > 光学仪器 > 摘要二元离散antorovich …

[Chinese An accurate representation of the binary discrete antorovich-Rubinstein-Wasserstein L2-distance]

A geometric study of Wasserstein spaces: Hadamard spaces

J Bertrand, B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity) probability measures on any (not too wild) metric space X, called its Wasserstein space. In this paper we investigate the geometry of when X is a Hadamard space, by which we mean …

A GEOMETRIC STUDY OF WASSERSTEIN SPACES: HADAMARD SPACES

By: Bertrand, Jerome; Kloeckner, Benoit

JOURNAL OF TOPOLOGY AND ANALYSIS Volume: ‏ 4 Issue: ‏ 4 Pages: ‏ 515-542 Published: ‏ DEC 2012

Times Cited: 8

LP Lopes - 2012 - repositorio.bce.unb.br

Neste trabalho propomos testes não-paramétricos para classes de distribuições de cauda

pesada, que incluem as _-estáveis e as extremais de Fréchet. As estatísticas apresentadas,

funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F ...

issertation

LP Lopes - 2012 - repositorio.unb.br

Neste trabalho propomos testes não-paramétricos para classes de distribuições de cauda pesada, que incluem as _-estáveis e as extremais de Fréchet. As estatísticas apresentadas, funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F _a …

Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions *

Article ull-text available Dec 2012

Vadym Omelchenko

In this paper, we aim to explore the speed of convergence of the Wasserstein distance between stable cumulative distribution functions and their empirical counterparts. The theoretical results are compared with the results provided by simulations. The need to use simulations is explained by the fact that all the theoretical results which relate to...

<——2012—— —2012——— — -60—

2012 Peer-reviewed
Cone structure of L2-Wasserstein spaces
Author

Authors:Takatsu A., Yokota T.
Article, 2012
Publication:Journal of Topology and Analysis, 4, 2012 06 01, 237
Publisher:2012

First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces

By: Gigli, Nicola; Ohta, Shin-Ichi

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES Volume: ‏ 55 Issue: ‏ 4 Pages: ‏ 723-735 Published: ‏ DEC 2012

Times Cited: 8

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

By: Bolley, Francois; Gentil, Ivan; Guillin, Arnaud

JOURNAL OF FUNCTIONAL ANALYSIS Volume: ‏ 263 Issue: ‏ 8 Pages: ‏ 2430-2457 Published: ‏ OCT 15 2012

Method for enhancing and segmenting computed tomography angiography image of liver blood vessel, involves obtaining anisotropic characteristics of neighborhood image point based on liver and blood vessel Wasserstein distance

Times Cited: 31

Patent Number: CN102609913-A CN102609913-B

Patent Assignee: UNIV ZHEJIANG

Inventor(s): KONG D; PENG J; WANG J; et al.

2012 see 2013
Further results on probabilistic model validation in Wasserstein metric
Author

Authors:Halder A., Bhattacharya R., 51st IEEE Conference on Decision and Control, CDC 2012
Article, 2012
Publication:Proceedings of the IEEE Conference on Decision and Control, 2012 12 01, 5542
Publisher:2012

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

By: Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Volume: ‏ 44 Issue: ‏ 3-4 Pages: ‏ 419-454 Published: ‏ JUL 2012

A GENERALIZATION OF HAUSDORFF DIMENSION APPLIED TO HILBERT CUBES AND WASSERSTEIN SPACES

Times Cited: 24

By: Kloeckner, Benoit

JOURNAL OF TOPOLOGY AND ANALYSIS Volume: ‏ 4 Issue: ‏ 2 Pages: ‏ 203-235 Published: ‏ JUN 2012

Times Cited: 3

CONE STRUCTURE OF L-2-WASSERSTEIN SPACES

By: Takatsu, Asuka; Yokota, Takumi

JOURNAL OF TOPOLOGY AND ANALYSIS Volume: ‏ 4 Issue: ‏ 2 Pages: ‏ 237-253 Published: ‏ JUN 2012

Times Cited: 3

2012

Classification of Periodic Activities Using the Wasserstein Distance

By: Oudre, Laurent; Jakubowicz, Jeremie; Bianchi, Pascal; et al.

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Volume: ‏ 59 Issue: ‏ 6 Pages: ‏ 1610-1619 Published: ‏ JUN 2020

Times Cited: 14

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

By: Chodosh, Otis

JOURNAL OF FUNCTIONAL ANALYSIS Volume: ‏ 262 Issue: ‏ 10 Pages: ‏ 4570-4581 Published: ‏ MAY 15 2012

Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

Times Cited: 3

<——2012—— —2012——— — -70—

By: Komorowski, Tomasz; Walczuk, Anna

STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume: ‏ 122 Issue: ‏ 5 Pages: ‏ 2155-2184 Published: ‏ MAY 2012

Times Cited: 23

[PDF] unb.br

LP Lopes - 2012 - repositorio.unb.br

Neste trabalho propomos testes não-paramétricos para classes de distribuições de cauda

pesada, que incluem as _-estáveis e as extremais de Fréchet. As estatísticas apresentadas,

funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F _a …

Finsler structure in the p-Wasserstein space and gradient flows

[Portuguese Similarity tests in the weighted Mallows-Wasserstein distance for heavy tail distributions

2021 see 2011
Wasserstein geometry of Gaussian measures

Author:Takatsu, Asuka (Creator)
Downloadable Archival Material, 2012-09-22T12:51:06Z
English
Publisher:Osaka University and Osaka City University, Departments of Mathematics, 2012-09-22T12:51:06Z

By: Agueh, Martial

COMPTES RENDUS MATHEMATIQUE Volume: ‏ 350 Issue: ‏ 1-2 Pages: ‏ 35-40 Published: ‏ JAN 2012

Wasserstein Barycenter and Its Application to Texture Mixing

By: Rabin, Julien; Peyre, Gabriel; Delon, Julie; et al.

Conference: 3rd International Conference on Scale Space and Variational Methods in Computer Vision Location: ‏ Ein Gedi, ISRAEL Date: ‏ MAY 29-JUN 02, 2011

Sponsor(s): ‏Technion Dept Comp Sci; HP Lab Israel; Rafael Ltd; BBK Technol Ltd; European Commun FP7 ERC FIRST Programs

SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION Book Series: ‏ Lecture Notes in Computer Science Volume: ‏ 6667 Pages: ‏ 435-+ Published: ‏ 2012

A geometric study of Wasserstein spaces: Hadamard spaces

J Bertrand, B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity)

probability measures on any (not too wild) metric space X, called its Wasserstein space. In

this paper we investigate the geometry of when X is a Hadamard space, by which we mean …

[HTML] Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

T Komorowski, A Walczuk - Stochastic Processes and their Applications, 2012 - Elsevier

Suppose that {X t, t≥ 0} is a non-stationary Markov process, taking values in a Polish metric

space E. We prove the law of large numbers and central limit theorem for an additive

functional of the form∫ 0 T ψ (X s) ds, provided that the dual transition probability …

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

a general metric space. The main goal of this paper is to estimate the largeness of

Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its

solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

This asymptotic behaviour is related to a functional inequality, which links the distance with …

<——2012—— —2012——— — -80—

20112

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. eprint

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012

First variation formula in Wasserstein spaces over compact Alexandrov spaces

2012

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces $ X $ with curvature

bounded below. The gradient flow of a geodesically convex functional on the quadratic …

Entropic Burgers' equation via a minimizing movement ...

Cahn–Hilliard and thin film equations with nonlinear mobility ...

Apr 3, 2012 — Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. Nicola Gigli &; Felix Otto. Calculus of ...

2012

www.sciencedirect.com › science › article › abs › pii

Jul 15, 2012 — Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics ... in the form of a gradient flow for a perturbed Dirichlet energy with respect to a Wasserstein-like transport metric, ...

2012

Wasserstein active contours

G Peyré, J Fadili, J Rabin - 2012 19th IEEE International …, 2012 - ieeexplore.ieee.org

In this paper, we propose a novel and rigorous framework for region-based active contours

that combines the Wasserstein distance between statistical distributions in arbitrary

dimension and shape derivative tools. To speed-up the computation and be able to handle …

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its

solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

This asymptotic behaviour is related to a functional inequality, which links the distance with …

2012 [PDF] springer.com

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

Classification of periodic activities using the Wasserstein distance

[PDF] laurentoudre.fr

L Oudre, J Jakubowicz, P Bianchi… - IEEE transactions on …, 2012 - ieeexplore.ieee.org

In this paper, we introduce a novel nonparametric classification technique based on the use

of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the

analysis of recorded accelerometer data: the aim is to retrieve three types of periodic …

2012

Classification of periodic activities using the Wasserstein distance

L Oudre, J Jakubowicz, P Bianchi… - IEEE transactions on …, 2012 - ieeexplore.ieee.org

In this paper, we introduce a novel nonparametric classification technique based on the use

of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the

analysis of recorded accelerometer data: the aim is to retrieve three types of periodic …

Cited by 25 Related articles All 10 versions
<——2012—— —2012———— -90—

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

2012

[PDF] academia.edu

Further results on probabilistic model validation in Wasserstein metric

A Halder, R Bhattacharya - 2012 IEEE 51st IEEE Conference …, 2012 - ieeexplore.ieee.org

In a recent work [1], we have introduced a probabilistic formulation for the model validation

problem to provide a unifying framework for (in) validating nonlinear deterministic and

stochastic models, in both discrete and continuous time. As an extension to that work, this …

A geometric study of Wasserstein spaces: Hadamard spaces

J Bertrand, B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity)

probability measures on any (not too wild) metric space X, called its Wasserstein space. In

this paper we investigate the geometry of when X is a Hadamard space, by which we mean …

Wasserstein decay of one dimensional jump-diffusions

B Cloez - arXiv preprint arXiv:1202.1259, 2012 - arxiv.org

This work is devoted to the Lipschitz contraction and the long time behavior of certain

Markov processes. These processes diffuse and jump. They can represent some natural

phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac …

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces $ X $ with curvature

bounded below. The gradient flow of a geodesically convex functional on the quadratic …

2012

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

a general metric space. The main goal of this paper is to estimate the largeness of

Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

2012 [PDF] sciencedirect.com

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

[PDF] Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions

V Omelchenko - Bulletin of the Czech Econometric Society, 2012 - library.utia.cas.cz

In this paper, we aim to explore the speed of convergence of the Wasserstein distance

between stable cumulative distribution functions and their empirical counterparts. The

theoretical results are compared with the results provided by simulations. The need to use …

CONE STRUCTURE OF L²-WASSERSTEIN SPACES

A Takatsu, T Yokota - Journal of Topology and Analysis, 2012 - World Scientific

The aim of this paper is to obtain a better understanding of the geometric structure of

quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on

their cone and product structures, and prove that the quadratic Wasserstein space over any …

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

We examine the entropic measure, recently constructed by von Renesse and Sturm, a

measure over the metric space of probability measures on the unit interval equipped with the

2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over …

<——2012—— —2012———— -100—

Wasserstein geometry of porous medium equation

A Takatsu - Annales de l'Institut Henri Poincare (C) Non Linear …, 2012 - Elsevier

We study the porous medium equation with emphasis on q-Gaussian measures, which are

generalizations of Gaussian measures by using power-law distribution. On the space of q-

Gaussian measures, the porous medium equation is reduced to an ordinary differential …

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

[PDF] tohoku.ac.jp

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - math.tohoku.ac.jp

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

ttps://www.researchgate.net › publication › 266545618_...

2012 see 2010

An extension of the Weak KAM theory to the Wasserstein torus

This model represents the motion of pedestrian groups in a realistic way. The simulation results reveal that the walking behavior of groups has an important but ...

[CITATION] Gradient flows in Wasserstein spaces and applications to crowd movement, Séminaire XEDP, 2009-2010

F Santambrogio - Exp. No. XXVII, 2012

https://www.semanticscholar.org › paper › An-extension-...

2012

An extension of the Weak KAM theory to the Wasserstein torus

In this article we propose a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on P(T), the s

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

W Gangbo, A Tudorascu see 2044

Wasserstein geometry of porous medium equation

A Takatsu - Annales de l'Institut Henri Poincare (C) Non Linear …, 2012 - Elsevier

We study the porous medium equation with emphasis on q-Gaussian measures, which are

generalizations of Gaussian measures by using power-law distribution. On the space of q-

Gaussian measures, the porous medium equation is reduced to an ordinary differential …

2012 see 2011

Second order analysis on (𝒫₂ (ℳ), 𝒲₂)

N Gigli - 2012 - ams.org

… We develop a rigorous second order analysis on the space of probability measures on a

Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. Our …

Save Cite Cited by 1 Related articles All 2 versions

2012 video

Video: Benoît Kloeckner, "The size of Wasserstein spaces"

http://www.birs.ca › watch › 201205241010-Kloeckner

Benoît Kloeckner speaking at BIRS workshop, Optimal Transportation and Differential Geometry, on Thursday, May 24, 2012 on the topic: The ...

Banff International Research Station · Banff International Research Station · May 24, 2012

[CITATION] The size of Wasserstein spaces

B Kloeckner - 2012 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General

(Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

[CITATION] The size of Wasserstein spaces

B Kloeckner - 2012 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General

(Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

2012

A geometric study of Wasserstein spaces: Hadamard spaces

23 citations* for all

2012 JOURNAL OF TOPOLOGY AND ANALYSIS

Jérôme Bertrand ¹,Benoît Kloeckner ²

¹ Institut de Mathématiques de Toulouse ,² Institut Fourier

Hadamard space

Non-positive curvature

View More (8+)

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity) probability measures on any (not too wild) metric space X, called its Wasserstein space W(X). In this paper we investigate the geometry of W(X) when X is a Hadamard space, by which we mean that $X$ has... View Full Abstract

<——2012———2012————110—

二元离散 antorovich-Rubinstein-Wasserstein L2-距离的精确表示

沈银芳 - 科技信息, 2012 - cqvip.com

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论文检测 | 在线出版 | 优先出版 | 维普官方天猫店. 您的位置：网站首页 > 《中文科技期刊数据库》 >

工程技术 > 机械仪表 > 光学仪器 > 摘要二元离散antorovich-Rubinstein-Wasserstein …

[Chinese Binary Discrete antorovich-Rubinstein-Wasserstein L2-Exact representation of distance]

[PDF] unb.br

LP Lopes - 2012 - repositorio.unb.br

Neste trabalho propomos testes não-paramétricos para classes de distribuições de cauda

pesada, que incluem as _-estáveis e as extremais de Fréchet. As estatísticas apresentadas,

funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F _a …

数据挖掘中区间数据模糊聚类研究——基于 Wasserstein 测度

李红，孙秋碧 - 计算机工程与应用, 2012 - airitilibrary.com

针对目前区间数据模糊聚类研究中区间距离定义存在的局限性, 引入能够考虑区间数值分布特征

的Wasserstein 距离测度, 提出基于Wasserstein 距离测度的单指标和双指标自适应模糊聚类

算法及迭代模型. 通过仿真实验和CR 指数, 证实了该类模型的优势. 该算法在海量 …

][Chines research on Fuzzy Clustering of Interval Data in Data Mining——Based on Wasserstein Measure]

LP Lopes - 2012 - repositorio.unb.br

Neste trabalho propomos testes não-paramétricos para classes de distribuições de cauda

pesada, que incluem as _-estáveis e as extremais de Fréchet. As estatísticas apresentadas,

funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F _a …

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

012 [PDF] springer.com

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

2012

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

We examine the entropic measure, recently constructed by von Renesse and Sturm, a measure over the metric space of probability measures on the unit interval equipped with the 2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over …

2012

Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction

A Mielke, MA Peletier, G Savare, M Veneroni - 2012 - wias-berlin.de

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $

e> 0$, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by $1/e $, and in the limit $ eto0 …

2012

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space. We study the population barycenter in terms of existence and uniqueness. Using a duality argument, we give a precise characterization of the population barycenter for compactly …

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space (2012)

J Bigot, T Klein - arXiv preprint arXiv:1212.2562

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

2012

Quadratic Wasserstein metrics for von Neumann algebras via transport plans

R Duvenhage - arXiv preprint arXiv:2012.03564, 2020 - arxiv.org

We show how one can obtain a class of quadratic Wasserstein metrics, that is to say,

Wasserstein metrics of order 2, on the set of faithful normal states of a von Neumann algebra

$ A $, via transport plans, rather than through a dynamical approach. Two key points to …

<——2012— —2012——— -120———

Wasserstein geometry of porous medium equation

2012 ANNALES DE L'INSTITUT HENRI POINCARÉ C, ANALYSE NON LINÉAIRE

Nagoya University ,Institut des Hautes Études Scientifiques

Riccati equation

Matrix difference equation

View More (8+)

Abstract We study the porous medium equation with emphasis on q-Gaussian measures, which are generalizations of Gaussian measures by using power-law distribution. On the space of q-Gaussian measures, the porous medium equation is reduced to an ordinary differential equation for covariance matrix. ... View Full Abstract

Wasserstein geometry of porous medium equation

A Takatsu - Annales de l'Institut Henri Poincare (C) Non Linear …, 2012 - Elsevier

We study the porous medium equation with emphasis on q-Gaussian measures, which are generalizations of Gaussian measures by using power-law distribution. On the space of q-Gaussian measures, the porous medium equation is reduced to an ordinary differential …

6th International Conference on Stochastic Analysis and its Applications(Sep. 10{14, 2012 Bedlewo, Poland)

modified2017

www.math.tohoku.ac.jp › ~kuwada › talk › Tp_ICSA

PDF

An extension of Wasserstein contraction associated with the curvature-dimension condition ... extension of (ii)(iii)(iv) to singular spaces. [Ambrosio, Gigli ...

by K Kuwada · ‎Related articles

[PDF] tohoku.ac.jp

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - math.tohoku.ac.jp

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance

M Huang, S Ma, L Lai - arXiv preprint arXiv:2012.05199, 2020 - arxiv.org

The Wasserstein distance has become increasingly important in machine learning and deep

learning. Despite its popularity, the Wasserstein distance is hard to approximate because of

the curse of dimensionality. A recently proposed approach to alleviate the curse of …

Finsler structure in the p-Wasserstein space and gradient flows

www.sciencedirect.com › science › article › pii › pdf

by M Agueh · 2012 · Cited by 9 — of the p-Wasserstein space and its applications to partial differential ... that the p-Wasserstein space can be endowed with a Finsler structure, Fp. Using Fp, we ...
[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

[PDF] tum.de

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

A geometric study of Wasserstein spaces: Hadamard spaces

J Bertrand, B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity)

probability measures on any (not too wild) metric space X, called its Wasserstein space. In

this paper we investigate the geometry of when X is a Hadamard space, by which we mean …

Research articleOpen archive
Central limit theorem for Markov processes with spectral gap in the Wasserstein metric
Stochastic Processes and their ApplicationsMay 2012...

Tomasz KomorowskiAnna Walczuk

Download PDF

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction

A Mielke, MA Peletier, G Savare, M Veneroni - 2012 - wias-berlin.de

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $

e> 0$, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by $1/e $, and in the limit $ eto0 …

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

<——2012— —2012——— -130—

2012 see 2010 [PDF] cambridge.org

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces with curvature bounded

below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein …

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its

solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

This asymptotic behaviour is related to a functional inequality, which links the distance with …

[PDF] laurentoudre.fr

Classification of periodic activities using the Wasserstein distance

L Oudre, J Jakubowicz, P Bianchi… - IEEE transactions on …, 2012 - ieeexplore.ieee.org

In this paper, we introduce a novel nonparametric classification technique based on the use

of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the

analysis of recorded accelerometer data: the aim is to retrieve three types of periodic …

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

Wasserstein active contours

2012

G Peyré, J Fadili, J Rabin - 2012 19th IEEE International …, 2012 - ieeexplore.ieee.org

In this paper, we propose a novel and rigorous framework for region-based active contours

that combines the Wasserstein distance between statistical distributions in arbitrary

dimension and shape derivative tools. To speed-up the computation and be able to handle …

[PDF] academia.edu

Further results on probabilistic model validation in Wasserstein metric

A Halder, R Bhattacharya - 2012 IEEE 51st IEEE Conference …, 2012 - ieeexplore.ieee.org

In a recent work [1], we have introduced a probabilistic formulation for the model validation

problem to provide a unifying framework for (in) validating nonlinear deterministic and

stochastic models, in both discrete and continuous time. As an extension to that work, this …

[PDF] cas.cz

[PDF] Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions

V Omelchenko - Bulletin of the Czech Econometric Society, 2012 - library.utia.cas.cz

In this paper, we aim to explore the speed of convergence of the Wasserstein distance

between stable cumulative distribution functions and their empirical counterparts. The

theoretical results are compared with the results provided by simulations. The need to use …

[PDF] cambridge.org

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces $ X $ with curvature

bounded below. The gradient flow of a geodesically convex functional on the quadratic …

2012 see 2014

Generalized Wasserstein distance and its application to transport equations with source

2012 ARXIV: ANALYSIS OF PDES

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

101 citations* for all

101 citations*

2012 JOURNAL OF FUNCTIONAL ANALYSIS

François Bolley ¹,Ivan Gentil ²,Arnaud Guillin ³

¹ Centre de Recherches Mathématiques ,² Institut Camille Jordan [Villeurbanne],³ Institut Universitaire de France

Rate of convergence

Spectral gap

View More (8+)

We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensu... View Full Abstract

<–—2012—–—2012——— -140—

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

Differential forms and symplectic geometry on Wasserstein ...

2012 video

... and Differential Geometry, on Thursday, May 24, 2012 on the topic: Differential forms and symplectic ...

Banff International Research Station · Banff International Research Station · May 24, 2012

[CITATION] Differential forms and symplectic geometry on Wasserstein space

T Pacini - 2012 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General

(Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

year 2012 [PDF] tohoku.ac.jp

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - math.tohoku.ac.jp

An extension of Wasserstein contraction associated with the curvature-dimension condition …

Formulate a missing condition corresponding to (ii) Extension of the implication (ii) ⇔ (iii) …

⇒ Extension to more general situation …

A geometric study of Wasserstein spaces: Hadamard spaces

J Bertrand, B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity)

probability measures on any (not too wild) metric space X, called its Wasserstein space. In

this paper we investigate the geometry of when X is a Hadamard space, by which we mean …

[PDF] Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions

V Omelchenko - Bulletin of the Czech Econometric Society, 2012 - library.utia.cas.cz

In this paper, we aim to explore the speed of convergence of the Wasserstein distance

between stable cumulative distribution functions and their empirical counterparts. The

theoretical results are compared with the results provided by simulations. The need to use …

[PDF] tohoku.ac.jp

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - math.tohoku.ac.jp

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

Video: Benoît Kloeckner, "The size of Wasserstein spaces"

. at BIRS workshop, Optimal Transportation and Differential Geometry, on Thursday, May 24, 2012 on the topic ...

Banff International Research Station · Banff International Research Station · May 24, 2012

[CITATION] The size of Wasserstein spaces

B Kloeckner - 2012 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General

(Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

2012 see 12013

Entropic Burgers' equation via a minimizing movement ...

Apr 3, 2012 — Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric. Nicola Gigli &; Felix Otto. Calculus of ...

by N Gigli · ‎2013 · ‎Cited by 14 · ‎Related articles

Updated: 2 mar ...

2012 ebook
Entropic Burgers & rsquo; equation via a minimizing movement scheme based on the Wasserstein metric

[CITATION] Entropic Burgers & Rsquo; Equation Via a Minimizing Movement Scheme Based on the Wasserstein Metric

N Gigli, F Otto - 2012 - Niedersächsische Staats-und …

[CITATION] Entropic Burgers & Rsquo; Equation Via a Minimizing Movement Scheme Based on the Wasserstein Metric

N Gigli, F Otto - 2012 - Niedersächsische Staats-und

[CITATION] Entropic Burgers & Rsquo; Equation Via a Minimizing Movement Scheme Based on the Wasserstein Metric

N Gigli, F Otto - 2012 - Niedersächsische Staats-und … see 2010, 213

[CITATION] Entropic Burgers & Rsquo; Equation Via a Minimizing Movement Scheme Based on the Wasserstein Metric

N Gigli, F Otto - 2012 - Niedersächsische Staats-und …

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction

A Mielke, MA Peletier, G Savare, M Veneroni - 2012 - wias-berlin.de

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $

e> 0$, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by $1/e $, and in the limit $ eto0 …

0812.2752] Cone structure of $L^2$-Wasserstein spaces - arXiv

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

by A Takatsu · 2008 · Cited by 12 — Abstract: The purpose of this paper is to understand the geometric structure of the L^2-Wasserstein space \pp over the Euclidean space.

Missing: <F> ‎SUP> ‎SUP ‎F
Peer-reviewed
CONE STRUCTURE OF <F>L2</F>-WASSERSTEIN SPACES

Authors:ASUKA TAKATSU, TAKUMI YOKOTA
Summary:The aim of this paper is to obtain a better understanding of the geometric structure of quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on their cone and product structures, and prove that the quadratic Wasserstein space over any separable Hilbert space has a cone structure and splits the underlying space isometrically but no more than that. These are shown in more general settings, and one of our main results is that the quadratic Wasserstein space over a Polish space has a cone structure if and only if so does the underlying spaceShow more

Article, 2012
Publication:Journal of Topology and Analysis, 04, June 2012, 237
Publisher:2012

<——2012— —2012——— -150———

2012

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction

A Mielke, MA Peletier, G Savare, M Veneroni - 2012 - wias-berlin.de

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $

e> 0$, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by $1/e $, and in the limit $ eto0 …

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

2012 [PDF] arxiv.org

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

… The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense

to … of these new invariants in the case of some Wasserstein spaces, as well as the dynamical

… of any space inside its Wasserstein space and we prove that the Wasserstein space of a d-…

Fokker–Planck equations for a free energy functional or Markov process on a graph

SN Chow, W Huang, Y Li, H Zhou - Archive for Rational Mechanics and …, 2012 - Springer

… Formally, if the graph is a lattice, both Fokker–Planck equations I (8) and II (9) can be … in

the Fokker–Planck equation and the 2-Wasserstein metric, especially the theory … In Section 4,

we prove that Fokker–Planck equation I (8) is the gradient flow of free energy, and show some …

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction

A Mielke, MA Peletier, G Savare, M Veneroni - 2012 - wias-berlin.de

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $

e> 0$, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by $1/e $, and in the limit $ eto0 …

2012

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

We examine the entropic measure, recently constructed by von Renesse and Sturm, a

measure over the metric space of probability measures on the unit interval equipped with the

2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over …

2012

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

2012 [PDF] univ-toulouse.fr

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. eprint

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

2012

Wasserstein geometry of porous medium equation

A Takatsu - Annales de l'Institut Henri Poincare (C) Non Linear …, 2012 - Elsevier

We study the porous medium equation with emphasis on q-Gaussian measures, which are

generalizations of Gaussian measures by using power-law distribution. On the space of q-

Gaussian measures, the porous medium equation is reduced to an ordinary differential …

2012 arxiv.org › math

by S Lisini · 2012 · Cited by 44 —

Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn-Hilliard and certain thin film equations.

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted

Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare Department of

Mathematics, University of Pavia, Italy DIMO2013 Levico Terme, September 11, 2013 Jointly …

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367, 2012

Cited by 2 Related articles
Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

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[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

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[PDF] Behavior and Convergence of Wasserstein Metric in the Framework of Stable Distributions

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In this paper, we aim to explore the speed of convergence of the Wasserstein distance between stable cumulative distribution functions and their empirical counterparts. The theoretical results are compared with the results provided by simulations. The need to use …

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

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We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with …

PDF] academia.edu

Further results on probabilistic model validation in Wasserstein metric

A Halder, R Bhattacharya - … IEEE 51st IEEE Conference on …, 2012 - ieeexplore.ieee.org

In a recent work [1], we have introduced a probabilistic formulation for the model validation problem to provide a unifying framework for (in) validating nonlinear deterministic and stochastic models, in both discrete and continuous time. As an extension to that work, this …

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

We examine the entropic measure, recently constructed by von Renesse and Sturm, a measure over the metric space of probability measures on the unit interval equipped with the 2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over …

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and certain thin film equations. The considered evolution equations are in the form of a gradient …

2012

Cahn-Hilliard and Thin Film equations with nonlinear mobility ...

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

by S Lisini · 2012 · Cited by 44 — The considered evolution equations are in the form of a gradient flow for a ... Dirichlet energy with respect to a Wasserstein-like transport metric, ...

Missing: degCahn- ‎| Must include: degCahn-

<——2012— —2012——— -170———

PDF] univ-toulouse.fr

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. eprint

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012

2012

Finsler structure in the p-Wasserstein space and gradient flows

www.sciencedirect.com › science › article › pii › pdf

by M Agueh · 2012 · Cited by 9 — Partial Differential Equations/Differential Geometry. Finsler ... of the p-Wasserstein space and its applications to partial differential equations (pde). ... that the p-Wasserstein space can be endowed with a Finsler structure, Fp. Using Fp, we give ...

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

We examine the entropic measure, recently constructed by von Renesse and Sturm, a

measure over the metric space of probability measures on the unit interval equipped with the

2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over …

A geometric study of Wasserstein spaces: Hadamard spaces

J Bertrand, B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity)

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2012

[PDF] cambridge.org

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces with curvature bounded

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2012

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

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Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

2012

CONE STRUCTURE OF L²-WASSERSTEIN SPACES

A Takatsu, T Yokota - Journal of Topology and Analysis, 2012 - World Scientific

The aim of this paper is to obtain a better understanding of the geometric structure of

quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on

their cone and product structures, and prove that the quadratic Wasserstein space over any …

See 2013

Wasserstein decay of one dimensional jump-diffusions

B Cloez - arXiv preprint arXiv:1202.1259, 2012 - arxiv.org

This work is devoted to the Lipschitz contraction and the long time behavior of certain

Markov processes. These processes diffuse and jump. They can represent some natural

phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac …

First Variation Formula in Wasserstein Spaces over Compact ...

www.cambridge.org › core › journals › article › first-vari...

by N Gigli · ‎2012 · ‎Cited by 13 · ‎Related articles

J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces X with curvature bounded below. The gradient flow of a ...

<——2012— —2012——— -180———

[PDF] unb.br

LP Lopes - 2012 - repositorio.unb.br

Neste trabalho propomos testes não-paramétricos para classes de distribuições de cauda

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funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F _a …

[PDF] univ-toulouse.fr

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. eprint

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012

First variation formula in Wasserstein spaces over compact Alexandrov spaces

[PDF] cambridge.org

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces with curvature bounded

below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein …

[CITATION] First variation formula in Wasserstein spaces over compact Alexandrov spaces, to appear in Canad

N Gigli, SI Ohta - Math. Bull, 2010

Finsler structure in the p-Wasserstein space and gradient flows

www.sciencedirect.com › science › article › pii › pdf

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

Finsler structure in the p-Wasserstein space and gradient flows

www.sciencedirect.com › science › article › pii › pdf

by M Agueh · 2012 · Cited by 9 — I 350 (2012) 35–40. Contents lists available ... measures, i.e., the p-Wasserstein space, can be endowed with a Finsler metric whose induced ... of the p-Wasserstein space

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

Classification of periodic activities using the Wasserstein distance

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L Oudre, J Jakubowicz, P Bianchi… - IEEE transactions on …, 2012 - ieeexplore.ieee.org

In this paper, we introduce a novel nonparametric classification technique based on the use

of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the

analysis of recorded accelerometer data: the aim is to retrieve three types of periodic …

2012

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its

solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

This asymptotic behaviour is related to a functional inequality, which links the distance with …

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

[HTML] Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

T Komorowski, A Walczuk - Stochastic Processes and their Applications, 2012 - Elsevier

Suppose that {X t, t≥ 0} is a non-stationary Markov process, taking values in a Polish metric

space E. We prove the law of large numbers and central limit theorem for an additive

functional of the form∫ 0 T ψ (X s) ds, provided that the dual transition probability …

<——2012— —2012——— -190———

Further results on probabilistic model validation in Wasserstein metric

A Halder, R Bhattacharya - 2012 IEEE 51st IEEE Conference …, 2012 - ieeexplore.ieee.org

In a recent work [1], we have introduced a probabilistic formulation for the model validation

problem to provide a unifying framework for (in) validating nonlinear deterministic and

stochastic models, in both discrete and continuous time. As an extension to that work, this …

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

Further results on probabilistic model validation in Wasserstein metric

A Halder, R Bhattacharya - 2012 IEEE 51st IEEE Conference …, 2012 - ieeexplore.ieee.org

In a recent work [1], we have introduced a probabilistic formulation for the model validation

problem to provide a unifying framework for (in) validating nonlinear deterministic and

stochastic models, in both discrete and continuous time. As an extension to that work, this …

Wasserstein decay of one dimensional jump-diffusions

B Cloez - arXiv preprint arXiv:1202.1259, 2012 - arxiv.org

This work is devoted to the Lipschitz contraction and the long time behavior of certain

Markov processes. These processes diffuse and jump. They can represent some natural

phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac …

2012. modified 2021

Linear models for histogram data based on Wasserstein distance: scalar and functional models

Antonio Irpino - Rosanna Verde

Second University of Naples

Workshop on New Perspectives in Functional Data Analysis (FDA) Caserta, September 26-27 2012

2012

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

An extension of the Weak KAM theory to the Wasserstein torus

https://www.semanticscholar.org › paper › An-extension-...

In this article we propose a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on P(T), the space of probability ...

year 2012

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

2012

[PDF] [PDF] arxiv.org

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

a general metric space. The main goal of this paper is to estimate the largeness of

Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

2012 [PDF] tohoku.ac.jp

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - math.tohoku.ac.jp

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

<——2012— —2012——— -200———

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted

Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare Department of Mathematics,

University of Pavia, Italy DIMO2013 Levico Terme, September 11, 2013 Jointly with S. Lisini, D …

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367, 2012

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

2012 [PDF] tohoku.ac.jp

K Kuwada - math.tohoku.ac.jp

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

[PDF] laurentoudre.fr

Classification of periodic activities using the Wasserstein distance

L Oudre, J Jakubowicz, P Bianchi… - IEEE transactions on …, 2012 - ieeexplore.ieee.org

In this paper, we introduce a novel nonparametric classification technique based on the use

of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the

analysis of recorded accelerometer data: the aim is to retrieve three types of periodic …

Wasserstein decay of one dimensional jump-diffusions

B Cloez - arXiv preprint arXiv:1202.1259, 2012 - arxiv.org

This work is devoted to the Lipschitz contraction and the long time behavior of certain

Markov processes. These processes diffuse and jump. They can represent some natural

phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac …

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

O Chodosh - Journal of Functional Analysis, 2012 - Elsevier

We examine the entropic measure, recently constructed by von Renesse and Sturm, a

measure over the metric space of probability measures on the unit interval equipped with the

2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over …

2012

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

a general metric space. The main goal of this paper is to estimate the largeness of

Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

CONE STRUCTURE OF L²-WASSERSTEIN SPACES

A Takatsu, T Yokota - Journal of Topology and Analysis, 2012 - World Scientific

The aim of this paper is to obtain a better understanding of the geometric structure of

quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on

their cone and product structures, and prove that the quadratic Wasserstein space over any …

Wasserstein geometry of porous medium equation

A Takatsu - Annales de l'Institut Henri Poincare (C) Non Linear …, 2012 - Elsevier

We study the porous medium equation with emphasis on q-Gaussian measures, which are

generalizations of Gaussian measures by using power-law distribution. On the space of q-

Gaussian measures, the porous medium equation is reduced to an ordinary differential …

Wasserstein gradient flows from large deviations of thermodynamic limits

MH Duong, V Laschos, M Renger - arXiv preprint arXiv:1203.0676, 2012 - arxiv.org

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the rate

functional, that characterizes the large deviations from the hydrodynamic limit, in a way that …

[CITATION] Wasserstein gradient flows from large deviations of thermodynamic limits (accepted for publication in ESAIM: COCV)

MH Duong, V Laschos, M Renger - 2012

PDF] An extension of the Weak KAM theory to the ...

https://www.semanticscholar.org › paper › An-extension-...

... a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on P(T), the space of probability measures on the torus, ...

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

<——2012— —2012——— -210———

https://arxiv.org › math

Decomposition of geodesics in the Wasserstein space ... - arXiv

by F Cavalletti · 2012 · Cited by 34 — Abstract: We will prove a decomposition for Wasserstein geodesics in the following sense: let (X,d,m) be a non-branching metric measure ...

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

Differential forms and symplectic geometry on Wasserstein ...

https://open.library.ubc.ca › handle

May 24, 2012 — Differential forms and symplectic geometry on Wasserstein space Pacini, Tommaso 2012-05-24. mp4. 00:00 00:00 ...

[CITATION] Differential forms and symplectic geometry on Wasserstein space

T Pacini - 2012 - open.library.ubc.ca

… Education Library; Irving K. Barber Learning Centre; Koerner Library; Law Library; Music, Art

and Architecture Library; Rare Books and Special Collections; University Archives; Woodward

Library; Xwi7xwa Library. UBC Okanagan; Innovation Library; Okanagan Library; Special …

Finsler structure in the p-Wasserstein space and gradient flows

https://www.sciencedirect.com › science › article › pii › pdf

by M Agueh · 2012 · Cited by 9 — that the p-Wasserstein space can be endowed with a Finsler structure, Fp. Using ... Lp-norm of (0,1) t ↦→ F(c(t), ˙c(t)) as it more convenient for our applications.

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

2012 see 2011
Problèmes d'interaction discret-continu et distances de Wasserstein

Authors:Emmanuel Boissard, Patrick Cattiaux, Pierre Degond, Université Toulouse 3 Paul Sabatier (1969-....).
Summary:On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur pour l'approximation particulaire des solutions de certaines équations aux dérivées partielles. Elles jouent également le rôle de mesures de distorsion naturelles dans les problèmes de quantification et de partitionnement ("clustering"). Un problème associé à ces questions est d'étudier la vitesse de convergence dans la loi des grands nombres empirique pour cette distorsion. La première partie de cette thèse établit des bornes non-asymptotiques, en particulier dans des espaces de Banach de dimension infinie, ainsi que dans les cas où les observations sont non-indépendantes. La seconde partie est consacrée à l'étude de deux modèles issus de la modélisation des déplacements de populations d'animaux. On introduit un nouveau modèle individu-centré de formation de pistes de fourmis, que l'on étudie expérimentalement à travers des simulations numériques et une représentation en terme d'équations cinétiques. On étudie également une variante du modèle de Cucker-Smale de mouvement d'une nuée d'oiseaux : on montre le caractère bien posé de l'équation de transport de type Vlasov associée, et on établit des résultats sur le comportement en temps long de cette équation. Enfin, dans une troisième partie, on étudie certaines applications statistiques de la notion de barycentre dans l'espace des mesures de probabilités muni de la distance de Wasserstein, récemment introduite par M. Agueh et G. CarlierShow more
Computer Program, 2012
French
Publisher:Université Paul Sabatier, Toulouse 3, Toulouse, 2012

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

[HTML] Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

T Komorowski, A Walczuk - Stochastic Processes and their Applications, 2012 - Elsevier

Suppose that {X t, t≥ 0} is a non-stationary Markov process, taking values in a Polish metric

space E. We prove the law of large numbers and central limit theorem for an additive

functional of the form∫ 0 T ψ (X s) ds, provided that the dual transition probability …

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its

solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

This asymptotic behaviour is related to a functional inequality, which links the distance with …

<——2012—–—2012——— 220——

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

2012

Passing to the limit in a Wasserstein gradient flow: From diffusion to reaction

A Mielke, MA Peletier, G Savare, M Veneroni - 2012 - wias-berlin.de

We study a singular-limit problem arising in the modelling of chemical reactions. At finite $

e> 0$, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by $1/e $, and in the limit $ eto0 …

[CITATION] Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

S Arnrich, A Mielke, MA Peletier, G Savaré… - Calculus of Variations …, 2012 - Springer

We study a singular-limit problem arising in the modelling of chemical reactions. At finite

ε\,>\, 0, the system is described by a Fokker-Planck convection-diffusion equation with a

double-well convection potential. This potential is scaled by 1/ε, and in the limit ε\to0, the …

Characterization of barycenters in the Wasserstein space by ...

by J Bigot · 2012 · Cited by 30 — [Submitted on 11 Dec 2012 (v1), last revised 29 Nov 2017 (this version, v6)] ... In this setting, the problem of estimating a population barycenter from n ...

Missing: eprint ‎| Must include: eprint

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. eprint

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012

Finsler structure in the p-Wasserstein space and gradient flows

https://www.sciencedirect.com › science › article › pii › pdf

by M Agueh · 2012 · Cited by 9 — I 350 (2012) 35–40 ... Partial Differential Equations/Differential Geometry ... of the p-Wasserstein space and its applications to partial differential equations (pde). ... that the p-Wasserstein space can be endowed with a Finsler structure, Fp.

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

Finsler structure in the p-Wasserstein space and gradient flows

https://www.sciencedirect.com › science › article › pii › pdf

Author:Martial Agueh
Summary:It is known from the work of F. Otto (2001) , that the space of probability measures equipped with the quadratic Wasserstein distance, i.e., the 2-Wasserstein space, can be viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced by a general homogeneous cost of degree p > 1 , the corresponding space of probability measures, i.e., the p-Wasserstein space, can be endowed with a Finsler metric whose induced distance function is the p-Wasserstein distance. Using this Finsler structure of the p-Wasserstein space, we give definitions of the differential and gradient of functionals defined on this space, and then of gradient flows in this space. In particular we show in this framework that the parabolic q-Laplacian equation is a gradient flow in the p-Wasserstein space, where p = q / ( q − 1 ) . When p = 2 , we recover the Riemannian structure introduced by F. Otto, which confirms that the 2-Wasserstein space is a Riemann-Finsler manifold. Our approach is confined to a smooth situation where probability measures are absolutely continuous with respect to the Lebesgue measure on R n , and they have smooth and strictly positive densities.

Il est connu que lʼespace des mesures de probabilités muni de la distance de Wasserstein L 2 (lʼespace de Wasserstein L 2 ) est une variété Riemanienne (voir F. Otto (2001) ). Ici, nous montrons que lorsquʼon change le coût quadratique en un coût plus general, homogène de degré p > 1 , lʼespace correspondant (lʼespace de Wasserstein L p ) admet une structure de Finsler dont la distance induite est la distance de Wasserstein L p . Grâce à cette structure de Finsler, nous donnons une définition de la différentiel et du gradient des fonctionelles définies sur cet espace, et aussi des flux de gradient sur cet espace. En particulier nous montrons que lʼéquation parabolique q-Laplacien est un flux de gradient dans lʼespace de Wasserstein L p pour p = q / ( q − 1 ) . Quand p = 2 , nous retrouvons la structure Remannienne de F. Otto, ce qui confirme que lʼespace de Wasserstein L 2 est une variété Riemanienne de Finsler. Notre méthode sʼapplique à des mesures de probabilité absolument continues par rapport à la mesure de Lebesgue dans R n , et dont les densités sont strictement positivesShow more
rticle, 2012
Publication:Comptes rendus - Mathématique, 350, 201201, 35
Publisher:2012

2012

urenruzie in het Jodendom' [Review of: B. Wasserstein. Aan de ...

https://pure.knaw.nl › publications

Houwink Ten Cate, J. T. M. (2012). 'Burenruzie in het Jodendom' [Review of: B. Wasserstein. Aan de vooravond]. Historisch Nieuwsblad, 12, 81-82. Houwink ...

[CITATION] Gradient flows in Wasserstein spaces and applications to crowd movement, Séminaire XEDP, 2009-2010

F Santambrogio - Exp. No. XXVII, 2012

Cahn-Hilliard and Thin Film equations with nonlinear mobility ...

by S Lisini · 2012 · Cited by 46 — [Submitted on 11 Jan 2012]. Title:Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics ... The considered evolution equations are in the form of a gradient flow for a perturbed ... Our main assumption is that the mobility of the particles is a concave function of their ...

Missing: FCahn- ‎| Must include: FCahn-

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367, 2012

[PDF] An extension of the Weak KAM theory to the ...

https://www.semanticscholar.org › paper › An-extension-...

... a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on P(T), the space of probability measures on the torus, ...

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

'Burenruzie in het Jodendom' [Review of: B. Wasserstein. Aan de ...

https://pure.knaw.nl › publications

Houwink Ten Cate, J. T. M. (2012). 'Burenruzie in het Jodendom' [Review of: B. Wasserstein. Aan de vooravond]. Historisch Nieuwsblad, 12, 81-82. Houwink ...

[CITATION] 'Burenruzie in het Jodendom'[Review of: B. Wasserstein. Aan de vooravond]

JTM Houwink Ten Cate - Historisch Nieuwsblad, 2012 - narcis.nl

KNAW Narcis. Back to search results. Publication 'Burenruzie in het Jodendom' [Review

of: B. Wasserstein. Aan de vooravond] (2012). Pagina-navigatie: Main …

2012

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

<——2012— —2012——— -230———

Convergence to equilibrium in Wasserstein distance for Fokker–Planck equations

F Bolley, I Gentil, A Guillin - Journal of Functional Analysis, 2012 - Elsevier

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its

solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance.

This asymptotic behaviour is related to a functional inequality, which links the distance with …

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

a general metric space. The main goal of this paper is to estimate the largeness of

Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

Further results on probabilistic model validation in Wasserstein metric

A Halder, R Bhattacharya - 2012 IEEE 51st IEEE Conference …, 2012 - ieeexplore.ieee.org

In a recent work [1], we have introduced a probabilistic formulation for the model validation

problem to provide a unifying framework for (in) validating nonlinear deterministic and

stochastic models, in both discrete and continuous time. As an extension to that work, this …

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

2012

2012 [PDF] cambridge.org

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces with curvature bounded

below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein …

2013

Cahn-Hilliard and Thin Film equations with nonlinear mobility ...

by S Lisini · 2012 · Cited by 46 — ... nonlinear mobility as gradient flows in weighted-Wasserstein metrics ... of fourth order, like the Cahn-Hilliard and certain thin film equations.

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in

weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare

Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367, 2012

2012

[HTML] Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

T Komorowski, A Walczuk - Stochastic Processes and their Applications, 2012 - Elsevier

Suppose that {X t, t≥ 0} is a non-stationary Markov process, taking values in a Polish metric

space E. We prove the law of large numbers and central limit theorem for an additive

functional of the form∫ 0 T ψ (X s) ds, provided that the dual transition probability …

2012

Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

S Lisini, D Matthes, G Savaré - Journal of Differential Equations, 2012 - Elsevier

In this paper, we establish a novel approach to proving existence of non-negative weak

solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and

certain thin film equations. The considered evolution equations are in the form of a gradient …

2012

[PDF] cambridge.org

First variation formula in Wasserstein spaces over compact Alexandrov spaces

N Gigli, S Ohta - Canadian Mathematical Bulletin, 2012 - cambridge.org

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively

curved Alexandrov spaces to general compact Alexandrov spaces with curvature bounded

below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein …

<——2012— —2012——— -240——

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

2012 [PDF] arxiv.org

CONE STRUCTURE OF L²-WASSERSTEIN SPACES

A Takatsu, T Yokota - Journal of Topology and Analysis, 2012 - World Scientific

The aim of this paper is to obtain a better understanding of the geometric structure of

quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on

their cone and product structures, and prove that the quadratic Wasserstein space over any …

2012 video

Sliced wasserstein autoencoder - Rvx

Implementation for Topic Modeling with Wasserstein Autoencoders. Demonstration of Wasserstein GAN. Using ...

Oct 2, 2012 · Uploaded by CodeEmporium

2012 video

A Non-Commutative Analog of the 2-Wasserstein Metric for which the ...

- Uploaded by Institute for Advanced Study

A Non-Commutative Analog of the 2-Wasserstein Metric for which the Fermionic Fokker-Planck Equation is ...
Nov 13, 2012

Central limit theorem for Markov processes with spectral gap ...

https://www.sciencedirect.com › science › article › pii

by T Komorowski · 2012 · Cited by 69 — In [34]

Markov processes stable in the Wasserstein type metric, stronger than the one considered here, have been examined and an analogue of Theorem 2.1 has ...

2012

2012 zzz

[CITATION] An extension of the Weak KAM theory to the Wasserstein torus

W Gangbo, A Tudorascu

<——2012—–—2012——— -246—end 2012

start 2013 Wasserstein

Localisation de masse et espaces de Wasserstein

by Le Gouic, Thibaut 2013 Dissertation :

Le travail de cette thèse est basé sur deux outils : le packing d'un ensemble et les espaces de Wasserstein. Une première partie s'intéresse à...

Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

MR3220453 Kuwada, Kazumasa Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula. Potential theory and its related fields, 61–80, RIMS Kôkyûroku Bessatsu, B43, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013. 60J35 (39B62 49N15 60B10 70H20)

K KUWADA - RIMS Kokyuroku Bessatsu, 2013 - ci.nii.ac.jp

... ISSN, 巻, 号, ページ, 出版者, 参考文献, 出版年, 年から年まで. すべて CiNiiに本文あり

CiNiiに本文あり、または連携サービスへのリンクあり. 論文検索. 著者検索. 論文検索. Gradient estimate

for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related ...

2013

[pdf] On the rate of convergence in Wasserstein distance of the empirical measure

Nicolas Fournier Arnaud Guillin 2013

Application of the Wasserstein metric to seismic signals

L Ning, T Georgiou - SIAM

2013 Prcedings of the Conference on Control and its Applications

Abstract We consider the problem of approximating a (nonnegative definite) covariance

matrix by the sum of two structured covariances–one which is diagonal and one which has

low-rank. Such an additive decomposition follows the dictum of factor analysis where ...

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org INRIA PARIS

Abstract: Seismic signals are typically compared using travel time difference or $ L_2 $

difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit

in seismology. It exhibits properties from both of the traditional measures mentioned ...

Times Cited: 41

MR3187785 Communications in Mathematical Sciences

Volume 12 (2014) Number 5

[PDF] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013 - lp.uni-goettingen.de

Abstract So far we have studied the structure of (P2 (X), W2)(ie the space of Borel probability

measures with finite second moments equipped with the Wasserstein distance W2) both for

X being a Polish and a geodesic space. We have seen that (P2 (X), W2) inherits crucial ...

[CITATION] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013

[CITATION] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013

On Interpolation and Curvature via Wasserstein Geodesics

M Kell - arXiv preprint arXiv:1311.5407, 2013 - arxiv.org

Abstract: In this article, a proof of the interpolation inequality along geodesics in $ p $-

Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove

the Borel-Brascamp-Lieb inequality for general Riemannian and Finsler manifolds and led ...

Sliced and radon wasserstein barycenters of measures

N Bonneel, J Rabin, G Peyré, H Pfister - 2013 - hal.archives-ouvertes.fr

Abstract This article details two approaches to compute barycenters of measures using 1-D

Wasserstein distances along radial projections of the input measures. The first method

makes use of the Radon transform of the measures, and the second is the solution of a ...

J. Math. Imaging Vision 51 (2015), no. 1, 22–45. 9

<——2013———2013——— -10—

[PDF] On properties of the Generalized Wasserstein distance

B Piccoli, F Rossi - arXiv preprint arXiv:1304.7014, 2013 - lsis.org

Abstract In this article, we continue the investigation of the generalized Wasserstein distance

Wa, bp, that we introduced in [12]. We first prove that the particular choice W1, 1 1 coincides

with the so-called flat metric. This provides a dual formulation for the flat metric, in the spirit ...

Behaviour and convergence of Wasserstein metric in the framework of stable distributions

V Omelchenko - Bulletin of the Czech Econometric Society, 2013 - ces.utia.cas.cz

Abstract In the paper, we aim to demonstrate the behaviour of approximate empirical optimal

values of stochastic problems involving stable distributions. Such empirical optimal values

under mere conditions converge to the optimal value of the initial problem. The precision ...

Contractivity of the Wasserstein metric for the kinetic Kuramoto equation

JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim - arXiv preprint arXiv: …, 2013 - arxiv.org

Abstract: We present synchronization and contractivity estimates for the kinetic Kuramoto

model obtained from the Kuramoto phase model in the mean-field limit. For identical

Kuramoto oscillators, we present an admissible class of initial data leading to time- ...

Frequency Domain Model Validation in Wasserstein Metric - Tamu.edu IEEE

Further Results on Probabilistic Model Validation in Wasserstein Metric. A. Halder and R. Bhattacharya Submitted, 2013. Preprint.

Abstract:This paper connects the time-domain uncertainty propagation approach for model validation in Wasserstein distance 2W2, introduced by the authors in [1], with the frequency domain model validation in the same. To the best of our knowledge, this is the first frequency domain interpretation of Monge-Kantorovich optimal transport. It is shown that the asymptotic 2W2 can be written as functions of the H2 norms of the system gains, which have intuitive meaning. A geometric interpretation for this newly derived frequency-domain formula is given. The geometric interpretation helps us in comparing Wasserstein distance with classical frequency-domain validation metrics like nu-gap.

MR3126070 Bertrand, Jérôme; Kloeckner, Benoît R. A geometric study of Wasserstein spaces: an addendum on the boundary. Geometric science of information, 405–412, Lecture Notes in Comput. Sci., 8085, Springer, Heidelberg, 2013. 53C23 (28A33 49Q20)

A geometric study of Wasserstein spaces: an addendum on the boundary

J Bertrand, B Kloeckner - arXiv preprint arXiv:1302.1424, 2013 - arxiv.org

Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally

compact metric space. The set of its Borel probability measures with finite second moment can

be endowed with a natural distance defined using optimal transportation, giving birth to ...

MR2731158 (2011h:53045) Geometric Science of Information, 2013 - Springer

2013

Minimax rates of convergences for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - arXiv preprint arXiv:1302.6103, 2013 - arxiv.org

Abstract: The subject of this paper is the estimation of a probability measure on ${\ mathbb

R}^ d $ from data observed with an additive noise, under the Wasserstein metric of order $ p

$(with $ p\ geq 1$). We assume that the distribution of the errors is known and belongs to ...

[PDF] from cam.ac.uk

[PDF] A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring, CB Schönlieb - maths.cam.ac.uk

Abstract. We consider a nonlinear fourth-order diffusion equation that arises in denoising of

image densities. We propose an implicit timestepping scheme that employs a primal-dual

method for computing the subgradient of the total variation semi-norm. The constraint on ...

Self-improvement of the Bakry-\'Emery condition and Wasserstein contraction of the heat flow in RCD (K,\ infty) metric measure spaces

G Savaré - arXiv preprint arXiv:1304.0643, 2013 - arxiv.org

Abstract: We prove that the linear heat flow in a RCD (K,\ infty) metric measure space (X, d,

m) satisfies a contraction property with respect to every L^ p-Kantorovich-Rubinstein-

Wasserstein distance. In particular, we obtain a precise estimate for the optimal W_\ infty- ...

A geometric study of Wasserstein spaces: ultrametrics

B Kloeckner - arXiv preprint arXiv:1304.5219, 2013 - arxiv.org

Abstract: We study the geometry of the space of measures of a compact ultrametric space X,

endowed with the L^ p Wassertein distance from optimal transportation. We show that the

power p of this distance makes this Wasserstein space affinely isometric to a convex ...

The derivation of Swarming models: Mean-Field Limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - arXiv preprint arXiv:1304.5776, 2013 - arxiv.org

Abstract: These notes are devoted to a summary on the mean-field limit of large ensembles

of interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We ...

Collective Dynamics from Bacteria to …, 2014 - Springer

<——2013———2013—————— -20—

[PDF] Object Segmentation by Shape Matching with Wasserstein Modes

B Schmitzer, C Schnörr - graphmod.iwr.uni-heidelberg.de

Abstract. We gradually develop a novel functional for joint variational object segmentation

and shape matching. The formulation, based on the Wasserstein distance, allows modelling

of local object appearance, statistical shape variations and geometric invariance in a ...

Energy Minimization Methods in Computer Vision …, 2013 - Springer

GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE

SM WALCZAK - faculty.ms.u-tokyo.ac.jp

The lecture will be devoted to the Wassertein distance of Borel probability measures, which

arises from the optimal transportation theory [4][5]. A number of examples will illustrate the

nature of this metric, which is defined on the space of all Borel probability measures. Weak ...

Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

F Cacciafesta, AS de Suzzoni - arXiv preprint arXiv:1304.3005, 2013 - arxiv.org

Abstract: In this paper, we prove the continuity of the flow of KdV on spaces of probability

measures with respect to a combination of Wasserstein distances on $ H^ s $, $ s> 0$ and $

L^ 2$. We are motivated by the existence of an invariant measure belonging to the spaces ...

MR3189324 Dedecker, Jérôme; Michel, Bertrand Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. J. Multivariate Anal. 122 (2013), 278–291. 62G05 (62C20)

Minimax rates of convergence for Wasserstein deconvolution with ...

by J Dedecker - ‎2013 - ‎Cited by 6 - ‎Related articles

Feb 25, 2013 - ... is known and belongs to a class of supersmooth distributions, and we give optimal rates of convergence for the Wasserstein metric of order .

Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance

R Guan, Y Lechevallier… - … TECHNOLOGIES DE L' …, 2013 - hal.archives-ouvertes.fr

... REVUE DES NOUVELLES TECHNOLOGIES DE L'INFORMATION RNTI E.25 (2013) 15-30.

Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein

Distance. Rong Guan 1 , Yves Lechevallier 2 , Huiwen Wang 1. (2013). ...

Stein factors for negative binomial approximation in Wasserstein distance

A. D. Barbour, H. L. Gan, A. Xia (Submitted on 22 Oct 2013) arXiv:1310.6074 [

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour & Xia (2006). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.

Fast Computation of Wasserstein Barycenters Marco Cuturi,

Arnaud Doucet (Submitted on 16 Oct 2013) arXiv:1310.4375

Wasserstein barycenters (Agueh and Carlier, 2011) define a new family of barycenters between N probability measures that builds upon optimal transport theory. We argue using a simple example that Wasserstein barycenters have interesting properties that differentiate them from other barycenters proposed recently, which all build either or both on kernel smoothing and Bregman divergences. We propose two algorithms to compute Wasserstein barycenters for finitely supported measures, one of which can be shown to be a generalization of Lloyd's algorithm. A naive implementation of these algorithms is intractable, because it would involve numerous resolutions of optimal transport problems, which are notoriously expensive to compute. We propose to follow recent work by Cuturi (2013) and smooth these transportation problems to recover faster optimization procedures. We apply these algorithms to the visualization of perturbed images and resampling in particle filters.

ICML 2014 22.06.14 Kyoto University University of Oxford

All 15 versions [PDF] unipv.it

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

François Bolley (CEREMADE), Ivan Gentil (ICJ), Arnaud Guillin (IUF)

(Submitted on 17 Oct 2011 (v1), last revised 18 Sep 2012 (this version, v2)) arXiv:1110.3606

We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solu-

tions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This

asymptotic behaviour is related to a functional inequality, which links the distance with its dis-

sipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this

inequality and compare it to classical ones. The key point isto quantify the contribution of the

diffusion term to the rate of convergence, in any dimension, which to our knowledge is a novelty.

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold Ivan Gentil (ICJ) (Submitted on 16 Oct 2013) arXiv:1310.4264

Abstract We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a Riemannian manifold taking account of the dimension. The result generalizesin a Riemannian context, the dimensional contraction estab

lished in [BGG13] for the Euclidean heat equation. The theorem is proved by using a dimensional c

oercive estimate for the Hodge-deRham semigroup on 1-forms.

Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates

K Kuwada - arXiv preprint arXiv:1308.5471, 2013 - arxiv.org

Abstract: The duality in Bakry-\'Emery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry-Ledoux's refined gradient estimate involving an upper ...

<——2013—————2013———————— -30—

MR3380344 Stannat, Wilhelm Two remarks on the Wasserstein Dirichlet form. Seminar on Stochastic Analysis, Random Fields and Applications VII, 235–255, Progr. Probab., 67, Birkhäuser/Springer, Basel, 2013. 60J60 (31C25 58J65)

Two Remarks on the Wasserstein Dirichlet Form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

Abstract. The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all probability

measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse constructed

in [6] this process in the case of probability measures over the unit interval using Dirichlet ...

Variational Image Segmentation and Cosegmentation with the Wasserstein Distance

P Swoboda, C Schnörr - Energy Minimization Methods in Computer Vision …, 2013 - Springer

Abstract. We present novel variational approaches for segmenting and cosegmenting

images. Our supervised segmentation approach extends the classical Continuous Cut approach

by a global appearance-based data term enforcing closeness of aggregated appearance ...

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

MH Duong - arXiv preprint arXiv:1307.5184, 2013 - arxiv.org

Abstract: In this paper, we study the Wasserstein gradient flow structure of the porous

medium equation. We prove that, for the case of $ q $-Gaussians on the real line, the

functional derived by the JKO-discretization scheme is asymptotically equivalent to a rate- ...

2013 eBook
Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equationShow more

Authors:M.H. Duong, Duong, M.H. (Creator)
Summary:In this paper, we study the Wasserstein gradient flow structure of the porous medium equation. We prove that, for the case of q -Gaussians on the real line, the functional derived by the JKO-discretization scheme is asymptotically equivalent to a rate-large-deviation-like functional. The result explains why the Wasserstein metric as well as the combination of it with the Tsallis-entropy play an important roleShow more
eBook, 2013
English
Publication:s.n., arXiv.org, (2013), 17 pp.
Publisher:s.n, 2013

013 book
Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein

GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE

SM WALCZAK - faculty.ms.u-tokyo.ac.jp

The lecture will be devoted to the Wassertein distance of Borel probability measures, which

arises from the optimal transportation theory [4][5]. A number of examples will illustrate the

nature of this metric, which is defined on the space of all Borel probability measures. Weak ...

The derivation of Swarming models: Mean-Field Limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - arXiv preprint arXiv:1304.5776, 2013 - arxiv.org

Abstract: These notes are devoted to a summary on the mean-field limit of large ensembles

of interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We ...

Approximation in the Wasserstein distance with application to clustering

FP Carli, L Ning, TT Georgiou - arXiv preprint arXiv:1307.5459, 2013 - arxiv.org

Abstract: We consider approximating distributions within the framework of optimal transport

and specialize to problems of clustering data sets. Distances between distributions are

measured in the Wasserstein metric. The main problem we consider is that of ...

2013

Nonlinear diffusion: Geodesic Convexity is equivalent to Wasserstein Contraction

F Bolley, JA Carrillo - arXiv preprint arXiv:1309.1932, 2013 - arxiv.org

Abstract: It is well known that nonlinear diffusion equations can be interpreted as a gradient

flow in the space of probability measures equipped with the Euclidean Wasserstein

distance. Under suitable convexity conditions on the nonlinearity, due to RJ McCann, the ...

MR3250977

Minimax rates of convergences for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - arXiv preprint arXiv:1302.6103, 2013 - arxiv.org

Abstract: The subject of this paper is the estimation of a probability measure on ${\ mathbb

R}^ d $ from data observed with an additive noise, under the Wasserstein metric of order $ p

$(with $ p\ geq 1$). We assume that the distribution of the errors is known and belongs to ...

MR3024100 Bassetti, Federico; Perversi, Eleonora Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations. Electron. J. Probab. 18 (2013), no. 6, 35 pp. 60B10 (60E07 60F05 82C40)

peed of convergence to equilibrium in Wasserstein metrics for Kac ...

by F Bassetti - ‎2013 - ‎Cited by 8 - ‎Related articles

This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial ...

2013 [PDF] projecteuclid.org

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

… of one-dimensional measure-valued kinetic equations, which … to equilibrium in

Kantorovich-Wasserstein distances of order p>α… for the finiteness of the Kantorovich-Wasserstein …

Fast Computation of Wasserstein Barycenters

M Cuturi, A Doucet - arXiv preprint arXiv:1310.4375, 2013 - arxiv.org

Abstract: Wasserstein barycenters (Agueh and Carlier, 2011) define a new family of

barycenters between N probability measures that builds upon optimal transport theory. We

argue using a simple example that Wasserstein barycenters have interesting properties ...

<——2013—————2013————— -40—

[PDF] DECOMPOSITION OF GEODESICS IN THE WASSERSTEIN SPACE AND THE GLOBALIZATION PROBLEM

F CAVALLETTI - cvgmt.sns.it

Abstract. We will prove a decomposition for Wasserstein geodesics in the following sense:

let (X, d, m) be a non-branching metric measure space verifying CDloc (K, N) or equivalently

CD*(K, N). Then every geodesic µt in the L2-Wasserstein space, with µt≪ m, is ...

Geometric and Functional Analysis - Springer

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

Decomposition Of Geodesics In The ... - Gyan Books

2013 see 2012

https://www.gyanbooks.com › Book=Decomposition of...

Reprinted in 2013 with the help of original edition published long back 2013-08-20T00:00:00Z. This book is Paperback edition printed in black & white, sewing ...

$5.20

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - arXiv preprint arXiv: …, 2013 - arxiv.org

Abstract: We consider a nonlinear fourth-order diffusion equation that arises in denoising of

image densities. We propose an implicit time-stepping scheme that employs a primal-dual

method for computing the subgradient of the total variation seminorm. The constraint on ...

Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - arXiv preprint arXiv:1310.3866, 2013 - arxiv.org

Abstract: We perform a systemic study of optimization problems in the Wasserstein spaces

that are analogs of infinite horizon, deterministic control problems. We derive necessary

conditions on action minimizing paths and present a sufficient condition for their existence. ...

MR3302526

The Exponential Formula for the Wasserstein Metric

K Craig - arXiv preprint arXiv:1310.2912, 2013 - arxiv.org

Abstract: We adapt Crandall and Liggett's method from the Banach space case to give a new

proof of the exponential formula for the Wasserstein metric. In doing this, we introduce a new

class of metrics--transport metrics--that have stronger convexity properties than the ...

.... In recent years, there has been significant interest in gradient flow on the space of probability measures endowed with the Wasserstein metric...

Rutgers The State University of New Jersey - New Brunswick Dissertation :

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

L Zhu, Z Cao - Eighth International Symposium on …, 2013 - proceedings.spiedigitallibrary.org

abstract Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not ...

2013

MR3189324 Dedecker, Jérôme; Michel, Bertrand Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. J. Multivariate Anal. 122 (2013), 278–291. 62G05 (62C20)

Minimax rates of convergence for Wasserstein deconvolution with ...

by J Dedecker - ‎2013 - ‎Cited by 6 - ‎Related articles

Feb 25, 2013 - ... is known and belongs to a class of supersmooth distributions, and we give optimal rates of convergence for the Wasserstein metric of order .

2013 [PDF] kyoto-u.ac.jp

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 数理解析研究所講究録別冊= RIMS …, 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For the …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula

K Kuwada - math.ocha.ac.jp

Abstract We extend the duality between gradient estimates of the Markov kernel and

Wasserstein controls of that studied by the author (2010). Especially, the gauge norm-Orlicz

norm type duality holds on Polish geodesic space without any assumption on the Markov ...

MR3182684 Duong, Manh Hong; Laschos, Vaios; Renger, Michiel Wasserstein gradient flows from large deviations of many-particle limits. ESAIM Control Optim. Calc. Var. 19 (2013), no. 4, 1166–1188. 35Q84 (35A15)

Wasserstein gradient flows from large deviations of many-particle limits

MH Duong, V Laschos… - … : Control, Optimisation and …, 2013 - Cambridge Univ Press

Abstract We study the Fokker–Planck equation as the many-particle limit of a stochastic

particle system on one hand and as a Wasserstein gradient flow on the other. We write the

path-space rate functional, which characterises the large deviations from the expected ...

arXiv:1203.0676 [pdf, ps, other]

Contractivity of the Wasserstein metric for the kinetic Kuramoto equation

JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim - arXiv preprint arXiv: …, 2013 - arxiv.org

Abstract: We present synchronization and contractivity estimates for the kinetic Kuramoto

model obtained from the Kuramoto phase model in the mean-field limit. For identical

Kuramoto oscillators, we present an admissible class of initial data leading to time- ...

Geodesic PCA in the Wasserstein space

J Bigot, R Gouet, A López - arXiv preprint arXiv:1307.7721, 2013 - arxiv.org

Annales de l'Institut Henri …, 2015 - math.u-bordeaux1.fr

Abstract: We introduce the method of Geodesic Principal Component Analysis (GPCA)

analysis on the space of probability measures on the line, with finite second moments,

endowed with the Wasserstein metric. We discuss the advantages of this approach over a ...

<——2013——2013——— -50—

Value functions on a finite time horizon in the Wasserstein spaces

R Hynd, HK Kim - arXiv preprint arXiv:1307.4667, 2013 - arxiv.org

Abstract: We study analogs of value functions arising in classical mechanics in the space of

probability measures endowed with the Wasserstein metric $ W_p $, for $1< p<\ infty $. Our

main result is that each of these generalized value functions is a type of viscosity solution ...

Microscopic interpretation of Wasserstein gradient flows

DRM Renger - 2013 - … 2013. http://alexandria. tue. nl/extra2 …

Permalink Technische Universiteit Eindhoven Dissertation :
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MR3126088 Caillerie, Claire; Chazal, Frédéric; Dedecker, Jérôme; Michel, Bertrand Deconvolution for the Wasserstein metric and geometric inference. Geometric science of information, 561–568, Lecture Notes in Comput. Sci., 8085, Springer, Heidelberg, 2013. 94A17 (53C23)

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M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

MR3039437 Schmitzer, Bernhard; Schnörr, Christoph Modelling convex shape priors and matching based on the Gromov-Wasserstein distance. J. Math. Imaging Vision 46 (2013), no. 1, 143–1

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

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Modelling Convex Shape Priors and Matching Based on the Gromov ...

59. 68U10 (94A08)

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Behaviors of $φ$-exponential distributions in Wasserstein geometry ...

A φ-exponential distribution is a generalization of an exponential distribution associated to functions φ in an appropriate class, and the space of φ-exponential ...

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One-Dimensional Numerical Algorithms for Gradient Flows in the p ...

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We numerically approximate, on the real line, solutions to a large class of parabolic partial differential equations which are “gradient flows” of some energy ...

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Entropic Burgers' equation via a minimizing movement ... - Springer Link

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Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein space. In particular, we consider the Cauchy problem for a transport ...

<——2013————2013———— 60-

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Moreau–Yosida approximation and convergence of Hamiltonian ...

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A new procedure for testing normality based on the L2 ... - Springer Link

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Conformal Wasserstein distance: II. computational aspects and extensions ... for computing the alignment of and distance between two disk-type surfaces.

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Mathematics of Computation of the American Mathematical Society, 01/2013, Volume 82, Issue 281

Conformal Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math. (ELS), (2011), no. 3, 1047-1077, (2011)]. We provide numerical procedures...

Journal Article: Full Text Online 2013

Times Cited: 10 See 2011

Microscopic interpretation of Wasserstein gradient flows

DRM Renger - 2013 - oatd.org

The discovery of Wasserstein gradient flows provided a mathematically precise formulation for the way in which thermodynamic systems are driven by entropy. Since the entropy of a system in equilibrium can be related to the large deviations of stochastic particle systems, the question arises whether a similar relation exists between Wasserstein gradient flows and stochastic particle systems. In the work presented in this thesis, such relation is studied for a number of systems. As explained in the introduction chapter, central to this research is the …

Cited by 9 Related arti

Entropic Gradient Flows on the Wasserstein Space via Large Deviations fromThermodynamic Limit

PDF U of Bath 2013 Ph.D.

by V Laschos - ‎2013 - ‎Related articles

Feb 7, 2014 - This copy of the thesis has been supplied on the condition that ... the Wasserstein space, bringing this way the statistical mechanics point of ...

Sliced Wasserstein barycenter of multiple densities

N Bonneel, H Pfister - 2013 - dash.harvard.edu

The optimal mass transportation problem provides a framework for interpolating between

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JOURNAL OF MULTIVARIATE ANALYSIS Volume: ‏ 122 Pages: ‏ 278-291 Published: ‏ NOV 2013

WASSERSTEIN GRADIENT FLOWS FROM LARGE DEVIATIONS OF MANY-PARTICLE LIMITS

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<——2013———2013——— 70—

A Wasserstein-type Distance to Measure Deviation from Equilibrium of Quantum Markov Semigroups

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OPEN SYSTEMS & INFORMATION DYNAMICS Volume: ‏ 20 Issue: ‏ 2 Article Number: 1350009 Published: ‏ JUN 2013

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One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

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ACTA APPLICANDAE MATHEMATICAE Volume: ‏ 125 Issue: ‏ 1 Pages: ‏ 121-134 Published: ‏ JUN 2013

Times Cited: 6

[PDF] academia.edu

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

Modelling Convex Shape Priors and Matching Based on the Gromov-Wasserstein Distance

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JOURNAL OF MATHEMATICAL IMAGING AND VISION Volume: ‏ 46 Issue: ‏ 1 Pages: ‏ 143-159 Published: ‏ MAY 2013

Times Cited: 9 8.

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ACTA APPLICANDAE MATHEMATICAE Volume: ‏ 124 Issue: ‏ 1 Pages: ‏ 73-105 Published: ‏ APR 2013

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Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

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JOURNAL OF DIFFERENTIAL EQUATIONS Volume: ‏ 254 Issue: ‏ 7 Pages: ‏ 2861-2876 Published: ‏ APR 1 2013

The derivation of Swarming models: Mean-Field Limit and Wasserstein distances

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2013 ARXIV: ANALYSIS OF PDES

Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces

126 citations* for all

119 citations*

2013 DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Giuseppe Savaré

Dirichlet form

Ricci curvature

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We prove that the linear ``heat'' flow in a $RCD (K, \infty)$ metric measure space $(X, d, m)$ satisfies a contraction property with respect to every $L^p$-Kantorovich-Rubinstein-Wasserstein distance, $p\in [1,\infty]$. In particular, we obtain a precise estimate for the optimal $W_\i... View Full Abstract

2013

2013 ARXIV: MACHINE LEARNING

26 citations*

Sliced and Radon Wasserstein Barycenters of Measures

224 citations*

2015 JOURNAL OF MATHEMATICAL IMAGING AND VISION

Nicolas Bonneel ¹,Julien Rabin ²,Gabriel Peyré ³,Hanspeter Pfister ¹

¹ Harvard University ,² University of Caen Lower Normandy ,³ Paris Dauphine University

Radon transform

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This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The first method makes use of the Radon transform of the measures, and the second is the solution of a convex optimization problem over the space of ... View Full Abstract

Frequency Domain Model Validation in Wasserstein Metric

By: Halder, Abhishek; Bhattacharya, Raktim

Conference: American Control Conference (ACC) Location: ‏ Washington, DC Date: ‏ JUN 17-19, 2013

Sponsor(s): ‏Boeing; Eaton; Halliburton; Honeywell; MathWorks; Mitsubishi Elect Res Labs; Natl Instruments; United Technologies Res Ctr; Xerox; dSpace; Journal Franklin Inst; GE Global Res; Quanser; SIAM; Springer; Taylor & Francis Grp, CRC Press; Wiley

2013 AMERICAN CONTROL CONFERENCE (ACC) Book Series: ‏ Proceedings of the American Control Conference Pages: ‏ 5845-5850 Published: ‏ 2013

Times Cited: 1

Salient Region Detection Using Wasserstein Distance Measure Based on Nonlinear Scale Space

By: Zhu, Lei; Cao, Zhiguo

Conference: 8th Symposium on Multispectral Image Processing and Pattern Recognition (MIPPR) - Pattern Recognition and Computer Vision Location: ‏ Wuhan, PEOPLES R CHINA Date: ‏ OCT 26-27, 2013

Sponsor(s): ‏Huazhong Univ Sci & Technol; Natl Key Lab Sci & Technol Multi Spectral Informat Proc; SPIE

MIPPR 2013: PATTERN RECOGNITION AND COMPUTER VISION Book Series: ‏ Proceedings of SPIE Volume: ‏ 8919 Article Number: UNSP 89190A Published: ‏ 2013

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BEHAVIORS OF phi-EXPONENTIAL DISTRIBUTIONS IN WASSERSTEIN GEOMETRY AND AN EVOLUTION EQUATION

By: Takatsu, Asuka

SIAM JOURNAL ON MATHEMATICAL ANALYSIS Volume: ‏ 45 Issue: ‏ 4 Pages: ‏ 2546-2556 Published: ‏ 2013

Times Cited: 3

<——2013— ——2013——— —— -80—

Two Remarks on the Wasserstein Dirichlet Form

By: Stannat, Wilhelm

Conference: 7th Seminar on Stochastic Analysis, Random Fields and Applications Location: ‏ Centro Stefano Franscini, Ascona, SWITZERLAND Date: ‏ MAY 23-27, 2011

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SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS VII Book Series: ‏ Progress in Probability Volume: ‏ 67 Pages: ‏ 235-255 Published: ‏ 2013

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Journal of Differential Equations, 2013 - Elsevier

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein

space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the

Moreau–Yosida approximation and denote it by H τ. We show that solutions of the …

Contractivity of the Wasserstein metric for the kinetic Kuramoto equation

JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim - arXiv preprint arXiv …, 2013 - arxiv.org

We present synchronization and contractivity estimates for the kinetic Kuramoto model

obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto

oscillators, we present an admissible class of initial data leading to time-asymptotic …

THE L2-WASSERSTEIN DISTANCE

CM Bea, JMR Rodríguez - Distributions With Given Marginals …, 2013 - books.google.com

Let Q be a probability measure on R* and let S be a family of probability measures on R*

which will be considered as a pattern. For suitable patterns we consider the closest law to Q

in S, through the L2-Wasserstein distance, as a descriptive measure associated to Q. The …

2013See 2018 [PDF] uni-goettingen.de

[PDF] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013 - lp.uni-goettingen.de

So far we have studied the structure of (P2 (X), W2)(ie the space of Borel probability

measures with finite second moments equipped with the Wasserstein distance W2) both for

X being a Polish and a geodesic space. We have seen that (P2 (X), W2) inherits crucial …

[CITATION] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013

2013 [PDF] uni-goettingen.de

[PDF] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013 - lp.uni-goettingen.de

So far we have studied the structure of (P2 (X), W2)(ie the space of Borel probability

measures with finite second moments equipped with the Wasserstein distance W2) both for

X being a Polish and a geodesic space. We have seen that (P2 (X), W2) inherits crucial …

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[CITATION] Wasserstein Distance on Riemannian Manifolds

M Kersting - 2013

2013 Proceedings of the Conference on Control and its Applications (CT)2013

Lipeng Ning and Tryphon Georgiou

L Ning, T Georgiou - 2013 Proceedings of the Conference on Control and its …, 2013 - SIAM

We consider the problem of approximating a (nonnegative definite) covariance matrix by the

sum of two structured covariances–one which is diagonal and one which has low-rank. Such

an additive decomposition follows the dictum of factor analysis where linear relations are …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

2013 [PDF] arxiv.org

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

<——2013———2013-----90–

DISSERTATION

Entropic gradient flows on the wasserstein space via large deviations from thermodynamic limits

Laschos, Vaios ; 2013

Entropic gradient flows on the wasserstein space via large deviations from thermodynamic limits

Online Access Available

[PDF] Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

V Laschos - 2013 - researchportal.bath.ac.uk

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation

can be described as a gradient flow of the free energy functional in the Wasserstein space,

bringing this way the statistical mechanics point of view on the diffusion phenomenon to the …

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in

weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare

Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in

weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare

Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

Self-improvement of the Bakry-\'Emery condition and Wasserstein contraction of the heat flow in RCD (K,\infty) metric measure spaces

G Savaré - arXiv preprint arXiv:1304.0643, 2013 - arxiv.org

We prove that the linear heat flow in a RCD (K,\infty) metric measure space (X, d, m) satisfies

a contraction property with respect to every L^ p-Kantorovich-Rubinstein-Wasserstein

distance. In particular, we obtain a precise estimate for the optimal W_\infty-coupling

between two fundamental solutions in terms of the distance of the initial points. The result is

a consequence of the equivalence between the RCD (K,\infty) lower Ricci bound and the

corresponding Bakry-Émery condition for the canonical Cheeger-Dirichlet form in (X, d, m) …

Self-improvement of the Bakry-\'Emery condition and ...

Apr 2, 2013 — Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces. Authors: ...

by G Savaré · ‎2013 · ‎Cited by 123 · ‎Related articles

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[CITATION] Self-improvement of the Bakry-mery condition and Wasserstein contraction of the heat flow in RCD (K,∞) metric measure spaces, to appear in Disc

G Savaré - Cont. Dyn. Sist. A, 2013

On the rate of convergence in Wasserstein distance of the empirical measure

Application of the Wasserstein metric to seismic signals

2013 ARXIV: PROBABILITY

151 citations* for all

138 citations*

2014 COMMUNICATIONS IN MATHEMATICAL SCIENCES

Björn Engquist ,Brittany D. Froese

University of Texas at Austin

Numerical analysis

View More (8+)

Seismic signals are typically compared using travel time difference or $L_2$ difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology. It exhibits properties from both of the traditional measures mentioned above. The numerical computation is based o... View Full Abstract

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

2013 [PDF] mpg.de

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme

involving the Wasserstein metric in the limit of vanishing time step size (Otto, Commun Pure …

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical

computation is based on the recent development of fast numerical methods for the Monge-

Ampere equation and optimal transport. Applications to waveform inversion and registration

are discussed and simple numerical examples are presented.

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

[PDF] sysmath.com

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

Weak KAM Theory on the Wasserstein Torus with ...

2013

http://www.math.ucla.edu › GanTud-2013

http://www.math.ucla.edu › GanTud-2013PDF

by W GANGBO · 2013 · Cited by 24 — Said compactness remains true for the multidimensional torus T ... Given a Hamiltonian functional H defined on the Wasserstein space P2.

56 pages

2013 see 2012

Wasserstein active contours | IEEE Conference Publication

https://ieeexplore.ieee.org › abstract › document

by G Peyré · Cited by 57 — In this paper, we propose a novel and rigorous framework for region-based active contours that combines the Wasserstein distance between statistical ...

Date Added to IEEE Xplore: 21 February 2013

<——2013— ——2013——— ——— -100 —

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

Deconvolution for the Wasserstein metric and geometric inference

C Caillerie, F Chazal, J Dedecker, B Michel - International Conference on …, 2013 - Springer

This paper is a short presentation of recent results about Wasserstein deconvolution for

topological inference published in [1]. A distance function to measures has been defined in

[2] to answer geometric inference problems in a probabilistic setting. According to their …

Conformal Wasserstein distance: II. Computational aspects and extensions

Y Lipman, J Puente, I Daubechies - Mathematics of Computation, 2013 - JSTOR

This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformai

Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math.(ELS), 227

(2011), no. 3, 1047-1077,(2011)]. We provide numerical procedures and algorithms for …

[PDF] esaim-cocv.org

Wasserstein gradient flows from large deviations of many-particle limits

MH Duong, V Laschos, M Renger - ESAIM: Control, Optimisation …, 2013 - esaim-cocv.org

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the path-

space rate functional, which characterises the large deviations from the expected …

[PDF] abhishekhalder.org

Frequency domain model validation in Wasserstein metric

A Halder, R Bhattacharya - 2013 American Control Conference, 2013 - ieeexplore.ieee.org

This paper connects the time-domain uncertainty propagation approach for model validation

in Wasserstein distance 2 W 2, introduced by the authors in [1], with the frequency domain

model validation in the same. To the best of our knowledge, this is the first frequency domain …

Object segmentation by shape matching with Wasserstein modes

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We gradually develop a novel functional for joint variational object segmentation and shape

matching. The formulation, based on the Wasserstein distance, allows modelling of local

object appearance, statistical shape variations and geometric invariance in a uniform way …

Geodesic PCA in the Wasserstein space

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1307.7721, 2013 - arxiv.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

image segmentation. Starting point is the Gromov-Wasserstein Distance which is

successfully applied in shape recognition and classification tasks but involves solving a non …

Variational image segmentation and cosegmentation with the wasserstein distance

P Swoboda, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We present novel variational approaches for segmenting and cosegmenting images. Our

supervised segmentation approach extends the classical Continuous Cut approach by a

global appearance-based data term enforcing closeness of aggregated appearance …

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

<— 2013— ——2013————— -110—

Microscopic interpretation of Wasserstein gradient flows

DRM Renger - 2013 - oatd.org

The discovery of Wasserstein gradient flows provided a mathematically precise formulation

for the way in which thermodynamic systems are driven by entropy. Since the entropy of a

system in equilibrium can be related to the large deviations of stochastic particle systems …

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

[HTML] Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - Journal of Multivariate Analysis, 2013 - Elsevier

The subject of this paper is the estimation of a probability measure on R d from the data

observed with an additive noise, under the Wasserstein metric of order p (with p≥ 1). We

assume that the distribution of the errors is known and belongs to a class of supersmooth …

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to

functions φ in an appropriate class, and the space of φ-exponential distributions has a dually

flat structure. We study features of the space of φ-exponential distributions, such as the …

Sliced Wasserstein barycenter of multiple densities

N Bonneel, H Pfister - 2013 - dash.harvard.edu

The optimal mass transportation problem provides a framework for interpolating between

different probability density functions (pdfs), warping one function toward another.

Interpolating between two arbitrary pdfs can be challenging, but interpolating between more …

A geometric study of Wasserstein spaces: an addendum on the boundary

J Bertrand, BR Kloeckner - International Conference on Geometric …, 2013 - Springer

Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally

compact metric space. Mainly, X is a space where triangles are “thin”: points on the opposite

side to a vertex are closer to the vertex than they would be in the Euclidean plane. This assumption …

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

Two remarks on the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all

probability measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse

constructed in [6] this process in the case of probability measures over the unit interval using …

<—-2013— ——2013-----120 —

基于 l_1-正则化的分位数回归及 Wasserstein 距离下分布的 Bernstein 逼近

田崝 - 2013 - cdmd.cnki.com.cn

本文研究了统计学习框架下的两个问题. 一个是关于分位数回归的问题. 不同于应用最为广泛的

最小二乘回归, 本文在再生核Hilbert 空间下考虑了分位数回归. 具体给出了前人研究过但没有给

出的基于Hk-正则化的分位数回归的算法和本文所研究的基于e1-正则化的分位数回归的算法 …

2013 zzz 28

[CITATION] 基于 Wasserstein 距离的颜色迁移算法的设计与实现

冯文雅 - 2013 - 万方数据资源系统

[Chinese Quantile regression based on l_1-regularization and Bernstein approximation of distribution under Wasserstein distance]

[PDF] ups-tlse.fr

Localisation de masse et espaces de Wasserstein

T Le Gouic - 2013 - thesesups.ups-tlse.fr

Le travail de cette thèse est basé sur deux outils: le packing d'un ensemble et les espaces

de Wasserstein. Une première partie s' intéresse à la localisation de la masse d'une mesure

de probabilité Mu. Lorsque Mu est régulière, les ensembles de niveau de sa densité …

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

[PDF] abhishekhalder.org

Frequency domain model validation in Wasserstein metric

A Halder, R Bhattacharya - 2013 American Control Conference, 2013 - ieeexplore.ieee.org

This paper connects the time-domain uncertainty propagation approach for model validation

in Wasserstein distance 2 W 2, introduced by the authors in [1], with the frequency domain

model validation in the same. To the best of our knowledge, this is the first frequency domain …

GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE

SM Walczak - Citeseer

Wasserstein distance and optimal transportation The lecture will be devoted to the

Wassertein distance of Borel probability measures, which arises from the optimal

transportation theory [4][5]. A number of examples will illustrate the nature of this metric

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

Two remarks on the Wasserstein Dirichlet form

Fast Computation of Wasserstein Barycenters - arXivhttps://arxiv.org › pdfhttps://arxiv.org › pdfPDFby M Cuturi 2013 · Cited by 539 — We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric.
CITATION] Fast Computation of Wasserstein Barycenters. arXiv e-prints

M Cuturi, A Doucet - arXiv preprint arXiv:1310.4375, 2013

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all

probability measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse

constructed in [6] this process in the case of probability measures over the unit interval using …

2013

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Journal of Differential Equations, 2013 - Elsevier

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein

space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the

Moreau–Yosida approximation and denote it by H τ. We show that solutions of the …

<—-2013— ——2013-----130 —

2013

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

2013

Self-improvement of the Bakry-\'Emery condition and Wasserstein contraction of the heat flow in RCD (K,\infty) metric measure spaces

G Savaré - arXiv preprint arXiv:1304.0643, 2013 - arxiv.org

We prove that the linear heat flow in a RCD (K,\infty) metric measure space (X, d, m) satisfies

a contraction property with respect to every L^ p-Kantorovich-Rubinstein-Wasserstein

distance. In particular, we obtain a precise estimate for the optimal W_\infty-coupling …

2013

Sliced Wasserstein barycenter of multiple densities

N Bonneel, H Pfister - 2013 - dash.harvard.edu

The optimal mass transportation problem provides a framework for interpolating between

different probability density functions (pdfs), warping one function toward another.

Interpolating between two arbitrary pdfs can be challenging, but interpolating between more …

[CITATION] CONS

2013ISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 20

2013 many 2014

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

2013

Geodesic PCA in the Wasserstein space

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1307.7721, 2013 - arxiv.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space of probability measures on the line, with finite second moment, endowed with the Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to functions φ in an appropriate class, and the space of φ-exponential distributions has a dually flat structure. We study features of the space of φ-exponential distributions, such as the …

Self-improvement of the Bakry-\'Emery condition and Wasserstein contraction of the heat flow in RCD (K,\infty) metric measure spaces

G Savaré - arXiv preprint arXiv:1304.0643, 2013 - arxiv.org

We prove that the linear heat flow in a RCD (K,\infty) metric measure space (X, d, m) satisfies

a contraction property with respect to every L^ p-Kantorovich-Rubinstein-Wasserstein

distance. In particular, we obtain a precise estimate for the optimal W_\infty-coupling …

Sliced Wasserstein barycenter of multiple densities

N Bonneel, H Pfister - 2013 - dash.harvard.edu

The optimal mass transportation problem provides a framework for interpolating between

different probability density functions (pdfs), warping one function toward another.

Interpolating between two arbitrary pdfs can be challenging, but interpolating between more …

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

<—-2013— ——2013————— -140 —

A geometric study of Wasserstein spaces: an addendum on the boundary

J Bertrand, BR Kloeckner - International Conference on Geometric …, 2013 - Springer

Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally

compact metric space. Mainly, X is a space where triangles are “thin”: points on the opposite

side to a vertex are closer to the vertex than they would be in the Euclidean plane. This assumption …

Wasserstein gradient flows from large deviations of many-particle limits

MH Duong, V Laschos, M Renger - ESAIM: Control, Optimisation …, 2013 - esaim-cocv.org

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the path-

space rate functional, which characterises the large deviations from the expected …

Microscopic interpretation of Wasserstein gradient flows

DRM Renger - 2013 - oatd.org

The discovery of Wasserstein gradient flows provided a mathematically precise formulation

for the way in which thermodynamic systems are driven by entropy. Since the entropy of a

system in equilibrium can be related to the large deviations of stochastic particle systems …

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

Conformal Wasserstein distance: II. Computational aspects and extensions

Y Lipman, J Puente, I Daubechies - Mathematics of Computation, 2013 - JSTOR

This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformai

Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math.(ELS), 227

(2011), no. 3, 1047-1077,(2011)]. We provide numerical procedures and algorithms for …

Variational image segmentation and cosegmentation with the wasserstein distance

P Swoboda, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We present novel variational approaches for segmenting and cosegmenting images. Our

supervised segmentation approach extends the classical Continuous Cut approach by a

global appearance-based data term enforcing closeness of aggregated appearance …

GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE

SM Walczak - Citeseer

Wasserstein distance and optimal transportation The lecture will be devoted to the

Wassertein distance of Borel probability measures, which arises from the optimal

transportation theory [4][5]. A number of examples will illustrate the nature of this metric …

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

THE L2-WASSERSTEIN DISTANCE

CM Bea, JMR Rodríguez - Distributions With Given Marginals …, 2013 - books.google.com

Let Q be a probability measure on R* and let S be a family of probability measures on R*

which will be considered as a pattern. For suitable patterns we consider the closest law to Q

in S, through the L2-Wasserstein distance, as a descriptive measure associated to Q. The …

2013 [PDF] harvard.edu

Sliced Wasserstein barycenter of multiple densities

N Bonneel, H Pfister - 2013 - dash.harvard.edu

The optimal mass transportation problem provides a framework for interpolating between

different probability density functions (pdfs), warping one function toward another.

Interpolating between two arbitrary pdfs can be challenging, but interpolating between more …

<—-2013— ——2013————— -150——

On the rate of convergence in Wasserstein distance of ... - arXiv

by N Fournier · 2013 · Cited by 714 — Title:On the rate of convergence in Wasserstein distance of the empirical measure ; Subjects: Probability (math.PR); Statistics Theory (math.ST

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

Variational image segmentation and cosegmentation with the wasserstein distance

2013 [PDF] psu.edu

P Swoboda, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We present novel variational approaches for segmenting and cosegmenting images. Our

supervised segmentation approach extends the classical Continuous Cut approach by a …

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

Deconvolution for the Wasserstein metric and geometric inference

C Caillerie, F Chazal, J Dedecker, B Michel - International Conference on …, 2013 - Springer

This paper is a short presentation of recent results about Wasserstein deconvolution for

topological inference published in [1]. A distance function to measures has been defined in

[2] to answer geometric inference problems in a probabilistic setting. According to their …

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

[PDF] abhishekhalder.org

Frequency domain model validation in Wasserstein metric

A Halder, R Bhattacharya - 2013 American Control Conference, 2013 - ieeexplore.ieee.org

This paper connects the time-domain uncertainty propagation approach for model validation

in Wasserstein distance 2 W 2, introduced by the authors in [1], with the frequency domain

model validation in the same. To the best of our knowledge, this is the first frequency domain …

Contractivity of the Wasserstein metric for the kinetic Kuramoto equation

JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim - arXiv preprint arXiv …, 2013 - arxiv.org

We present synchronization and contractivity estimates for the kinetic Kuramoto model

obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto

oscillators, we present an admissible class of initial data leading to time-asymptotic …

L Ning, T Georgiou - 2013 Proceedings of the Conference on Control and its …, 2013 - SIAM

We consider the problem of approximating a (nonnegative definite) covariance matrix by the

sum of two structured covariances–one which is diagonal and one which has low-rank. Such

an additive decomposition follows the dictum of factor analysis where linear relations are …

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

image segmentation. Starting point is the Gromov-Wasserstein Distance which is

successfully applied in shape recognition and classification tasks but involves solving a non …

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

<—-2013— ——2013————— -160 —-

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Journal of Differential Equations, 2013 - Elsevier

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein

space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the

Moreau–Yosida approximation and denote it by H τ. We show that solutions of the …

Microscopic interpretation of Wasserstein gradient flows

DRM Renger - 2013 - oatd.org

The discovery of Wasserstein gradient flows provided a mathematically precise formulation

for the way in which thermodynamic systems are driven by entropy. Since the entropy of a

system in equilibrium can be related to the large deviations of stochastic particle systems …

A geometric study of Wasserstein spaces: an addendum on the boundary

J Bertrand, BR Kloeckner - International Conference on Geometric …, 2013 - Springer

Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally

compact metric space. Mainly, X is a space where triangles are “thin”: points on the opposite

side to a vertex are closer to the vertex than they would be in the Euclidean plane. This assumption …

GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE

SM Walczak - Citeseer

Wasserstein distance and optimal transportation The lecture will be devoted to the

Wassertein distance of Borel probability measures, which arises from the optimal

transportation theory [4][5]. A number of examples will illustrate the nature of this metric …

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

SIAM J. MATH. ANAL. c 2013 Society for Industrial and Applied Mathematics Vol.

45, No. 4, pp. 2546–2556 BEHAVIORS OF ϕ-EXPONENTIAL …

2013

[CITATION] Fast Computation of Wasserstein Barycenters. arXiv e-prints

M Cuturi, A Doucet - arXiv preprint arXiv:1310.4375, 2013

[PDF] An extension of Wasserstein contraction associated with the curvature-dimension condition

K Kuwada - impan.pl

Page 1. An extension of Wasserstein contraction associated with the curvature-dimension

condition Kazumasa Kuwada (Ochanomizu University) 6th International Conference on

Stochastic Analysis and its Applications (Sep. 10–14, 2012 Bedlewo, Poland) 1 / 15 Page …

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

2013

Self-improvement of the Bakry-\'Emery condition and ...

by G Savaré · 2013 · Cited by 118 — Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces. ... The result is a consequence of the equivalence between the RCD(K,\infty) lower Ricci bound and the corresponding Bakry-Émery condition for the canonical Cheeger-Dirichlet form in (X,d,m).

Missing: mery ‎| Must include: mery

[CITATION] Self-improvement of the Bakry-mery condition and Wasserstein contraction of the heat flow in RCD (K,∞) metric measure spaces, to appear in Disc

G Savaré - Cont. Dyn. Sist. A, 2013

[CITATION] Self-improvement of the Bakry-mery condition and Wasserstein contraction of the heat flow in RCD (K,∞) metric measure spaces, to appear in Disc

G Savaré - Cont. Dyn. Sist. A, 2013

[PDF] Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

V Laschos - 2013 - core.ac.uk

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation

can be described as a gradient flow of the free energy functional in the Wasserstein space,

bringing this way the statistical mechanics point of view on the diffusion phenomenon to the …

Wasserstein gradient flows from large deviations of many-particle limits

<—-2013— ——2013————— -170 —

[PDF] esaim-cocv.org

MH Duong, V Laschos, M Renger - ESAIM: Control, Optimisation …, 2013 - esaim-cocv.org

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the path-

space rate functional, which characterises the large deviations from the expected …

CITATION] Wasserstein gradient flows from large deviations of many-particle limits, ESAIM Contr

MH Duong, V Laschos, DRM Renger - Optim. CA, 2013

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

2013

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

Microscopic interpretation of Wasserstein gradient flows

DRM Renger - 2013 - oatd.org

The discovery of Wasserstein gradient flows provided a mathematically precise formulation

for the way in which thermodynamic systems are driven by entropy. Since the entropy of a

system in equilibrium can be related to the large deviations of stochastic particle systems …

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

[PDF] Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

V Laschos - 2013 - core.ac.uk

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation

can be described as a gradient flow of the free energy functional in the Wasserstein space,

bringing this way the statistical mechanics point of view on the diffusion phenomenon to the …

2013

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted

Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare Department of

Mathematics, University of Pavia, Italy DIMO2013 Levico Terme, September 11, 2013 Jointly …

Wasserstein gradient flows from large deviations of many-particle limits

[PDF] esaim-cocv.org

MH Duong, V Laschos, M Renger - ESAIM: Control, Optimisation …, 2013 - esaim-cocv.org

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the path-

space rate functional, which characterises the large deviations from the expected …

2013

Object segmentation by shape matching with Wasserstein modes

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We gradually develop a novel functional for joint variational object segmentation and shape

matching. The formulation, based on the Wasserstein distance, allows modelling of local

object appearance, statistical shape variations and geometric invariance in a uniform way …

<—-2013— ——2013————— -18

2013

[PDF] mpg.de2013

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

2013

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 数理解析研究所講究録別冊= RIMS …, 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

2013 [PDF] msp.org

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

Welcome to My Rash, Scene 1: [Excerpt] : Academic Medicine

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

2013

Variational image segmentation and cosegmentation with the wasserstein distance

P Swoboda, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We present novel variational approaches for segmenting and cosegmenting images. Our supervised segmentation approach extends the classical Continuous Cut approach by a global appearance-based data term enforcing closeness of aggregated appearance …

2013

[CITATION] Optimal transport and Wasserstein barycenters in computer vision, image and video processing

J Delon - Optimal transport and vision-Teaser, 2013

Consistent estimation of a population barycenter in the ...

2013

hal.archives-ouvertes.fr › barycenter_optimal_transport

by J Bigot · 2013 · Cited by 55 — Keywords: Wasserstein space; Empirical and population barycenters; Fréchet mean; Convergence of random variables; Optimal transport; Duality ...

[CITATION] CONSISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 2013
[PDF] mpg.de

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - … of Variations and Partial Differential Equations, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

<—-2013— ——2013————— -190

2013

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

2013

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to

functions φ in an appropriate class, and the space of φ-exponential distributions has a dually

flat structure. We study features of the space of φ-exponential distributions, such as the …

2013

Contractivity of the Wasserstein metric for the kinetic Kuramoto equation

JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim - arXiv preprint arXiv …, 2013 - arxiv.org

We present synchronization and contractivity estimates for the kinetic Kuramoto model

obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto

oscillators, we present an admissible class of initial data leading to time-asymptotic …

2013

by M Cuturi · 2013 · Cited by 426 — We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances to each element in that set.

Journal reference: Proceedings of the 31st Inte...

[CITATION] Fast Computation of Wasserstein Barycenters. arXiv e-prints

M Cuturi, A Doucet - arXiv preprint arXiv:1310.4375, 2013

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

2013 [PDF] projecteuclid.org

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

2013 [HTML] sciencedirect.com

[HTML] Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - Journal of Multivariate Analysis, 2013 - Elsevier

The subject of this paper is the estimation of a probability measure on R d from the data observed with an additive noise, under the Wasserstein metric of order p (with p≥ 1). We assume that the distribution of the errors is known and belongs to a class of supersmooth …

2013

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Journal of Differential Equations, 2013 - Elsevier

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the Moreau–Yosida approximation and denote it by H τ. We show that solutions of the …

2013 see 2014

On the rate of convergence in Wasserstein distance of the ...

by N Fournier · 2013 · Cited by 497 — On the rate of convergence in Wasserstein distance of the empirical measure. Let \mu_N be the empirical measure associated to a N-sample of a given probability distribution \mu on \mathbb{R}^d. We are interested in the rate of convergence of \mu_N to \mu, when measured in the Wasserstein distance of order p>0.

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

Object segmentation by shape matching with Wasserstein modes

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We gradually develop a novel functional for joint variational object segmentation and shape matching. The formulation, based on the Wasserstein distance, allows modelling of local object appearance, statistical shape variations and geometric invariance in a uniform way …

<—-2013— ——2013————— -200—

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational image segmentation. Starting point is the Gromov-Wasserstein Distance which is successfully applied in shape recognition and classification tasks but involves solving a non …

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational image segmentation. Starting point is the Gromov-Wasserstein Distance which is successfully applied in shape recognition and classification tasks but involves solving a non …

2013 [PDF] mpg.de

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers' equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

A geometric study of Wasserstein spaces: an addendum on the boundary

J Bertrand, BR Kloeckner - … Conference on Geometric Science of …, 2013 - Springer

Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally compact metric space. Mainly, X is a space where triangles are “thin”: points on the opposite side to a vertex are closer to the vertex than they would be in the Euclidean plane. This assumption …

Two remarks on the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all probability measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse constructed in [6] this process in the case of probability measures over the unit interval using …

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local prominence by building the Gaussian scale space. As a kind of linear scale space, it is a natural representation of human perception. However the Gaussian filtering does not …

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was shown that Markov chains satisfying the reversibility condition (also called detailed balance …

[PDF] Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

V Laschos - 2013 - core.ac.uk

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation can be described as a gradient flow of the free energy functional in the Wasserstein space, bringing this way the statistical mechanics point of view on the diffusion phenomenon to the …

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

Entropic Wasserstein Gradient Flows - Archive ouverte HAL

<—-2013— ——2013————— -210—

https://hal.archives-ouvertes.fr › hal-01121359

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful ...

2013 Dec

Adaptive Dynamic Clustering Algorithm for Interval-valued ...

www.researchgate.net › ... › Clustering Algorithms

Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance · No full-text available · Citations (0) · References (0).

[CITATION] Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance

R Guan, Y Lechevallier, H Wang - 2013 - hal.inria.fr

… ouvrage. Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance. Rong Guan 1 Yves Lechevallier 2 Huiwen Wang 1 Détails. 1 BUAA - School of Economics and Management [Beijing]. 2 AxIS - Usage-centered design …

2013 modified

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367, 2012

2013 modified

[PDF] Gromov-Wasserstein stable signatures for object matching and the role of persistence

F Mémoli - geometrica.saclay.inria.fr

Page 1. 1 Gromov-Wasserstein stable signatures for object matching and the role of persistence Facundo Mémoli memoli@math.stanford.edu Page 2. 2 Some definitions.. • Let (Z, d) be a compact metric space. • For closed A, B ⊂ Z, we define the Hausdorff distance as: d Z H (A, B) = max(max …

2013

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm. The constraint on the dual …

A Primal-Dual Approach for a Total Variation Wasserstein Flow ...

link.springer.com/chapter/10.1007/978-3-642...

Aug 28, 2013 · Abstract. We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm.

Author: Martin Benning, Luca Calatroni, Bertram Düring, Carola-Bibiane Schönlieb

Cited by: 8

[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

ptimal transport and Wasserstein barycenters in computer ...

www.msri.org › schedules › documents › assets

Aug 22, 2013 — ... barycenters in computer vision, image and video processing. ... Optimal transport and image processing - Teaser. Matching distributions ...

[CITATION] Optimal transport and Wasserstein barycenters in computer vision, image and video processing

J Delon - Optimal transport and vision-Teaser, 2013

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a stepwise contraction property for the proximal map and an “above the tangent line” …

The Wasserstein metric in Factor Analysis

L Ning, T Georgiou - 2013 Proceedings of the Conference on Control and its …, 2013 - SIAM

We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances–one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are …

2013

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 数理解析研究所講究録別冊= RIMS …, 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

Consistent estimation of a population barycenter in the ...

[PDF] Gradient estimate for Markov kernels, Wasserstein control and

K KUWADA - Appl. Math, 2013 - core.ac.uk

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm-Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

hal.archives-ouvertes.fr › barycenter_optimal_transport

PDF by J Bigot · 2013 · Cited by 55 — Keywords: Wasserstein space; Empirical and population barycenters; Fréchet mean; Convergence of random variables; Optimal transport; Duality ...

Missing: eprint ‎| Must include: eprint

[CITATION] CONSISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 2013

[CITATION] CONSISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 2013

<—-2013— ——2013————— -220—

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to

functions φ in an appropriate class, and the space of φ-exponential distributions has a dually

flat structure. We study features of the space of φ-exponential distributions, such as the …

Optimal transport and Wasserstein barycenters in computer ...

www.msri.org › schedules › documents › assets

PDF

Aug 22, 2013 — Optimal transport and Wasserstein barycenters in computer vision, image and video processing. Julie Delon. CNRS, LTCI, Télécom ...

[CITATION] Optimal transport and Wasserstein barycenters in computer vision, image and video processing

J Delon - Optimal transport and vision-Teaser, 2013

2013

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to

functions φ in an appropriate class, and the space of φ-exponential distributions has a dually

flat structure. We study features of the space of φ-exponential distributions, such as the …

2013 PDF

Etude des contraintes et des déformations au cours de la ...

tel.archives-ouvertes.fr › tel-00919097 › document

Dec 16, 2013 — multiplient, mais les modèles existants ne sont pas encore en ... la relation entre les contraintes et les déformations est établie à partir de la théorie de ... distribution gaussienne de voisins autour de l'atome central, donne la ..

[PDF] sfds.asso.fr

[PDF] Etude de modeles de déformations entre distributions avec la distance de Wasserstein

H Lescornel, JM Loubes - Nous - papersjds14.sfds.asso.fr

Etude de mod`eles de déformations entre distributions avec la distance de Wasserstein …

Hél`ene Lescornel 1 & Jean-Michel Loubes 2 … 1 Institut de Mathématiques de Toulouse 118

route de Narbonne 31000 Toulouse helene.lescornel@math.univ-toulouse.fr 2 Institut de Mathématiques …

2013

[PDF] ups-tlse.fr

Localisation de masse et espaces de Wasserstein

T Le Gouic - 2013 - thesesups.ups-tlse.fr

Le travail de cette thèse est basé sur deux outils: le packing d'un ensemble et les espaces

de Wasserstein. Une première partie s' intéresse à la localisation de la masse d'une mesure

de probabilité Mu. Lorsque Mu est régulière, les ensembles de niveau de sa densité …

2013

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 数理解析研究所講究録別冊= RIMS …, 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

2013

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

Approximation in the Wasserstein distance with application to ... - dblp

2013

dblp.uni-trier.de › rec › journals › corr › CarliNG13

Bibliographic details on Approximation in the Wasserstein distance with application to clustering.

[CITATION] Approximation in the Wasserstein Distance with Application to Clustering

FP Carli, L Ning, TT Georgiou - CoRR, 2013

Approximation in the Wasserstein distance with application to ...

2013

https://www.aminer.cn › pub › approximation-in-the-w...

Approximation in the Wasserstein distance with application to clustering. CoRR, (2013). Cited: 2|Views5. EI. Get fulltext within 24h. Other Links.

[CITATION] Approximation in the Wasserstein Distance with Application to Clustering

FP Carli, L Ning, TT Georgiou - CoRR, 2013

[CITATION] Approximation in the Wasserstein Distance with Application to Clustering

FP Carli, L Ning, TT Georgiou - CoRR, 2013

[CITATION] Approximation in the Wasserstein Distance with Application to Clustering

FP Carli, L Ning, TT Georgiou - CoRR, 2013

[CITATION] Approximation in the Wasserstein Distance with Application to Clustering

FP Carli, L Ning, TT Georgiou - CoRR, 2013

2013see 2019

[CITATION] Approximation in the Wasserstein Distance with Application to Clustering

FP Carli, L Ning, TT Georgiou - CoRR, 2013

<—-2013— ——2013————— -230—

[PDF] Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

V Laschos - 2013 - core.ac.uk

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation

can be described as a gradient flow of the free energy functional in the Wasserstein space,

bringing this way the statistical mechanics point of view on the diffusion phenomenon to the …

GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE

SM Walczak - Citeseer

Wasserstein distance and optimal transportation The lecture will be devoted to the

Wassertein distance of Borel probability measures, which arises from the optimal

transportation theory [4][5]. A number of examples will illustrate the nature of this metric …

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

2013

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in

weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare

Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

2013

(PDF) On the rate of convergence in Wasserstein distance of ...

www.researchgate.net › publication › 259211997_On

Dec 07, 2013 · convergence of the empirical measure 5 Concerning moment estimates (as in Theorem 1), some results can be found in Horowitz- Karandikar [25], Rachev-R¨ uschendorf [35] and Mischler-Mouhot [32].

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

2013

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

2013

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

2013

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

image segmentation. Starting point is the Gromov-Wasserstein Distance which is

successfully applied in shape recognition and classification tasks but involves solving a non …

2013

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

<—-2013— ——2013————— -240—

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

2013

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

2013

Object segmentation by shape matching with Wasserstein modes

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We gradually develop a novel functional for joint variational object segmentation and shape

matching. The formulation, based on the Wasserstein distance, allows modelling of local

object appearance, statistical shape variations and geometric invariance in a uniform way …

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

Cited by 5 Related articles
[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

[pdf] On asymptotics for Vaserstein coupling of a Markov chain

2013

[HTML] On asymptotics for Vaserstein coupling of Markov chains

OA Butkovsky, AY Veretennikov - Stochastic Processes and their …, 2013 - Elsevier

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

2013

MR3071388 Butkovsky, O. A.; Veretennikov, A. Yu. On asymptotics for Vaserstein coupling of Markov chains. Stochastic Process. Appl. 123 (2013), no. 9, 3518–3541. 60J05 (60B10 60J22)

4 Citations

[HTML] On asymptotics for Vaserstein coupling of Markov chains

OA Butkovsky, AY Veretennikov - Stochastic Processes and their …, 2013 - Elsevier

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

On asymptotics for Vaserstein coupling of a Markov chain

Veretennikov A. (With O.A.Butkovsky) International Mathematical Conference "50 years of IPPI", July 25-29 2011 Moscow, Russia, Proceedings, ISBN 978-5-901158-15-9
Go to publication Download (241.6 KB)

On asymptotics for Vaserstein coupling of Markov chains

by OA Butkovsky - 2013 - Cited by 3 - Related articles

2013 Stochastic Processes and their Applications volume 123 issue 9 pp 3518-3541

Apr 25, 2013 - We prove that strong ergodicity of a Markov process is linked with a spectral radius of a certain “associated” semigroup operator, although, not a “natura.

Stochastic Processes and their …, 2013 - Elsevier

Zbl 1294.60095

2013
[HTML] On asymptotics for Vaserstein coupling of Markov chains

OA Butkovsky, AY Veretennikov - Stochastic Processes and their …, 2013 - Elsevier

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

2013

[HTML] On asymptotics for Vaserstein coupling of Markov chains

OA Butkovsky, AY Veretennikov - Stochastic Processes and their …, 2013 - Elsevier

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

2013 [HTML] sciencedirect.com

[HTML] On asymptotics for Vaserstein coupling of Markov chains

OA Butkovsky, AY Veretennikov -Stochastic Processes and their Applications, 123(9), 2013, - Elsevier

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

2013
[HTML] On asymptotics for Vaserstein coupling of Markov chains

OA Butkovsky, AY Veretennikov - Stochastic Processes and their …, 2013 - Elsevier

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a

certain “associated” semigroup operator, although, not a “natural” one. We also give

sufficient conditions for weak ergodicity and provide explicit estimates of the convergence …

<—-2013— ——2013————— -250—

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 数理解析研究所講究録別冊= RIMS …, 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

[PDF] msp.org

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

2013

[PDF] esaim-cocv.org

Wasserstein gradient flows from large deviations of many-particle limits

MH Duong, V Laschos, M Renger - ESAIM: Control, Optimisation …, 2013 - esaim-cocv.org

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the path-

space rate functional, which characterises the large deviations from the expected …

[CITATION] Wasserstein gradient flows from large deviations of many-particle limits, ESAIM Contr

MH Duong, V Laschos, DRM Renger - Optim. CA, 2013

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

2013

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

2013

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

2013

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

2013

Two remarks on the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all

probability measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse

constructed in [6] this process in the case of probability measures over the unit interval using …

2013

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

Salient region detection Using Wasserstein distance measure based on nonlinear scale space

2013

L Zhu, Z Cao - … 2013: Pattern Recognition and Computer Vision, 2013 - spiedigitallibrary.org

Many existing bottom-up saliency detection methods measure the multi-scale local

prominence by building the Gaussian scale space. As a kind of linear scale space, it is a

natural representation of human perception. However the Gaussian filtering does not …

<—-2013— ——2013————— -260—

[PDF] esaim-cocv.org

Wasserstein gradient flows from large deviations of many-particle limits

MH Duong, V Laschos, M Renger - … , Optimisation and Calculus of …, 2013 - esaim-cocv.org

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle

system on one hand and as a Wasserstein gradient flow on the other. We write the path-

space rate functional, which characterises the large deviations from the expected …

[CITATION] Wasserstein gradient flows from large deviations of many-particle limits, ESAIM Contr

MH Duong, V Laschos, DRM Renger - Optim. CA, 2013

Self-improvement of the Bakry-\'Emery condition and Wasserstein contraction of the heat flow in RCD (K,\infty) metric measure spaces

G Savaré - arXiv preprint arXiv:1304.0643, 2013 - arxiv.org

We prove that the linear heat flow in a RCD (K,\infty) metric measure space (X, d, m) satisfies

a contraction property with respect to every L^ p-Kantorovich-Rubinstein-Wasserstein

distance. In particular, we obtain a precise estimate for the optimal W_\infty-coupling …

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to

functions φ in an appropriate class, and the space of φ-exponential distributions has a dually

flat structure. We study features of the space of φ-exponential distributions, such as the …

[HTML] Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - Journal of Multivariate Analysis, 2013 - Elsevier

The subject of this paper is the estimation of a probability measure on R d from the data

observed with an additive noise, under the Wasserstein metric of order p (with p≥ 1). We

assume that the distribution of the errors is known and belongs to a class of supersmooth …

2013

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

Sliced Wasserstein barycenter of multiple densities

[PDF] harvard.edu

N Bonneel, H Pfister - 2013 - dash.harvard.edu

The optimal mass transportation problem provides a framework for interpolating between

different probability density functions (pdfs), warping one function toward another.

Interpolating between two arbitrary pdfs can be challenging, but interpolating between more …

Contractivity of the Wasserstein metric for the kinetic Kuramoto equation

JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim - arXiv preprint arXiv …, 2013 - arxiv.org

We present synchronization and contractivity estimates for the kinetic Kuramoto model

obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto

oscillators, we present an admissible class of initial data leading to time-asymptotic …

Contraction of the proximal map and generalized convexity of the Moreau–Yosida regularization in the 2-Wasserstein metric

E Carlen, K Craig - Mathematics and Mechanics of Complex Systems, 2013 - msp.org

Abstract We investigate the Moreau–Yosida regularization and the associated proximal map

in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a

stepwise contraction property for the proximal map and an “above the tangent line” …

Moreau–Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

HK Kim - Journal of Differential Equations, 2013 - Elsevier

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein

space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the

Moreau–Yosida approximation and denote it by H τ. We show that solutions of the …

<—-2013— ——2013————— -270—

2013 thesis

Microscopic interpretation of Wasserstein gradient flows

Authors:D.R.M. Renger, Renger, D.R.M. (Creator)
Summary:The discovery of Wasserstein gradient flows provided a mathematically precise formulation for the way in which thermodynamic systems are driven by entropy. Since the entropy of a system in equilibrium can be related to the large deviations of stochastic particle systems, the question arises whether a similar relation exists between Wasserstein gradient flows and stochastic particle systems. In the work presented in this thesis, such relation is studied for a number of systems. As explained in the introduction chapter, central to this research is the study of two types of large deviations for stochastic particle systems. The first type is related to the probability of the empirical measure of the particle system, after a fixed time step, conditioned on the initial empirical measure. The large-deviation rate provides a variational formulation of the transition between two macroscopic measures, in fixed time. This formulation can then be related to a discrete-time formulation of a gradient flow, known as minimising movement. To this aim, a specific small-time development of the rate is used, based on the concept of Mosco- or Gamma-convergence. The other type of large deviations concerns the probability of the trajectory of the empirical measure in a time interval. For these large deviations, the rate provides a variational formulation for the trajectory of macroscopic measures. For some systems, this rate can be related to a continuous-time formulation of gradient flows, known as an entropy-dissipation inequality. Chapter 2 serves as background, where a number of results from particle system theory and large deviations are proven in a general setting. In particular, the generator of the empirical measure is calculated, the many-particle limit of the empirical measure is proven, and the discrete-time large deviation principle is proven. In Chapter 3, the discrete-time large-deviation rate is studied for a system of independent Brownian particles in a force field, whichShow more
Thesis, Dissertation, 2013
English
Publisher:Technische Universiteit Eindhoven, 2013

2013 book
Microscopic interpretation of Wasserstein gradient flows

Author:D.R.M. Renger
Summary:The discovery of Wasserstein gradient flows provided a mathematically precise formulation for the way in which thermodynamic systems are driven by entropy. Since the entropy of a system in equilibrium can be related to the large deviations of stochastic particle systems, the question arises whether a similar relation exists between Wasserstein gradient flows and stochastic particle systems. In the work presented in this thesis, such relation is studied for a number of systems. As explained in the introduction chapter, central to this research is the study of two types of large deviations for stochastic particle systems. The first type is related to the probability of the empirical measure of the particle system, after a fixed time step, conditioned on the initial empirical measure. The large-deviation rate provides a variational formulation of the transition between two macroscopic measures, in fixed time. This formulation can then be related to a discrete-time formulation of a gradient flow, known as minimising movement. To this aim, a specific small-time development of the rate is used, based on the concept of Mosco- or Gamma-convergence. The other type of large deviations concerns the probability of the trajectory of the empirical measure in a time interval. For these large deviations, the rate provides a variational formulation for the trajectory of macroscopic measures. For some systems, this rate can be related to a continuous-time formulation of gradient flows, known as an entropy-dissipation inequality. Chapter 2 serves as background, where a number of results from particle system theory and large deviations are proven in a general setting. In particular, the generator of the empirical measure is calculated, the many-particle limit of the empirical measure is proven, and the discrete-time large deviation principle is proven. In Chapter 3, the discrete-time large-deviation rate is studied for a system of independent Brownian particles in a force field, which yields the Fokker-Planck equation in the many-particle limit. Based on an estimate for the fundamental solution of the Fokker-Planck equation, it is proven that the small-time development of the rate functional coincides with the minimising movement of the Wasserstein gradient flow, under the conjecture that a similar relation holds if there is no force field. The Fokker-Planck equation is studied further in Chapter 4, but with a different technique. Here, an alternative formulation of the discrete-time large-deviation rate is derived from the continuous-time large-deviation rate. With this alternative formulation, the small-time development is proven in a much more general context, so that the conjecture of the previous chapter can indeed be dropped. To complete the discussion, it is mentioned that the continuous-time large deviations can be coupled to a Wasserstein gradient flow more directly, via an entropy-dissipation inequality. Chapter 5 discusses two related systems, whose evolutions are described by a system of reaction-diffusion equations, and by the diffusion equation with decay. In order to deal with the fact that the diffusion equation with decay is not mass-conserving, the decayed mass is added back to the system as decayed matter, which results in a system of reactiondiffusion equations. This allows for the construction of a system of independent particles whose probability evolves according to the reaction-diffusion equations. Similar to the previous chapters, a small-time development of the discrete-time large-deviation rate is proven. It turns out that in general the resulting functional can not be associated with a minimising movement formulation of a Wasserstein gradient flow. Nevertheless, it is proven that this functional defines a variational scheme that approximates the system of reaction-diffusion equations. As such, the functional, which involves entropy terms and Wasserstein distances, can be interpreted as a generalisation of a minimising movement. Chapter 6 is concerned with the effect of trivial Dirichlet boundary conditions on the discrete-time rate functional and its small-time development. Since the diffusion equation with trivial Dirichlet boundary conditions loses mass at the boundaries, the system is first transformed into a mass-conserving system by adding the amount of lost mass back to the system in two delta measures at the boundaries. This again allows for the construction of a corresponding microscopic particle system. For this particle system, the discrete-time large-deviation rate is calculated, and its small-time development is proven. It is still unclear whether the resulting functional can be used to define an variational approxiation scheme for the diffusion equation with Dirichlet boundary conditions. In Chapter 7, general Markov chains on a finite state space are studied. The macroscopic equation is then a linear system of ordinary differential equations, and the microscopic particle system consists of independent Markovian particles on the finite state space. First, the discrete-time rate functional for this particle system is calculated, and its small-time asymptotic development is proven for a two-state system. Although the resulting function looks like a minimising movement, it is still unknown whether this function defines a variational formulation for the system of linear differential equations. Next, the continuous-time rate functional is calculated, at least formally, using the Feng-Kurtz formalism. It is then shown that the continous-time rate function can be rewritten into an entropy-dissipation inequality. However, this inequality may imply unphysical behaviour unless the Markov chain satisfies detailed balance. Finally, the used methods and techniques and the general results are evaluated in Chapter8. It is shown that one can expect to find a gradient-flow structure via large-deviations of microscopic particle systems, if the macroscopic equation satisfies a generalised version of the detailed balance condition. Some important implications of detailed balance are proven for both the discrete-time approach, as well as for the continuous-time approach. The chapter ends with a discussion of the results for the different systems, and the general methods that are used in this thesisShow more
Book, 2013
Publication:2013
Publisher:Technische Universiteit Eindhoven, 2013

Self-improvement of the Bakry-\'Emery condition and ...

by G Savaré · 2013 · Cited by 120 — Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces. ... In particular, we obtain a precise estimate for the optimal W_\infty-coupling between two fundamental solutions in terms of the distance of the initial points.

[CITATION] Self-improvement of the Bakry-mery condition and Wasserstein contraction of the heat flow in RCD (K,∞) metric measure spaces, to appear in Disc

G Savaré - Cont. Dyn. Sist. A, 2013

On the rate of convergence in Wasserstein distance of the ...

by N Fournier · 2013 · Cited by 528 — On the rate of convergence in Wasserstein distance of the empirical measure. Let \mu_N be the empirical measure associated to a N-sample of a given probability distribution \mu on \mathbb{R}^d. We are interested in the rate of convergence of \mu_N to \mu, when measured in the Wasserstein distance of order p>0.

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

[CITATION] Fast Computation of Wasserstein Barycenters. arXiv e-prints

M Cuturi, A Doucet - arXiv preprint arXiv:1310.4375, 2013

http://cvgmt.sns.it › paper

Decomposition of geodesics in the Wasserstein space ... - cvgmt

Decomposition of geodesics in the Wasserstein space and the globalization problem. created by cavallett on 20 Aug 2013. [BibTeX]. Accepted Paper Inserted: ...

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

Consistent estimation of a population barycenter in the ...

2013

https://hal.archives-ouvertes.fr › docid › filename

by J Bigot · 2013 · Cited by 61 — Abstract. We define a notion of barycenter for random probability measures in the Wasserstein space. We study the population barycenter in ...

33 pages

[CITATION] CONSISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 2013

[PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

2013

Deconvolution for the Wasserstein metric and geometric inference

C Caillerie, F Chazal, J Dedecker, B Michel - International Conference on …, 2013 - Springer

This paper is a short presentation of recent results about Wasserstein deconvolution for

topological inference published in [1]. A distance function to measures has been defined in

[2] to answer geometric inference problems in a probabilistic setting. According to their …

2013

Conformal Wasserstein distance: II. Computational aspects and extensions

Y Lipman, J Puente, I Daubechies - Mathematics of Computation, 2013 - JSTOR

This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformai

Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math.(ELS), 227

(2011), no. 3, 1047-1077,(2011)]. We provide numerical procedures and algorithms for …

2013

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

image segmentation. Starting point is the Gromov-Wasserstein Distance which is

successfully applied in shape recognition and classification tasks but involves solving a non …

2013

Variational image segmentation and cosegmentation with the wasserstein distance

P Swoboda, C Schnörr - … Minimization Methods in Computer Vision and …, 2013 - Springer

We present novel variational approaches for segmenting and cosegmenting images. Our

supervised segmentation approach extends the classical Continuous Cut approach by a

global appearance-based data term enforcing closeness of aggregated appearance …

[PDF] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

K Kuwada - 数理解析研究所講究録別冊= RIMS …, 2013 - repository.kulib.kyoto-u.ac.jp

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm‐Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

<—-2013— ——2013————— -280—

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

[PDF] Gradient estimate for Markov kernels, Wasserstein control and

K KUWADA - Appl. Math, 2013 - core.ac.uk

We extend the duality between gradient estimates of the Markov kernel and Wasserstein

controls of that studied by the author (2010). Especially, the gauge norm-Orlicz norm type

duality holds on Polish geodesic space without any assumption on the Markov kernel. For …

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

2013

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in

weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare

Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

[CITATION] Optimal transport and Wasserstein barycenters in computer vision, image and video processing

J Delon - Optimal transport and vision-Teaser, 2013

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

2013

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

2013

Deconvolution for the Wasserstein metric and geometric inference

C Caillerie, F Chazal, J Dedecker, B Michel - International Conference on …, 2013 - Springer

This paper is a short presentation of recent results about Wasserstein deconvolution for

topological inference published in [1]. A distance function to measures has been defined in

[2] to answer geometric inference problems in a probabilistic setting. According to their …

2013

Geodesic PCA in the Wasserstein space

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1307.7721, 2013 - arxiv.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

image segmentation. Starting point is the Gromov-Wasserstein Distance which is

successfully applied in shape recognition and classification tasks but involves solving a non …

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

2013 [PDF] mpg.de

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

<—-2013— ——2013————— -290—

Variational image segmentation and cosegmentation with the wasserstein distance

P Swoboda, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We present novel variational approaches for segmenting and cosegmenting images. Our

supervised segmentation approach extends the classical Continuous Cut approach by a

global appearance-based data term enforcing closeness of aggregated appearance …

Two remarks on the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all

probability measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse

constructed in [6] this process in the case of probability measures over the unit interval using …

2013

THE L2-WASSERSTEIN DISTANCE

CM Bea, JMR Rodríguez - Distributions With Given Marginals …, 2013 - books.google.com

Let Q be a probability measure on R* and let S be a family of probability measures on R*

which will be considered as a pattern. For suitable patterns we consider the closest law to Q

in S, through the L2-Wasserstein distance, as a descriptive measure associated to Q. The …

The Wasserstein metric in Factor Analysis

L Ning, T Georgiou - 2013 Proceedings of the Conference on Control and its …, 2013 - SIAM

We consider the problem of approximating a (nonnegative definite) covariance matrix by the

sum of two structured covariances–one which is diagonal and one which has low-rank. Such

an additive decomposition follows the dictum of factor analysis where linear relations are …

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

2013

[PDF] Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

V Laschos - 2013 - core.ac.uk

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation

can be described as a gradient flow of the free energy functional in the Wasserstein space,

bringing this way the statistical mechanics point of view on the diffusion phenomenon to the …

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

2013 [PDF] psu.edu

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

2013 [PDF] arxiv.org

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

2013

Adaptive Dynamic Clustering Algorithm for Interval-valued ...

https://www.researchgate.net › ... › Clustering Algorithms

Request PDF | On Dec 10, 2013, Rong Guan and others published Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on ...

[CITATION] Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance

R Guan, Y Lechevallier, H Wang - 2013 - hal.inria.fr

… ouvrage. Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on

Squared-Wasserstein Distance. Rong Guan 1 Yves Lechevallier 2 Huiwen Wang 1 Détails.

1 BUAA - School of Economics and Management [Beijing]. 2 AxIS - Usage-centered design …

[CITATION] Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance

R Guan, Y Lechevallier, H Wang - 2013 - hal.inria.fr

… ouvrage. Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on

Squared-Wasserstein Distance. Rong Guan 1 Yves Lechevallier 2 Huiwen Wang 1 Détails.

1 BUAA - School of Economics and Management [Beijing]. 2 AxIS - Usage-centered design …

A primal-dual approach for a total variation Wasserstein flow

<—-2013— ——2013————— -300—

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

2013 [PDF] abhishekhalder.org

Frequency domain model validation in Wasserstein metric

A Halder, R Bhattacharya - 2013 American Control Conference, 2013 - ieeexplore.ieee.org

This paper connects the time-domain uncertainty propagation approach for model validation

in Wasserstein distance 2 W 2, introduced by the authors in [1], with the frequency domain

model validation in the same. To the best of our knowledge, this is the first frequency domain …

2013

Geodesic PCA in the Wasserstein space

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1307.7721, 2013 - arxiv.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

2013

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - projecteuclid.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an $\alpha $-stable law, the solution of the equation …

Behaviors of -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

A Takatsu - SIAM Journal on Mathematical Analysis, 2013 - SIAM

A φ-exponential distribution is a generalization of an exponential distribution associated to

functions φ in an appropriate class, and the space of φ-exponential distributions has a dually

flat structure. We study features of the space of φ-exponential distributions, such as the …

A Wasserstein-type distance to measure deviation from equilibrium of quantum Markov semigroups

J Agredo - Open Systems & Information Dynamics, 2013 - World Scientific

In this paper we define a distance W between states in the non-commutative von Neumann

algebra of bounded operators on a separable Hilbert space, in order to measure deviations

from equilibrium using a rate ep W (·). The restriction of W to the diagonal subalgebra of …

[HTML] Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - Journal of Multivariate Analysis, 2013 - Elsevier

The subject of this paper is the estimation of a probability measure on R d from the data

observed with an additive noise, under the Wasserstein metric of order p (with p≥ 1). We

assume that the distribution of the errors is known and belongs to a class of supersmooth …

<——2013————2013——— -310—

[PDF] abhishekhalder.org

Frequency domain model validation in Wasserstein metric

A Halder, R Bhattacharya - 2013 American Control Conference, 2013 - ieeexplore.ieee.org

This paper connects the time-domain uncertainty propagation approach for model validation

in Wasserstein distance 2 W 2, introduced by the authors in [1], with the frequency domain

model validation in the same. To the best of our knowledge, this is the first frequency domain …

The Wasserstein metric in Factor Analysis

L Ning, T Georgiou - 2013 Proceedings of the Conference on Control and its …, 2013 - SIAM

We consider the problem of approximating a (nonnegative definite) covariance matrix by the

sum of two structured covariances–one which is diagonal and one which has low-rank. Such

an additive decomposition follows the dictum of factor analysis where linear relations are …

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

On the rate of convergence in Wasserstein distance of the ...

by N Fournier · 2013 · Cited by 527 — [Submitted on 7 Dec 2013]. Title:On the rate of convergence in Wasserstein distance of the empirical measure. Authors:Nicolas Fournier (LPMA), Arnaud Guillin · Download ... We are interested in the rate of convergence of \mu_N to \mu, when measured in the Wasserstein distance of order p>0. We provide some satisfying ...

[CITATION] On the rate of convergence in Wasserstein distance of the empirical measure. Available at

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013

Optimal transport and Wasserstein barycenters in computer ...

https://www.msri.org › documents › assets

PDF

Aug 22, 2013 — Optimal transport and Wasserstein barycenters in computer vision, image and video processing. ... Images from [Ferrandans et al., 2013].

Optimal transport and Wasserstein barycenters in computer ...

https://www.msri.org › documents › assets

https://www.msri.org › documents › assetsPDF

Aug 22, 2013 — Optimal transport and Wasserstein barycenters in computer vision, image and video processing. Julie Delon. CNRS, LT

[CITATION] Optimal transport and Wasserstein barycenters in computer vision, image and video processing

J Delon - Optimal transport and vision-Teaser, 2013

Variational image segmentation and cosegmentation with the wasserstein distance

2013

2013 [PDF] psu.edu

P Swoboda, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

… Wasserstein distance (i) on arbitrary images opposed to grayvalue images and (ii) as a truly

global data term that depends on the segmentation. … reasons as the one dimensional

Wasserstein distance is very fast to compute and is not an inherent limitation of the algorithm in [7]. …

2013 see 2012 2014

Decomposition of geodesics in the Wasserstein space and the ...

by F Cavalletti · ‎2012 · ‎Cited by 31 · ‎Related articles

Aug 20, 2013 — Decomposition of geodesics in the Wasserstein space and the globalization property. ... Assuming more regularity, namely in the setting of infinitesimally strictly convex metric measure space, the one dimensional density is the product of two differentials giving more insight on the density decomposition.

[CITATION] Decomposition of geodesics in the Wasserstein space and the globalization property. accepted on GAFA

F Cavalletti - preprint, 2013

Een cultuur die verdween: Europese joden in de jaren dertig [Bespreking van: B. Wasserstein (2012) Aan de vooravond: Europese Joden voor de Tweede …

B Wallet - Geschiedenis Magazine, 2013 - pure.uva.nl

General rights It is not permitted to download or to forward/distribute the text or part of it without

the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual

use, unless the work is under an open content license (like Creative Commons) …

PDF] Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - 2013 - hal.archives-ouvertes.fr

We define a notion of barycenter for random probability measures in the Wasserstein space.

We study the population barycenter in terms of existence and uniqueness. Using a duality

argument, we give a precise characterization of the population barycenter for compactly …

[CITATION] CONSISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 2013

A geometric study of Wasserstein spaces: an addendum on the boundary

J Bertrand, BR Kloeckner - International Conference on Geometric …, 2013 - Springer

Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally

compact metric space. Mainly, X is a space where triangles are “thin”: points on the opposite

side to a vertex are closer to the vertex than they would be in the Euclidean plane. This assumption …

Cited by 3

<——2013————2013——— -320—

Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric

N Gigli, F Otto - Calculus of Variations and Partial Differential …, 2013 - Springer

As noted by the second author in the context of unstable two-phase porous medium flow,

entropy solutions of Burgers' equation can be recovered from a minimizing movement

scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto …

[HTML] Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - Journal of Multivariate Analysis, 2013 - Elsevier

The subject of this paper is the estimation of a probability measure on R d from the data

observed with an additive noise, under the Wasserstein metric of order p (with p≥ 1). We

assume that the distribution of the errors is known and belongs to a class of supersmooth …

2013

[HTML] Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension

J Dedecker, B Michel - Journal of Multivariate Analysis, 2013 - Elsevier

The subject of this paper is the estimation of a probability measure on R d from the data

observed with an additive noise, under the Wasserstein metric of order p (with p≥ 1). We

assume that the distribution of the errors is known and belongs to a class of supersmooth …

2013 see 2014

2014 INTERNATIONAL CONFERENCE ON MACHINE LEARNING

482 citations* for all

456 citations*

Marco Cuturi ¹,Arnaud Doucet ²

¹ Kyoto University ,² University of Oxford

Subgradient method

View More (8+)

EXCERPTS (25)

[CITATION] Fast Computation of Wasserstein Barycenters. arXiv e-prints

M Cuturi, A Doucet - arXiv preprint arXiv:1310.4375, 2013

Deconvolution for the Wasserstein metric and geometric inference

2013 [PDF] projecteuclid.org

C Caillerie, F Chazal, J Dedecker, B Michel - International Conference on …, 2013 - Springer

This paper is a short presentation of recent results about Wasserstein deconvolution for topological inference published in [1]. A distance function to measures has been defined in [2] to answer geometric inference problems in a probabilistic setting. According to their …

2013

[CITATION] Correction: Central limit theorems for the Wasserstein distance between the empirical and the true distributions

E del Barrio, E Giné, C Matrán - Annals of Probability, 2003 - projecteuclid.org

There is an error in Proposition 6.4 of our paper. It comes from a wrong expression for the

covariance, K (ρ), between| Z1| and| Z2|, where (Z1, Z2) is a centered random vector with

bivariate normal distribution such that Var (Z1)= Var (Z2)= 1 and Cov (Z1, Z2)= ρ. The …

2013

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

2013 [PDF] 213.230.96.51

Two remarks on the Wasserstein Dirichlet form

W Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2013 - Springer

The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all

probability measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse

constructed in [6] this process in the case of probability measures over the unit interval using …

2013 [PDF] uni-muenster.de

Object segmentation by shape matching with Wasserstein modes

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

… on the Wasserstein distance. We start with a functional for variational segmentation where we

regularize the segmentation with the Wasserstein … (i) The optimal segmentation & matching

become invariant under translations and approximately invariant wrt rotations and scale …

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

<——2013————2013——— -330 —

Conformal Wasserstein distance: II. Computational aspects and extensions

Y Lipman, J Puente, I Daubechies - Mathematics of Computation, 2013 - JSTOR

This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformai

Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math.(ELS), 227

(2011), no. 3, 1047-1077,(2011)]. We provide numerical procedures and algorithms for …

[PDF] sysmath.com

A new procedure for testing normality based on the L₂ Wasserstein distance

D He, X Xu, J Zhao - Journal of Systems Science and Complexity, 2013 - Springer

This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein

distance. The authors first construct a probability through the Bootstrap resampling. Although

the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is …

A primal-dual approach for a total variation Wasserstein flow

M Benning, L Calatroni, B Düring… - … Conference on Geometric …, 2013 - Springer

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image

densities. We propose an implicit time-stepping scheme that employs a primal-dual method

for computing the subgradient of the total variation seminorm. The constraint on the dual …

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

2013

Object segmentation by shape matching with Wasserstein modes

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We gradually develop a novel functional for joint variational object segmentation and shape

matching. The formulation, based on the Wasserstein distance, allows modelling of local

object appearance, statistical shape variations and geometric invariance in a uniform way …

2013

Modelling convex shape priors and matching based on the Gromov-Wasserstein distance

B Schmitzer, C Schnörr - Journal of mathematical imaging and vision, 2013 - Springer

We present a novel convex shape prior functional with potential for application in variational

image segmentation. Starting point is the Gromov-Wasserstein Distance which is

successfully applied in shape recognition and classification tasks but involves solving a non …

2013 PDF

Consistent estimation of a population barycenter in the ...

https://hal.archives-ouvertes.fr › docid › filename

by J Bigot · 2013 · Cited by 56 — Abstract. We define a notion of barycenter for random probability measures in the Wasserstein space. We study the population barycenter in ...

33 pages

[CITATION] CONSISTENT ESTIMATION OF A BARYCENTER IN THE WASSERSTEIN SPACE

J Bigot, T Klein - Statistics & its Interactions with Other Disciplines-2013, 2013

2013

A Primal-Dual Approach for a Total Variation Wasserstein Flow

https://link.springer.com › chapter

by M Benning · 2013 · Cited by 8 — GSI 2013: Geometric Science of Information pp 413-421 | Cite as. A Primal-Dual Approach for a Total Variation Wasserstein Flow. Authors; Authors and ...

[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

A primal-dual approach for a total variation Wasserstein ﬂow ...

https://www.see.asso.fr › fichier › 48...

Geometric Science of Information. 28 Août 2013 - 30 Août 2013 Mines ParisTech, ... A primal-dual approach for a total variation Wasserstein ﬂow.
[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

Object segmentation by shape matching with Wasserstein modes

2013

B Schmitzer, C Schnörr - … Workshop on Energy Minimization Methods in …, 2013 - Springer

We gradually develop a novel functional for joint variational object segmentation and shape

matching. The formulation, based on the Wasserstein distance, allows modelling of local

object appearance, statistical shape variations and geometric invariance in a uniform way …

2013 [PDF] arxiv.org

Conformal Wasserstein distance: II. Computational aspects and extensions

Y Lipman, J Puente, I Daubechies - Mathematics of Computation, 2013 - JSTOR

This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformai

Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math.(ELS), 227

(2011), no. 3, 1047-1077,(2011)]. We provide numerical procedures and algorithms for …

<——2013————2013——— -340 —

2013 [PDF] arxiv.org

Geodesic PCA in the Wasserstein space

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1307.7721, 2013 - arxiv.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

2013

Adaptive Dynamic Clustering Algorithm for Interval-valued ...

https://hal.archives-ouvertes.fr › hal-...

[CITATION] Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance

by R Guan · 2013 · Cited by 1 — Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on Squared-Wasserstein Distance. Rong Guan and Yves Lechevallier and ...

Collections: INRIA

R Guan, Y Lechevallier, H Wang - 2013 - hal.inria.fr

… ouvrage. Adaptive Dynamic Clustering Algorithm for Interval-valued Data based on

Squared-Wasserstein Distance. Rong Guan 1 Yves Lechevallier 2 Huiwen Wang 1 Détails.

1 BUAA - School of Economics and Management [Beijing]. 2 AxIS - Usage-centered design …

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

2013 [PDF] psu.edu

M Agueh, M Bowles - Acta applicandae mathematicae, 2013 - Springer

We numerically approximate, on the real line, solutions to a large class of parabolic partial

differential equations which are “gradient flows” of some energy functionals with respect to

the L p-Wasserstein metrics for all p> 1. Our method relies on variational principles involving …

Self-improvement of the Bakry-\'Emery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces

2013 ARXIV: FUNCTIONAL ANALYSIS

On Properties of the Generalized Wasserstein Distance

65 citations* for all

55 citations*

2016 ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Benedetto Piccoli ¹,Francesco Rossi ²

¹ Rutgers University ,² Aix-Marseille University

Lipschitz continuity

Duality (optimization)

View More (9+)

The Wasserstein distances Wp (p ${\geqq}$ 1), defined in terms of a solution to the Monge–Kantorovich problem, are known to be a useful tool to investigate transport equations. In particular, the Benamou–Brenier formula characterizes the square of the Wasserstein distance W2 as the infimum of the ... View Full Abstract

EXCERPTS (17)∑

2013 see 2016

On properties of the Generalized Wasserstein distance

10 citations*

2013 ARXIV: ANALYSIS OF PDES

The Efficacy of Platelet-Rich Plasma in the Treatment of Symptomatic Knee Osteoarthritis: A Systematic Review With Quantitative Synthesis

238 citations*

2013 ARTHROSCOPY

Amir Khoshbin ,Timothy Leroux ,David Wasserstein ,Paul Marks ,John Theodoropoulos see all 10 authors

Women's College Hospital

Randomized controlled trial

Platelet-rich plasma

View More (22+)

Purpose The purpose of this systematic review was to synthesize the available Level I and Level II literature on platelet-rich plasma (PRP) as a therapeutic intervention in the management of symptomatic knee osteoarthritis (OA). Methods A systematic review of Medline, Embase, Cochrane Central Reg... View Full Abstract

2013

2013 [PDF] arxiv.org

Application of the Wasserstein metric to seismic signals

B Engquist, BD Froese - arXiv preprint arXiv:1311.4581, 2013 - arxiv.org

Seismic signals are typically compared using travel time difference or $ L_2 $ difference. We

propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology.

It exhibits properties from both of the traditional measures mentioned above. The numerical …

Wasserstein cnn: Learning invariant features for nir-vis face recognition

R He, X Wu, Z Sun, T Tan - IEEE transactions on pattern …, 2018 - ieeexplore.ieee.org

Heterogeneous face recognition (HFR) aims at matching facial images acquired from

different sensing modalities with mission-critical applications in forensics, security and

commercial sectors. However, HFR presents more challenging issues than traditional face …

[CITATION] Application of the Wasserstein metric to seismic signals

EBF BD - arXiv preprint arXiv:1311.4581, 2013

https://bookstore.ams.org › memo-211-993

2013 see 2011
Differential Forms on Wasserstein Space ... - AMS Bookstore

Mar 17, 2013 — In this paper the authors develop a calculus for the corresponding class of differential forms on M. In particular they prove an analogue of ...

2013 video

Wha is … a Wasserstein distance?

'Berlin November 29, 2013,

Nov 29, 2013

2013
Behaviors of 𝜑-Exponential Distributions in Wasserstein Geometry and an Evolution Equation

Asuka Takatsu

SIAM Journal on Mathematical Analysis Vol. 45, No. 4, pp. 2546–25562013

<——2013————2013——— -350—

Peer-reviewed
A new procedure for testing normality based on the L 2 Wasserstein distance

Authors:Daojiang He, Xingzhong Xu, Jianxin Zhao
Summary:This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein distance. The

Authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust testShow more
Article, 2013
Publication:Journal of Systems Science and Complexity, 26, 201308, 572
Publisher:2013

2013 see 2012 Peer-reviewed
Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

Author:Hwa Kil Kim
Summary:In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the Moreau-Yosida approximation and denote it byShow more
Article
Publication:Journal of Differential Equations, 254, 2013-04-01, 2861

2013 see 2012 Peer-reviewed
Transport Equation with Nonlocal Velocity in Wasserstein Spaces: Convergence of Numerical Schemes

Authors:Benedetto Piccoli, Francesco Rossi
Summary:Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein space. In particular, we consider the Cauchy problem for a transport equation, where the velocity field depends on the measure itself.We deal with numerical schemes for this problem and prove convergence of a Lagrangian scheme to the solution, when the discretization parameters approach zero. We also prove convergence of an Eulerian scheme, under more strict hypotheses. Both schemes are discretizations of the push-forward formula defined by the transport equation. As a by-product, we obtain existence and uniqueness of the solution.All the results of convergence are proved with respect to the Wasserstein distance. We also show that L 1 spaces are not natural for such equations, since we lose uniqueness of the solutionShow more
Article, 2013
Publication:Acta Applicandae Mathematicae : An International Research Journal on Applying Mathematics and Mathematical Applications, 124, 201304, 73
Publisher:2013

Peer-reviewed
Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric

Authors:Nicola Gigli, Felix Otto
Summary:As noted by the second

Author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto, Commun Pure Appl Math, 1999). In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equationShow more
Article, 2013
Publication:Calculus of Variations and Partial Differential Equations, 47, 201305, 181
Publisher:2013

Peer-reviewed
A new procedure for testing normality based on the L2 Wasserstein distance

Authors:He D., Xu X., Zhao J
Article, 2013
Publication:Journal of Systems Science and Complexity, 26, 2013 08 01, 572
Publisher:2013
Peer-reviewed
Behaviors of φ-exponential distributions in wasserstein geometry and an evolution equation

Author:Takatsu A.
Article, 2013
Publication:SIAM Journal on Mathematical Analysis, 45, 2013 12 06, 2546
Publisher:2013

2013

Peer-reviewed
A Wasserstein-type Distance to Measure Deviation from Equilibrium of Quantum Markov Semigroups

Author:Julián Agredo
Summary:In this paper we define a distance W between states in the non-commutative von Neumann algebra $\mathfrak{B}(\mathfrak{h})$ of bounded operators on a separable Hilbert space $\mathfrak{h}$, in order to measure deviations from equilibrium using a rate epW(·). The restriction of W to the diagonal subalgebra of $\mathfrak{B}(\mathfrak{h})$ coincides with the Wasserstein distance used in optimal transport. Moreover, if ρ is a normal invariant state of a quantum Markov semigroup $\mathcal{T}=(\mathcal{T}_t)_{t\geq 0}$, then epW(ρ) = 0 if and only if a detailed balance condition holdsShow more
Article, 2013
Publication:Open Systems & Information Dynamics, 20, June 2013, 1350009-1
Publisher:2013

Peer-reviewed
Entropic Burgersâ equation via a minimizing movement scheme based on the Wasserstein metric

Authors:N. Gigli, F. Otto
Article, 2013
Publication:CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 47, 2013, 181
Publisher:2013

Peer-reviewed
Behaviors of phi (variant) -Exponential Distributions in Wasserstein Geometry and an Evolution Equation

Author:A. Takatsu
Article, 2013
Publication:SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 45, 2013, 2546
Publisher:2013

2013 see 2014 ebook
On gradient structures for Markov chains and the passage to Wasserstein gradient flows

Authors:Karoline Disser, Matthias Liero (

Author)
eBook, 2013
English
Publisher:WIAS, Weierstraß-Inst. für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e. V. Niedersächsische Staats- und Universitätsbibliothek Technische Informationsbibliothek u. Universitätsbibliothek, Berlin, Göttingen, Hannover, 2013
Also available asPrint Book
View AllFormats & Editions

2013 see 2012
Localisation de masse et espaces de Wasserstein

Author:Le Gouic, Thibaut (Creator)
Summary:Le travail de cette thèse est basé sur deux outils : le packing d'un ensemble et les espaces de Wasserstein. Une première partie s'intéresse à la localisation de la masse d'une mesure de probabilité Mu. Lorsque Mu est régulière, les ensembles de niveau de sa densité fournissent une bonne notion pour localiser les zones "denses" de masse, mais perdent leur sens pour les mesures à support fini, comme dans le cas de la mesure empirique. Nous définissons alors une fonction Tau dite de taille, sur les fermés d'un espace métrique, basée sur leur packing. Les ensembles de plus petite Tau-taille ayant une masse 1 − alpha donnée permettent de localiser les zones denses de Mu, même dans les cas irréguliers. Nous montrons que les ensembles de plus petite Tau-taille pour Mu et alpha fixés dépendent continuement de Mu et de alpha, pour la distance de Hausdorff. Nous en tirons une nouvelle méthode de quantification de Mu, robuste et stable. Une seconde partie s'intéresse à la distance de Wasserstein entre une probabilité mu et la mesure empirique associée. Nous obtenons une majoration non asymptotique de l'espérance de cette distance, dans la cadre d'un espace métrique quelconque. Une particularisation aux espaces de dimension finie permet de mettre en valeur la précision de cette majoration. Nous obtenons aussi dans le cas des mesures gaussiennes sur les espaces de Banach, de nouvelles majorations qui coïncident asymptotiquement avec celles des meilleurs quantifieurs possibles. À l'aide d'inégalités de concentration, nous établissons des bornes de déviations. Enfin, nous utilisons ces résultats pour définir des tests statistiques non asymptotiques et non paramétriques d'adéquation à une famille de lois. Une troisième partie s'intéresse au barycentre d'une famille finie de mesures de probabilité. La moyenne de Fréchet fournit une extension de la notion de barycentre aux espaces métriques, nous permettant de le définir sur les espaces de Wasserstein. Nous montrons son existence, pShow more
Downloadable Archival Material, 2013-12-02
Undefined
Publisher:2013-12-02

2013 thesis
Localisation de masse et espaces de Wasserstein

<——2013————2013——— -360— end 2013

including 6 titles with Vaserstein

start 2014 Wasserstein

Wasserstein propagation for semi-supervised learning

by J Solomon - ‎2014 - ‎Cited by 32 - ‎Related articles

Published in: Proceeding ICML'14 Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32 Pages I-306-I-314

Jun 21, 2014 - Probability distributions and histograms are natural representations for product ratings, traffic measurements, and other data considered in many machine learning applications. Thus, this paper introduces a technique for graph-based semi-supervised learning of histograms, derived from

[PDF] Wasserstein Propagation for Semi-Supervised Learning - CSAIL People

by J Solomon - ‎Cited by 37 - ‎Related articles

Wasserstein Propagation for Semi-Supervised Learning. Justin Solomon. JUSTIN.SOLOMON@STANFORD.EDU. Raif M. Rustamov. RUSTAMOV@STANFORD.EDU. Leonidas Guibas. GUIBAS@CS.STANFORD.EDU. Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, California 94305 USA.

The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow

Mauro Carfora (Submitted on 5 May 2014)

The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow

M Carfora - arXiv preprint arXiv:1405.0827, 2014 - arxiv.org

Abstract: Non linear sigma models are quantum field theories describing, in the large

deviations sense, random fluctuations of harmonic maps between a Riemann surface and a

Riemannian manifold. Via their formal renormalization group analysis, they provide a ...

[PDF] from uvic.ca

[PDF] CONTRACTION IN THE WASSERSTEIN METRIC FOR SOME MARKOV CHAINS, AND APPLICATIONS TO THE DYNAMICS OF EXPANDING MAPS.

B Kloeckner, AO Lopes, M Stadlbauer - Preprint, 2014 - perso-math.univ-mlv.fr

Abstract.—We employ techniques from optimal transport in order to prove decay of transfer

operators associated to iterated functions systems and expanding maps, giving rise to a new

proof without requiring a Doeblin-Fortet (or Lasota-Yorke) inequality.

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2014 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on ...

MR3304897 I

[PDF] First and second moments for self-similar couplings and Wasserstein distances

JM Fraser - arXiv preprint arXiv:1401.1443, 2014 - 128.84.21.199

Abstract We study aspects of the Wasserstein distance in the context of self-similar

measures. Computing this distance between two measures involves minimising certain

moment integrals over the space of couplings, which are measures on the product space ...

[PDF] Estimation of Deformations between Distributions with the Wasserstein Distance

H Lescornel, JM Loubes - iip.ist.i.kyoto-u.ac.jp

Abstract We consider the issue of estimating a deformation acting on measures. For this we

study a parametric deformation model on an empirical sample and provide a new matching

criterion for cloud points. The deformation estimator is obtained by minimizing the ...

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

by Lescornel, Hélène 2014 Dissertation :

La première partie de cette thèse est consacrée à l'estimation de covariance de processus stochastiques non stationnaires. Le modèle étudié amène à estimer la...
2014[PDF] arxiv.org

2014 thesis
Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

Epidemiology of primary anterior shoulder dislocation requiring closed reduction in Ontario, Canada

T Leroux, D Wasserstein, C Veillette… - … American journal of …, 2014 - journals.sagepub.com

… for socioeconomic status, was calculated via an established technique based on Statistics

Canada census data, which determines the median household income for each postal code …

q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - arXiv preprint arXiv:1401.0840, 2014 - arxiv.org

Abstract: Based on the idea of a recent paper by Ambrosio-Gigli-Savar\'e in Invent.

Math.(2013), we show that flow of the $ q $-Cheeger energy, called $ q $-heat flow, solves

the gradient flow problem of the Renyi entropy functional in the $ p $-Wasserstein. For that ...

Wasserstein Barycenters over Riemannian manfolds

YH Kim, B Pass - arXiv preprint arXiv:1412.7726, 2014 - arxiv.org

Abstract: We study barycenters in the space of probability measures on a Riemannian

manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we

establish absolute continuity of the barycenter of general measures $\ Omega\ in P (P (M)) ...

<——2014—————2014—— ———— -10—

MR3182620 Indexed Qiao, Motong; Wang, Wei; Ng, Michael Multi-phase texture segmentation using Gabor features histograms based on Wasserstein distance. Commun. Comput. Phys. 15 (2014), no. 5, 1480–1500. 94A08 (68U10)

[PDF] Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance

M Qiao, W Wang, M Ng - global-sci.com

Abstract. We present a multi-phase image segmentation method based on the histogram of

the Gabor feature space, which consists of a set of Gabor-filter responses with various

orientations, scales and frequencies. Our model replaces the error function term in the ...

Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance

By: Qiao, Motong; Wang, Wei; Ng, Michael

COMMUNICATIONS IN COMPUTATIONAL PHYSICS Volume: ‏ 15 Issue: ‏ 5 Pages: ‏ 1480-1500 Published: ‏ MAY 2014

Times Cited: 2

New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - arxiv.org

Abstract: In this paper, we provide sufficient conditions for the existence of the invariant

distribution and subgeometric rates of convergence in the Wasserstein distance for general

state-space Markov chains which are not phi-irreducible. Our approach is based on a ...

The Annals of Applied Probability Volume 24, Number 2 (2014), 526-552.

Title: SELF-IMPROVEMENT OF THE BAKRY-EMERY CONDITION AND WASSERSTEIN CONTRACTION OF THE HEAT FLOW IN RCD(K, infinity) METRIC MEASURE SPACES

Author(s): Savare, Giuseppe

Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume: 34 Issue: 4 Special Issue: SI Pages: 1641-1661 DOI: 10.3934/dcds.2014.34.1641 Published: APR 2014

MR3192034 Cavalletti, Fabio Decomposition of geodesics in the Wasserstein space and the globalization problem. Geom. Funct. Anal. 24 (2014), no. 2, 493–551. 53C23 (53C22)

Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem Fabio Cavalletti Geometric and Functional Analysis

January 2014

Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem

By: Cavalletti, Fabio

GEOMETRIC AND FUNCTIONAL ANALYSIS Volume: ‏ 24 Issue: ‏ 2 Pages: ‏ 493-551 Published: ‏ APR 2014

Times Cited: 16 8.

Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Interval Data

LI HONG - TELKOMNIKA Indonesian Journal of Electrical …, 2014 - iaesjournal.com

Abstract The aim of this paper is to present new wasserstein metric based adaptive fuzzy

clustering methods for partitioning symbolic interval data. In two methods, fuzzy partitions

and prototypes for clusters are determined by optimizing adequacy criteria based on ...

2014

[PDF] A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ISOMETRIC RIGIDITY IN NEGATIVE CURVATURE

J Bertrand, BR Kloeckner - math.univ-toulouse.fr

Abstract.—We continue the geometric study of the Wasserstein space# 2 (X) of simply

connected, negatively curved metric spaces X, by proving that in many cases, they are

isometrically rigid: any isometry of the Wasserstein space is the action on measures of an ...

A geometric study of Wasserstein spaces: Isometric rigidity in negative curvature

J Bertrand, B Kloeckner - arXiv preprint arXiv:1404.1734, 2014 - arxiv.org

Abstract: This article deals with the space of probability measures (with finite second order

moments) over a CAT (0) space. The Wasserstein metric turns this space of measures into a

geodesic space called Wasserstein space. We are interested in the geometric properties ...

Wasserstein Propagation for Semi-Supervised Learning

J Solomon, R Rustamov, G Leonidas… - Proceedings of The 31st …, 2014 - jmlr.org

Abstract Probability distributions and histograms are natural representations for product

ratings, traffic measurements, and other data considered in many machine learning

applications. Thus, this paper introduces a technique for graph-based semi-supervised ...

[PDF] On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - opus4.kobv.de

Abstract We study the approximation of Wasserstein gradient structures by their

finitedimensional analog. We show that simple finite-volume discretizations of the linear

Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for ...

2014 [PDF] psu.edu

[PDF] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J Wangb - arXiv preprint arXiv:1407.1986, 2014 - Citeseer

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential contractivity of diffusion semigroups (Pt) t≥ 0 with

respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that …

<——2014—————2014————— ———— -20—

Wasserstein distances between self-similar measures

JM Fraser - arXiv preprint arXiv:1401.1443, 2014 - arxiv.org

Abstract: We study the Wasserstein distance between self-similar measures on the unit

interval. This involves minimising certain integrals over the space of couplings, which are

measures on the product space with the original measures as prescribed marginals. We ...

Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - arXiv preprint arXiv:1403.0291, 2014 - arxiv.org

Abstract: Based on the theory of M-matrix and Perron-Frobenius theorem, we provide some

criteria to justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily ...

Stochastic Process. Appl. 125 (2015), no. 2, 739–758.

OD matrix structural similarity: Wasserstein metric

A Ruiz de Villa, J Casas, M Breen - Transportation Research Board 93rd …, 2014 - trid.trb.org

Abstract: In this paper the authors introduce a metric and a method, considering the spatial

structure, for comparing OD matrices. It is based on mass transportation techniques, in

particular the notion of Wasserstein distance. The result of the comparison is measured in ...

Absolutely continuous curves in extended Wasserstein-Orlicz spaces

S Lisini - arXiv preprint arXiv:1402.7328, 2014 - arxiv.org

Abstract: In this paper we extend a previous result of the author [Lis07] of characterization of

absolutely continuous curves in Wasserstein spaces to a more general class of spaces: the

spaces of probability measures endowed with the Wasserstein-Orlicz distance constructed ...

[PDF] Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - arXiv preprint, 2014 - people.tamu.edu

Abstract This paper focuses on the performance and the robustness analysis of stochastic

jump linear systems. The realization of the state trajectory under stochastic jump processes

becomes random variables, which brings forth the probability distributions for the system ...

MR3284787 Automatica J. IFAC 51 (2015), 341–347.

[HTML] Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

A Irpino, R Verde, FAT De Carvalho - Expert Systems with Applications, 2014 - Elsevier

Abstract This paper presents a Dynamic Clustering Algorithm for histogram data with an

automatic weighting step of the variables by using adaptive distances. The Dynamic

Clustering Algorithm is a k-means-like algorithm for clustering a set of objects into a ...

Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

Abstract: In this work, we propose computational models and algorithms for point cloud

registration with non-rigid transformation. First, point clouds sampled from manifolds

originally embedded in some Euclidean space $\ mathbb {R}^ D $ are transformed to new ...

MR3331178 Carrillo, José Antonio; Choi, Young-Pil; Hauray, Maxime The derivation of swarming models: mean-field limit and Wasserstein distances. Collective dynamics from bacteria to crowds, 1–46, CISM Courses and Lectures, 553, Springer, Vienna, 2014. 82C22 (35Q82)

The derivation of swarming models: Mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective Dynamics from Bacteria to …, 2014 - Springer

Abstract These notes are devoted to a summary on the mean-field limit of large ensembles

of interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We ...

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

Zbl 06804337

MG Mora, M Peletier, L Scardia - arXiv preprint arXiv:1409.4236, 2014 - arxiv.org

Abstract: We consider systems of $ n $ parallel edge dislocations in a single slip system,

represented by points in a two-dimensional domain; the elastic medium is modelled as a

continuum. We formulate the energy of this system in terms of the empirical measure of the ...

Wasserstein Distance and the Rectifiability of Doubling Measures: Part I

J Azzam, G David, T Toro - arXiv preprint arXiv:1408.6645, 2014 - arxiv.org Mathematische Annalen - Springer

Abstract: Let $\ mu $ be a doubling measure in $\ mathbb {R}^ n $. We investigate

quantitative relations between the rectifiability of $\ mu $ and its distance to flat measures.

More precisely, for $ x $ in the support $\ Sigma $ of $\ mu $ and $ r> 0$, we introduce a ...

Mathematische Annalen - Springer

<—-2014———2014——— -30—

Information fusion via the wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknow correlation

AN Bishop NICTA, Australian Nat. Univ., Canberra, ACT, Australia (FUSION), 2014 17th International Conference on, 2014 - ieeexplore.ieee.org

Abstract—In this work, a general information fusion problem is formulated as an optimisation

protocol in the space of probability measures (ie the so-called Wasserstein metric space).

The highlevel idea is to consider the data fusion result as the probability measure that is ...

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

H Lescornel - 2014 - theses.fr

Résumé La première partie de cette thèse est consacrée à l'estimation de covariance de

processus stochastiques non stationnaires. Le modèle étudié amène à estimer la

covariance du processus dans différents espaces vectoriels de matrices. Nous étudions ...

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

H Lescornel - 2014 - theses.fr

Exponential Contractivity in the $ L^ p $-Wasserstein Distance for Diffusion Processes

D Luo, J Wang - arXiv preprint arXiv:1407.1986, 2014 - arxiv.org

Abstract: By adopting the coupling by reflection and choosing an auxiliary function which is

convex near infinity, we establish the exponential contractivity of diffusion semigroups $(P_t)

_ {t\ ge0} $ with respect to the standard $ L^ p $-Wasserstein distance for all $ p\ in [1,\ ...

[PDF] from iaesjournal.com

[PDF] Some evolution equations as Wasserstein gradient flows

A Takatsu - kurims.kyoto-u.ac.jp

Abstract In the workshop, I demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we used the notions of the information geometry). In this note, I discuss the ...

[PDF] Fast Computation of Wasserstein Barycenters

A Doucet - iip.ist.i.kyoto-u.ac.jp

Abstract We present new algorithms to compute the mean of a set of empirical probability

measures under the optimal transport metric. This mean, known as the Wasserstein

barycenter, is the measure that minimizes the sum of its Wasserstein distances to each ...

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2014 - Springer

Abstract A local existence and uniquness of the gradient flow of one dimensional Dirichlet

energy on the Wasserstein space is proved. The proofs are based on a relaxation of

displacement convexity in the Wasserstein space and can be applied to a family of higher ...

[PDF] from springer.com

MR3311904 P

On tangent cones and parallel transport in Wasserstein space arXiv

J Lott - arXiv preprint arXiv:1407.7245, 2014 - arxiv.org

Abstract: If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein

space of probability measures on M. If S is an embedded submanifold of M, and mu is an

absolutely continuous measure on S, we compute the tangent cone of P (M) at mu. We ...

[PDF] from gatech.edu

[PDF] The Gromov–Wasserstein Distance: A Brief Overview

F Mémoli - Axioms, 2014 - mdpi.com

... Article The Gromov–Wasserstein Distance: A Brief Overview Facundo Mémoli ... Published:

2 September 2014 Abstract: We recall the construction of the Gromov–Wasserstein

distance and concentrate on quantitative aspects of the definition. ...

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds arXiv

<——2014—————2014———40—

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

Abstract: We develop a new method for showing that a given sequence of random variables

verifies an appropriate law of the iterated logarithm. Our tools involve the use of general

estimates on multidimensional Wasserstein distances, that are in turn based on recently ...

Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow

M Bowles - 2014 - dspace.library.uvic.ca

In this thesis, we study a linear fractional Fokker-Planck equation that models non-local

(fractional') diffusion in the presence of a potential field. The non-locality is due to the

appearance of thefractional Laplacian'in the corresponding PDE, in place of the classical ...

[PDF] from arxiv.org Applied Mathematics Letters, 2014 - Elsevier

Globally Optimal Joint Image Segmentation and Shape Matching based on Wasserstein Modes

B Schmitzer, C Schnörr - arXiv preprint arXiv:1407.3956, 2014 - arxiv.org

Abstract: A functional for joint variational object segmentation and shape matching is

developed. The formulation is based on optimal transport wrt geometric distance and local

feature similarity. Geometric invariance and modelling of object-typical statistical ...

[PDF] from amstat.org

Journal of Mathematical Imaging and Vision, 2014 - Springer

[PDF] On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - 2014 - math.wvu.edu

Abstract The Lagrangian description of absolutely continuous curves of probability

measures on the real line is analyzed. Whereas each such curve admits a Lagrangian

description as a well-defined flow of its velocity field, further conditions on the curve and/or ...

[PDF] Estimation of deformations between distributions by minimal Wasserstein distance

L Hélène, L Jean-Michel - hal.inria.fr

Abstract: We consider the issue of estimating a deformation operator acting on measures.

For this we consider a parametric warping model on an empirical sample and provide a new

matching criterion for cloud points based on a generalization of the registration criterion …ƒ

[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.uc.cl

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the

Wasserstein Metric. Rio de Janeiro, 2014. 8 9p. Dissertaçao de Mestrado—Departamento

de Matemática, Pontifıcia Universidade Católica do Rio de Janeiro.

On curvature conditions using Wasserstein spaces

1). Paper, £22.99, US$39.99 (Cased, £60, US$110). ISBN …

[CITATION] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

高津飛鳥 - 数理解析研究所講究録, 2014 - ci.nii.ac.jp

... ISSN, 巻, 号, ページ, 出版者, 参考文献, 出版年, 年から年まで. すべて CiNiiに本文あり

CiNiiに本文あり、または連携サービスへのリンクあり. 論文検索. 著者検索. 論文検索. Some evolution

equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations). ...
Some evolution equations as Wasserstein gradient flows

Auhor:Asuka Takatsu
Article
Publication:数理解析研究所講究録 / 京都大学数理解析研究所 [編]., 2014-5, 98

[PDF] Etude de modeles de déformations entre distributions avec la distance de Wasserstein

H Lescornel, JM Loubes - Nous - papersjds14.sfds.asso.fr

Etude de mod`eles de déformations entre distributions avec la distance de Wasserstein ...

Hél`ene Lescornel 1 & Jean-Michel Loubes 2 ... 1 Institut de Mathématiques de Toulouse 118

route de Narbonne 31000 Toulouse helene.lescornel@math.univ-toulouse.fr 2 Institut de ...

Related articles Cite Save More
<——2014—————2014————— -50—

M Kell - 2014 - qucosa.de

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in

p-Wasserstein spaces is given and a new curvature condition on abstract metric measure spaces

is defined. In the second part

of the thesis a proof of the identification of the q-heat ...

Martin Kell - 2014 100 pages

All 2 versions [PDF] arxiv.org

Numerical methods for matching for teams and Wasserstein barycenters

E Oudet, A Oberman, G Carlier - 2014 - basepub.dauphine.fr

Résumé en anglais: Equilibrium multi-population matching (matching for teams) is a prob-

lem from mathematical economics which is related to multi-marginal op-timal transport. A

special but important case is the Wasserstein barycen-ter problem, which has applications ...

All 2 versions Cite Save More

Numerical methods for matching for teams and Wasserstein barycenters

G Carlier, A Oberman, E Oudet - 2014 - hal.archives-ouvertes.fr

Abstract Equilibrium multi-population matching (matching for teams) is a problem from

mathematical economics which is related to multi-marginal optimal transport. A special but

important case is the Wasserstein barycenter problem, which has applications in image ...

[HTML] from sciencedirect.com

OD matrix structural similarity: Wasserstein metric

Ruiz de Villa, Aleix Casas, Jordi Breen, Martijn

TRB 93rd Annual Meeting Compendium of Papers

Transportation Research Board 93rd Annual Meeting

Location: Washington DC Date: 2014-1-12 to 2014-1-16

MR3295393 Thesis Craig, Katy; The exponential formula for the Wasserstein metric. Thesis (Ph.D.)–Rutgers The State University of New Jersey - New Brunswick. 2014. 80 pp. ISBN: 978-1321-29355-5, ProQuest LLC

The Exponential Formula for the Wasserstein Metric - UCSB Math

by K Craig - ‎2014 - ‎Cited by 7 - ‎Related articles

Apr 6, 2014 - The Exponential Formula for the Wasserstein Metric. A dissertation submitted to Rutgers, The State University of New Jersey, in partial.

MR3248053 Carlen, Eric A.; Maas, Jan; An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy. Comm. Math. Phys. 331 (2014), no. 3, 887–926.. Zbl 06341594

An Analog of the 2-Wasserstein Metric in Non-Commutative ...

by EA Carlen - ‎2014 - ‎Cited by 26 - ‎Related articles

Jul 29, 2014 - An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow ...

[CITATION] … 2-Wasserstemmutative in metric in non-coprobability under which the Fermionic Fokker-Planck equation is gradient flow for the entropy. vol. 331, issue 3

EA Carlen - Commun. Math. Phys, 2014

MR3189084 Boissard, Emmanuel; Le Gouic, Thibaut; On the mean speed of convergence of empirical and occupation measures in Wasserstein distance. Ann. Inst. Henri Poincaré Probab. Stat. 50 (2014), no. 2, 539–563. Zbl 1294.60005

On the mean speed of convergence of empirical and occupation ...

by E Boissard - ‎2014 - ‎Cited by 39 - ‎Related articles

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. ... It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases.

MR3178490 Butkovsky, Oleg; Subgeometric rates of convergence of Markov processes in the Wasserstein metric. Ann. Appl. Probab. 24 (2014), no. 2, 526–552. Zbl 06291798

Subgeometric rates of convergence of Markov processes in the ... - arXiv

by O Butkovsky - ‎2012 - ‎Cited by 26 - ‎Related articles

We establish subgeometric bounds on convergence rate of gen- eral Markov processes in the Wasserstein metric. In the discrete time setting we prove that the ...

MR3206999 Bourne, D. P.; Peletier, M. A.; Theil, F. Optimality of the triangular lattice for a particle system with Wasserstein interaction. Comm. Math. Phys. 329 (2014), no. 1, 117–140. 82D25 (82D60)

Optimali of the Triangular Lattice for a Particle System with .

by DP Bourne - ‎Cited by 18 - ‎Related articles

Particle System with Wasserstein Interaction. D.P. Bourne1, M.A. ... the energy is bounded from below by the energy of a triangular lattice (called T );. (2) if the ...

Zbl 1294.82006

MR3187785 Engquist, Björn; Froese, Brittany D. Application of the Wasserstein metric to seismic signals. Commun. Math. Sci. 12 (2014), no. 5, 979–988. 86A15 (62P35 65K99 94A12)

<——2014—————2014—————— -60—

MR3182483 Piccoli, Benedetto; Rossi, Francesco Generalized Wasserstein distance and its application to transport equations with source. Arch. Ration. Mech. Anal. 211 (2014), no. 1, 335–358. 49Q20 (28Dxx 35F25). Zbl 06260964

Generalized Wasserstein Distance and its Application to Transport ...

by B Piccoli - ‎2014 - ‎Cited by 72 - ‎Related articles

In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of this distance. In particular, we show that it ...

MR3158572 Gangbo, Wilfrid; Tudorascu, Adrian Weak KAM theory on the Wasserstein torus with multidimensional underlying space. Comm. Pure Appl. Math. 67 (2014), no. 3, 408–463. 58D19 (37J40)

Weak KAM Theory on the Wasserstein Torus with Multidimensional ...

by W Gangbo - ‎2014 - ‎Cited by 13 - ‎Related articles

Nov 20, 2013 - In this article we propose a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on ( ^d), the ...

MR3121635 Savaré, Giuseppe Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,∞)

metric measure spaces. Discrete Contin. Dyn. Syst. 34 (2014), no. 4, 1641–1661. 49Q20

SELF-IMPROVEMENT OF THE BAKRY-ÉMERY CONDITION AND ...

by G Savaré - ‎2014 - ‎Cited by 80 - ‎Related articles

Abstract. We prove that the linear “heat” flow in a RCD(K, ∞) metric mea- sure space (X, d, m) satisfies a contraction property with respect to every Lp-.

[CITATION] 'e, Self-improvement ofthe -Emery condition and Wasserstein contraction of the heat flow in metric measure spaces

G Savar - Preprint. Available at

Wasserstein-Divergence transportation inequalities and polynomial ...

MR3257364 Ding, Ying; Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities. Statist. Probab. Lett. 94 (2014), 77–85.

by Y Ding - ‎2014 - ‎Cited by 3 - ‎Related articles

Although Theorem 1.6 is not as sharp as the equivalent one, the differences between the corresponding conclusions on Wasserstein-Divergence transportation inequalities and thus polynomial concentration inequalities when is close to 1 are not obvious.

MR3250977 Bolley, François; Carrillo, José A.; Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction. Comm. Partial Differential Equations 39 (2014), no. 10, 1860–1869.

Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein ...

by F Bolley - ‎2014 - ‎Cited by 3 - ‎Related articles

Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction. It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance.

MR3205035 S turm, Karl-Theodor g A monotone approximation to the Wasserstein diffusion. Singular phenomena and scaling in mathematical models, 25–48, Springer, Cham, 2014. 60J60

A Monotone Approximation to the Wasserstein Diffusion | SpringerLink

by KT Sturm - ‎2014 - ‎Cited by 5 - ‎Related articles

Jul 13, 2013 - The Wasserstein space [equation] on an Euclidean or Riemannian space M – i.e. the space of probability measures on M equipped with the ...

Numerical methods for matching for teams and Wasserstein barycenters

by G Carlier - ‎2014 - ‎Cited by 47 - ‎Related articles

Nov 13, 2014 - Numerical methods for matching for teams and Wasserstein barycenters. Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. ... Numerical results are presented which illustrate the efficiency of the algorithms.

A Parametric Registration model for warped distributions with ...

by MA Antolín - ‎Related articles

Aug 22, 2014 - Abstract. We consider a parametric deformation model for distributions. More precisely, we assume we observe J samples of random variables ...

Weak Solutions to a Fractional Fokker-Planck Equation ... - Find a team

by M Bowles - ‎Cited by 4 - ‎Related articles

Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and. Wasserstein ... Rd ρΨ dx w.r.t. W2 [6] (we will call this PDE the 'Wasserstein part' of (1)).

Butkovsky : Subgeometric rates of convergence of Markov processes ...

by O Butkovsky - ‎2014 - ‎Cited by 26 - ‎Related articles

We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the ...

[PDF]

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[PDF] The Wasserstein geometry of non-linear σ models and the Hamilton–Perelman Ricci flow

by M Carfora - ‎2014 - ‎Cited by 7 - ‎Related articles

May 5, 2014 - By exploiting the heat kernel embedding introduced by N. Gigli and C. Mantegazza, we show that the Wasserstein geometry of the space of ...

arXiv preprint arXiv:1405.0827, 2014

Optimal Transport and the Wasserstein Metric

PDF Rio de Janero

by PN Orenstein - ‎2014 - ‎Related articles

Jan 23, 2014 - Optimal Transport and the Wasserstein Metric. Dissertaç˜ao de Mestrado. Thesis presented to the Postgraduate Program in Applied Math-.

The Exponential Formula for the Wasserstein ... - UCSB Math

PDF Rutgers

by K Craig - ‎2014 - ‎Cited by 9 - ‎Related articles

Apr 6, 2014 - In this thesis, we consider gradient flow in the Wasserstein metric, a metric on the space of probability measures that shares many properties ...

Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities

By: Ding, Ying

STATISTICS & PROBABILITY LETTERS Volume: ‏ 94 Pages: ‏ 77-85 Published: ‏ NOV 2014

2014

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

M Giovanna Mora, M Peletier, L Scardia - arXiv e-prints, 2014 - ui.adsabs.harvard.edu

We consider systems of $ n $ parallel edge dislocations in a single slip system, represented

by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We

formulate the energy of this system in terms of the empirical measure of the dislocations, and …

Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

By: Irpino, Antonio; Verde, Rosanna; De Carvalho, Francisco de A. T.

EXPERT SYSTEMS WITH APPLICATIONS Volume: ‏ 41 Issue: ‏ 7 Pages: ‏ 3351-3366 Published: ‏ JUN 1 2014

Times Cited: 15

istances based on Wasserstein metric (Rüshendorff, 2001, Villani, 2003) permits to …

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

By: Boissard, Emmanuel; Le Gouic, Thibaut

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES Volume: ‏ 50 Issue: ‏ 2 Pages: ‏ 539-563 Published: ‏ MAY 2014

Contraction in the Wasserstein metric for some Markov chains ...

Times Cited: 18 6.

Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities

by B Kloeckner · 2014 · Cited by 18 — Title:Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps ; Subjects: Dynamical Systems (math.DS).

Y Ding - Statistics & Probability Letters, 2014 - Elsevier

In this paper, we study Wasserstein-Divergence transportation inequalities which are the

generalization of classical transportation inequalities. We present sufficient and necessary

conditions for them separately, which coincide in the limit case. Using this kind of …

SUBGEOMETRIC RATES OF CONVERGENCE OF MARKOV PROCESSES IN THE WASSERSTEIN METRIC

By: Butkovsky, Oleg

ANNALS OF APPLIED PROBABILITY Volume: ‏ 24 Issue: ‏ 2 Pages: ‏ 526-552 Published: ‏ APR 2014

Times Cited: 22

<——2014———2014————— -80—

SELF-IMPROVEMENT OF THE BAKRY-EMERY CONDITION AND WASSERSTEIN CONTRACTION OF THE HEAT FLOW IN RCD(K, infinity) METRIC MEASURE SPACES

By: Savare, Giuseppe

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume: ‏ 34 Issue: ‏ 4 Special Issue: ‏ SI Pages: ‏ 1641-1661 Published: ‏ APR 2014

Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space

Times Cited: 49 10.

By: Gangbo, Wilfrid; Tudorascu, Adrian

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Volume: ‏ 67 Issue: ‏ 3 Pages: ‏ 408-463 Published: ‏ MAR 2014

Times Cited: 11

Evolution in Measure Spaces with Wasserstein Distance

By: Cristiani, Emiliano; Piccoli, Benedetto; Tosin, Andrea

MULTISCALE MODELING OF PEDESTRIAN DYNAMICS Book Series: ‏ MS&A-Modeling Simulation and Applications Pages: ‏ 169-194 Published: ‏ 2014

Book
Multiscale modeling of pedestrian dynamics

Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction

By: Bolley, Francois; Carrillo, Jose A.

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS Volume: ‏ 39 Issue: ‏ 10 Pages: ‏ 1860-1869 Published: ‏ 2014

Times Cited: 2

Generalized Wasserstein Distance and its Application to Transport Equations with Source

By: Piccoli, Benedetto; Rossi, Francesco

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS Volume: ‏ 211 Issue: ‏ 1 Pages: ‏ 335-358 Published: ‏ JAN 2014

Times Cited: 48 16.

The derivation of swarming models: Mean-field limit and Wasserstein distances

By: Carrillo, Jose Antonio; Choi, Young-Pil; Hauray, Maxime

COLLECTIVE DYNAMICS FROM BACTERIA TO CROWDS: AN EXCURSION THROUGH MODELING, ANALYSIS AND SIMULATION Book Series: ‏ CISM Courses and Lectures Volume: ‏ 553 Pages: ‏ 1-46 Published: ‏ 2014

Wasserstein curvature of Markov processes

Bertrand Cloez Université Paul Sabatier

rstein Barycenters over Riemannian manifolds - NASA ...

ui.adsabs.harvard.edu › abs › abstract

We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric. Under reasonable assumptions ...

by YH Kim · ‎2014 · ‎Cited by 44 · ‎Related articles

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

<——2014—— —2014——— - 90—

PDF] jmlr.org
[PDF] Fast computation of Wasserstein barycenters

M Cuturi, A Doucet - 2014 - jmlr.org

We present new algorithms to compute the mean of a set of empirical probability measures

under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the

measure that minimizes the sum of its Wasserstein distances to each element in that set. We …

[CITATION] Fast computation of Wasserstein barycenters.(2014)

M Cuturi, A Doucet - 2014

[CITATION] vockley J, wasserstein M, Rice GM, Dorenbaum A, Neuenburg JK, Musson DG, Gu Z, Sile S. Single-Dose, subcutaneous recombinant phenylalanine …

N Longo, CO Harding, BK Burton, DK Grange - The Lancet, 2014

tCited by 120 Related articles All 17 versions

[PDF] Wasserstein propagation for semi-supervised learning

J Solomon, R Rustamov, L Guibas… - … Conference on Machine …, 2014 - jmlr.org

Probability distributions and histograms are natural representations for product ratings, traffic

measurements, and other data considered in many machine learning applications. Thus,

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the

empirical measure in the law of large numbers, in Wasserstein distance. We also consider

occupation measures of ergodic Markov chains. One motivation is the approximation of a …

The derivation of swarming models: mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of

interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We …

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - The Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition

and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

Decomposition of geodesics in the Wasserstein space and the globalization problem

F Cavalletti - Geometric and Functional Analysis, 2014 - Springer

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m)

be a non-branching metric measure space verifying CD _ loc (K, N) CD loc (K, N) or

equivalently CD^*(K, N) CD∗(K, N). We prove that every geodesic t μ t in the L 2 …

Decomposition of geodesics in the Wasserstein space and the globalization problem

F Cavalletti - Geometric and Functional Analysis, 2014 - Springer

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m)

be a non-branching metric measure space verifying CD _ loc (K, N) CD loc (K, N) or

equivalently CD^*(K, N) CD∗(K, N). We prove that every geodesic t μ t in the L 2 …

[PDF] kobv.de

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

2014 [HTML] mdpi.com

[HTML] The Gromov–Wasserstein distance: A brief overview

F Mémoli - Axioms, 2014 - mdpi.com

… Get Support. Feedback. Please let us know what you think of our products and services. Give

Feedback. Information. Our dedicated information section provides allows you to learn more about

MDPI. Get Information. clear. Open Access This article is: freely available; re-usable. Axioms …

Optimality of the Triangular Lattice for a Particle System with Wasserstein Interaction

By: Bourne, D. P.; Peletier, M. A.; Theil, F.

COMMUNICATIONS IN MATHEMATICAL PHYSICS Volume: ‏ 329 Issue: ‏ 1 Pages: ‏ 117-140 Published: ‏ JUL 2014

Free Accepted Article From Repository

Times Cited: 13

Optimality of the triangular lattice for a particle system with Wasserstein interaction

DP Bourne, MA Peletier, F Theil - Communications in Mathematical …, 2014 - Springer

We prove strong crystallization results in two dimensions for an energy that arises in the

theory of block copolymers. The energy is defined on sets of points and their weights, or

equivalently on the set of atomic measures. It consists of two terms; the first term is the sum …

<——2014—— —2014——— - 100—

[PDF] ucla.edu

Weak KAM theory on the Wasserstein torus with multidimensional underlying space

W Gangbo, A Tudorascu - Communications on Pure and …, 2014 - Wiley Online Library

The study of asymptotic behavior of minimizing trajectories on the Wasserstein space (

d) has so far been limited to the case d= 1 as all prior studies heavily relied on the isometric

identification of ( ) with a subset of the Hilbert space L2 (0, 1). There is no known …

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation

for ions with massless thermalized electrons. We prove new weak-strong stability estimates

in the Wasserstein metric that allow us to extend and improve previously known …

th massless thermalized electrons. We prove new weak-strong stability estimates …

An analog of the 2-Wasserstein metric in non-commutative probability under which the Fermionic Fokker–Planck equation is gradient flow for the entropy

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2014 - IET

Colour image enhancement is an important preprocessing phase of many image analysis

tasks such as image segmentation, pattern recognition and so on. This study presents a new

local brightness adaptive variational model using Wasserstein distance for colour image …

On curvature conditions using Wasserstein spaces

M Kell - 2014 - oatd.org

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics

in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure

spaces is defined. In the second part of the thesis a proof of the identification of the q-heat …

A monotone approximation to the Wasserstein diffusion

KT Sturm - Singular phenomena and scaling in mathematical …, 2014 - Springer

Abstract The Wasserstein space P (M) on an Euclidean or Riemannian space M–ie the

space of probability measures on M equipped with the L 2-Wasserstein distance d W–offers

a rich geometric structure. This allows to develop a far reaching first order calculus, with …

Nonlinear diffusion: geodesic convexity is equivalent to Wasserstein contraction

F Bolley, JA Carrillo - Communications in Partial Differential …, 2014 - Taylor & Francis

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the

space of probability measures equipped with the Euclidean Wasserstein distance. Under

suitable convexity conditions on the nonlinearity, due to McCann, the associated entropy is …

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

We develop a new method for showing that a given sequence of random variables verifies

an appropriate law of the iterated logarithm. Our tools involve the use of general estimates

on multidimensional Wasserstein distances, that are in turn based on recently developed …

OD matrix structural similarity: Wasserstein metric

A Ruiz de Villa, J Casas, M Breen - 2014 - trid.trb.org

In this paper the authors introduce a metric and a method, considering the spatial structure,

for comparing OD matrices. It is based on mass transportation techniques, in particular the

notion of Wasserstein distance. The result of the comparison is measured in total travel time …

<——2014—— —2014——— - 110—

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Distributed consensus in the Wasserstein metric space of probability measures is introduced

in this work. Convergence of each agent's measure to a common measure value is proven

under a weak network connectivity condition. The common measure reached at each agent …

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of

probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely

continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

We consider the issue of estimating a deformation operator acting on measures. For this we

consider a parametric warping model on an empirical sample and provide a new matching

criterion for cloud points based on a generalization of the registration criterion used in …

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and subgeometric rates of convergence in the Wasserstein distance for general state-space

Markov chains which are not phi-irreducible. Our approach is based on a coupling …

[PDF] global-sci.com

Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - cambridge.org

We present a multi-phase image segmentation method based on the histogram of the Gabor

feature space, which consists of a set of Gabor-filter responses with various orientations,

scales and frequencies. Our model replaces the error function term in the original fuzzy …

M Kell - 2014 - oatd.org

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics

in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure

spaces is defined. In the second part of the thesis a proof of the identification of the q-heat …

Transport equation with source and generalized Wasserstein distance

B Piccoli - 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc..

Such models were successfully employed in traffic monitoring projects. Then we will pass to …

2014

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation

for ions with massless thermalized electrons. We prove new weak-strong stability estimates

in the Wasserstein metric that allow us to extend and improve previously known …

Evolution in Measure Spaces with Wasserstein Distance

[PDF] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J Wangb - arXiv preprint arXiv:1407.1986, 2014 - Citeseer

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential contractivity of diffusion semigroups (Pt) t≥ 0 with

respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that …

E Cristiani, B Piccoli, A Tosin - Multiscale Modeling of Pedestrian …, 2014 - Springer

In this chapter, we provide a fairly general mathematical setting for the nonlinear transport

equation analyzed in Chap. 6 (namely Eqs.(5.1) and (6.6)). More precisely, we study the

evolution of solutions in measures spaces endowed with the Wasserstein distance and its …

<——2014—— ———2014—— - 120 -

[PDF] tum.de

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

X-ray crystallography is the main tool for the structural analysis of molecules today. One of its

main subtasks is the phase retrieval problem. In this thesis, the phase retrieval problem is

discussed in the context of the optimal transport. Phase retrieval is formulated as an energy …

[PDF] puc-rio.br

[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.puc-rio.br

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the

Wasserstein Metric. Rio de Janeiro, 2014. 89p. Dissertaçao de Mestrado—Departamento de

Matemática, Pontifıcia Universidade Católica do Rio de Janeiro. In this work, we study the so …

[PDF] Wasserstein Distance and the Rectifiability of Doubling Measures: Part II

JAGDT Toro - 2014 - imo.universite-paris-saclay.fr

We study the structure of the support of a doubling measure by analyzing its self-similarity

properties, which we estimate using a variant of the L1 Wasserstein distance. We show that

a measure satisfying certain self-similarity conditions admits a unique (up to multiplication by …

[PDF] kyoto-u.ac.jp

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of

the information geometry). In this note, I discuss …

Gradient flows in general metric and Wasserstein spaces

[PDF] tuwien.at

DL Forkert - 2014 - repositum.tuwien.at

In this thesis we approach gradient flows in metric spaces which are not necessarily

endowed with a natural linear structure. The first part is an introduction to the theory in

abstract metric spaces: We present three possible generalizations of gradient flows to the …

Wasserstein Metric Based Adaptive Fuzzy Clustering Methods ...

www.semanticscholar.org › paper › Wasserstein-Metric-B...

@inproceedings{Li2014WassersteinMB, title={Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data}, author={Hong Li}, year={2014} ...
[CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

H Li - 2014

Lescornel, Hélène. Covariance estimation and study of ...

thesesups.ups-tlse.fr › ...

Sep 22, 2014 — PDF (L'auteur ne souhaite pas la mise en ligne de sa thèse. ... de cette thèse concerne l'étude de modèles de déformations entre distributions. ... méthodes d'estimation basées sur la distance de Wasserstein en alignant les ...

by H Lescornel · ‎2014

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - The Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition

and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

[PDF] kobv.de

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

2014 [PDF] kobv.de

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

<—-—2014—————2014—— ———— - 130

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

A Lopes, M Stadlbauer, B Kloeckner - 2014 - hal-ens.archives-ouvertes.fr

We employ techniques from optimal transport in order to prove decay of transfer operators

associated to iterated functions systems and expanding maps, giving rise to a new proof

without requiring a Doeblin-Fortet (or Lasota-Yorke) inequality. Our main result is the …

Hélène Lescornel , Covariance estimation and ... - theses.fr

[CITATION] Etude de modeles de déformations entre distributions avec la distance de Wasserstein

H Lescornel, JM Loubes - Nous

On gradient structures for Markov chains and the ... - OPUS 4

opus4.kobv.de › index › index › year › docId

Jan 7, 2014 — We study the approximation of Wasserstein gradient structures by their ... entropic gradient-flow structure for reversible Markov chains. ... On gradient structures for Markov chains and the passage to Wasserstein gradient flows.

by K Disser · ‎2014 · ‎Cited by 23 · ‎Related articles

2014. [PDF] dtic.mil

Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

AN Bishop - 17th International Conference on Information …, 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

We develop a new method for showing that a given sequence of random variables verifies

an appropriate law of the iterated logarithm. Our tools involve the use of general estimates

on multidimensional Wasserstein distances, that are in turn based on recently developed …

Submission history

From: Ehsan Azmoodeh [view email]

[v1] Thu, 27 Mar 2014 12:47:45 UTC (22 KB)

[v2] Wed, 1 Oct 2014

2014

Wasserstein barycenters over Riemannian manifolds - Ricam

www.ricam.oeaw.ac.at › ricam_specsem2014_ws4_pass

Dec 10, 2014 — Let (X,d)=(P(M),W2) be the space of probability measures on a compact Riemannian manifold M, equipped with Wasserstein distance.

by B Pass · ‎2014 · ‎Cited by 44 · ‎Related articles

Dec 10, 2014 — Let (X,d)=(P(M),W2) be the space of probability measures on a compact Riemannian manifold M, equipped with Wasserstein distance.

by B Pass · ‎2014

Cited by 44 · ‎Related articles

[CITATION] Wasserstein barycenters over riemannian manfolds (2014) YH Kim, B Pass - arXiv preprint arXiv:1412.7726

Weak KAM theory on the Wasserstein torus with multidimensional underlying space

W Gangbo, A Tudorascu - Communications on Pure and …, 2014 - Wiley Online Library

The study of asymptotic behavior of minimizing trajectories on the Wasserstein space (

d) has so far been limited to the case d= 1 as all prior studies heavily relied on the isometric

identification of ( ) with a subset of the Hilbert space L2 (0, 1). There is no known …

2014

[PDF] Fast computation of Wasserstein barycenters

M Cuturi, A Doucet - 2014 - jmlr.org

We present new algorithms to compute the mean of a set of empirical probability measures

under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the

measure that minimizes the sum of its Wasserstein distances to each element in that set. We …

[CITATION] Fast computation of Wasserstein barycenters.(2014)

M Cuturi, A Doucet - 2014

Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

2014

[PDF] dtic.mil

AN Bishop - 17th International Conference on Information …, 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

2014

Wasserstein barycenters over Riemannian manifolds - Ricam

www.ricam.oeaw.ac.at › ricam_specsem2014_ws4_pass

PDF

Dec 10, 2014 — Let (X,d)=(P(M),W2) be the space of probability measures on a compact Riemannian manifold M, equipped with Wasserstein distance.

by B Pass · ‎2014 · ‎Cited by 45 · ‎Related articles

[CITATION] Wasserstein barycenters over riemannian manfolds (2014)

YH Kim, B Pass - arXiv preprint arXiv:1412.

<——2014—— 2014——— - 140—

Decomposition of geodesics in the Wasserstein space and the globalization problem

F Cavalletti - Geometric and Functional Analysis, 2014 - Springer

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m) be a non-branching metric measure space verifying CD _ loc (K, N) CD loc (K, N) or equivalently CD^*(K, N) CD∗(K, N). We prove that every geodesic t μ t in the L 2 …

2014

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

year 2014 master thesis

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

X-ray crystallography is the main tool for the structural analysis of molecules today. One of its main subtasks is the phase retrieval problem. In this thesis, the phase retrieval problem is discussed in the context of the optimal transport. Phase retrieval is formulated as an energy …

Nonlinear diffusion: geodesic convexity is equivalent to Wasserstein contraction

F Bolley, JA Carrillo - Communications in Partial Differential …, 2014 - Taylor & Francis

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the

space of probability measures equipped with the Euclidean Wasserstein distance. Under

suitable convexity conditions on the nonlinearity, due to McCann, the associated entropy is …

Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities

Y Ding - Statistics & Probability Letters, 2014 - Elsevier

In this paper, we study Wasserstein-Divergence transportation inequalities which are the

generalization of classical transportation inequalities. We present sufficient and necessary

conditions for them separately, which coincide in the limit case. Using this kind of …

2014

A monotone approximation to the Wasserstein diffusion

KT Sturm - Singular phenomena and scaling in mathematical …, 2014 - Springer

Abstract The Wasserstein space P (M) on an Euclidean or Riemannian space M–ie the

space of probability measures on M equipped with the L 2-Wasserstein distance d W–offers

a rich geometric structure. This allows to develop a far reaching first order calculus, with …

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

2014

Transport equation with source and generalized Wasserstein distance

B Piccoli - 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc..

Such models were successfully employed in traffic monitoring projects. Then we will pass to …

An analog of the 2-Wasserstein metric in non-commutative probability under which the Fermionic Fokker–Planck equation is gradient flow for the entropy

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

<——2014———— 2014————— - 150—

[HTML] mdpi.com

[HTML] The Gromov–Wasserstein distance: A brief overview

F Mémoli - Axioms, 2014 - mdpi.com

… Get Support. Feedback. Please let us know what you think of our products and services. Give

Feedback. Information. Our dedicated information section provides allows you to learn more about

MDPI. Get Information. clear. Open Access This article is: freely available; re-usable. Axioms …

M Kell - 2014 - oatd.org

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics

in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure

spaces is defined. In the second part of the thesis a proof of the identification of the q-heat …

Gradient flows in general metric and Wasserstein spaces

2014

[PDF] tuwien.at

DL Forkert - 2014 - repositum.tuwien.at

In this thesis we approach gradient flows in metric spaces which are not necessarily

endowed with a natural linear structure. The first part is an introduction to the theory in

abstract metric spaces: We present three possible generalizations of gradient flows to the …

2014

Evolution in Measure Spaces with Wasserstein Distance

E Cristiani, B Piccoli, A Tosin - Multiscale Modeling of Pedestrian …, 2014 - Springer

In this chapter, we provide a fairly general mathematical setting for the nonlinear transport equation

analyzed in Chap. 6 (namely Eqs. (5.1) and (6.6)). More precisely, we study the evolution of...

Optimality of the triangular lattice for a particle system with Wasserstein interaction

DP Bourne, MA Peletier, F Theil - Communications in Mathematical …, 2014 - Springer

We prove strong crystallization results in two dimensions for an energy that arises in the

theory of block copolymers. The energy is defined on sets of points and their weights, or

equivalently on the set of atomic measures. It consists of two terms; the first term is the sum …

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2014 - IET

Colour image enhancement is an important preprocessing phase of many image analysis

tasks such as image segmentation, pattern recognition and so on. This study presents a new

local brightness adaptive variational model using Wasserstein distance for colour image …

Evolution in Measure Spaces with Wasserstein Distance

E Cristiani, B Piccoli, A Tosin - Multiscale Modeling of Pedestrian …, 2014 - Springer

In this chapter, we provide a fairly general mathematical setting for the nonlinear transport

equation analyzed in Chap. 6 (namely Eqs.(5.1) and (6.6)). More precisely, we study the

evolution of solutions in measures spaces endowed with the Wasserstein distance and its …

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

The derivation of swarming models: mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of

interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We …

Cited by 175 Related articles All 17 versions
<—2014—— 2014——— - 160——

Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

A Irpino, R Verde, FAT De Carvalho - Expert Systems with Applications, 2014 - Elsevier

This paper presents a Dynamic Clustering Algorithm for histogram data with an automatic

weighting step of the variables by using adaptive distances. The Dynamic Clustering

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

We consider the issue of estimating a deformation operator acting on measures. For this we

consider a parametric warping model on an empirical sample and provide a new matching

criterion for cloud points based on a generalization of the registration criterion used in …

[CITATION] Estimation of Deformations between Distributions with the Wasserstein Distance

H Lescornel, JM Loubes

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the

empirical measure in the law of large numbers, in Wasserstein distance. We also consider

occupation measures of ergodic Markov chains. One motivation is the approximation of a …

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2014 - IET

Colour image enhancement is an important preprocessing phase of many image analysis

tasks such as image segmentation, pattern recognition and so on. This study presents a new

local brightness adaptive variational model using Wasserstein distance for colour image …

2014

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

2014 [PDF] archives-ouvertes.fr

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

We consider the issue of estimating a deformation operator acting on measures. For this we

consider a parametric warping model on an empirical sample and provide a new matching

criterion for cloud points based on a generalization of the registration criterion used in …

[PDF] global-sci.com

Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - cambridge.org

We present a multi-phase image segmentation method based on the histogram of the Gabor

feature space, which consists of a set of Gabor-filter responses with various orientations,

scales and frequencies. Our model replaces the error function term in the original fuzzy …

Transport equation with source and generalized Wasserstein distance

B Piccoli - 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc..

Such models were successfully employed in traffic monitoring projects. Then we will pass to …

All 3 versions
<——2014—— 2014——— - 170 —

Evolution in Measure Spaces with Wasserstein Distance

[PDF] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J Wangb - arXiv preprint arXiv:1407.1986, 2014 - Citeseer

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential contractivity of diffusion semigroups (Pt) t≥ 0 with

respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that …

E Cristiani, B Piccoli, A Tosin - Multiscale Modeling of Pedestrian …, 2014 - Springer

In this chapter, we provide a fairly general mathematical setting for the nonlinear transport

equation analyzed in Chap. 6 (namely Eqs.(5.1) and (6.6)). More precisely, we study the

evolution of solutions in measures spaces endowed with the Wasserstein distance and its …

[PDF] Wasserstein Distance and the Rectifiability of Doubling Measures: Part II

JAGDT Toro - 2014 - imo.universite-paris-saclay.fr

We study the structure of the support of a doubling measure by analyzing its self-similarity

properties, which we estimate using a variant of the L1 Wasserstein distance. We show that

a measure satisfying certain self-similarity conditions admits a unique (up to multiplication by …

2014

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

… We consider the issue of estimating a measure observed in a deformation framework. For

this we consider a parametric deformation model on … We study the asymptotic behaviour of

the estimators of the deformations and provide some examples to some particular deformation …

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

… criterion with respect to the Wasserstein’s barycenter of a deformation of the observed

distributions. This requires an equivalent … Wasserstein distances that we will apply to estimate

the asymptotic distribution of a statistic test based on an alignment with respect to the Wasserstein…

[CITATION] Estimation of Deformations between Distributions with the Wasserstein Distance

H Lescornel, JM Loubes

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - The Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition

and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

2014

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation

for ions with massless thermalized electrons. We prove new weak-strong stability estimates

An analog of the 2-Wasserstein metric in non-commutative probability under which the Fermionic Fokker–Planck equation is gradient flow for the entropy

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

OD matrix structural similarity: Wasserstein metric

A Ruiz de Villa, J Casas, M Breen - 2014 - trid.trb.org

In this paper the authors introduce a metric and a method, considering the spatial structure,

for comparing OD matrices. It is based on mass transportation techniques, in particular the

notion of Wasserstein distance. The result of the comparison is measured in total travel time …

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Distributed consensus in the Wasserstein metric space of probability measures is introduced

in this work. Convergence of each agent's measure to a common measure value is proven

under a weak network connectivity condition. The common measure reached at each agent …

[PDF] puc-rio.br

[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.puc-rio.br

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the

Wasserstein Metric. Rio de Janeiro, 2014. 89p. Dissertaçao de Mestrado—Departamento de

Matemática, Pontifıcia Universidade Católica do Rio de Janeiro. In this work, we study the so …

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

<——2014—— 2014——— - 180——

A Lopes, M Stadlbauer, B Kloeckner - 2014 - hal-ens.archives-ouvertes.fr

We employ techniques from optimal transport in order to prove decay of transfer operators

associated to iterated functions systems and expanding maps, giving rise to a new proof

without requiring a Doeblin-Fortet (or Lasota-Yorke) inequality. Our main result is the …

Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Interval Data

2014 zzz 29

[CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

H Li - 2014

2014[PDF] esperg.com

LI HONG - TELKOMNIKA Indonesian Journal of Electrical …, 2014 - journal.esperg.com

The aim of this paper is to present new wasserstein metric based adaptive fuzzy clustering

methods for partitioning symbolic interval data. In two methods, fuzzy partitions and

prototypes for clusters are determined by optimizing adequacy criteria based on wasserstein …

[CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

H Li - 2014

Fast computation of Wasserstein barycenters

M Cuturi, A Doucet - International conference on machine …, 2014 - proceedings.mlr.press

We present new algorithms to compute the mean of a set of N empirical probability

measures under the optimal transport metric. This mean, known as the Wasserstein

barycenter\citepagueh2011barycenters, rabin2012, is the measure that minimizes the sum …

[PDF] Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - global-sci.org

We present a multi-phase image segmentation method based on the histogram of the Gabor

feature space, which consists of a set of Gabor-filter responses with various orientations,

scales and frequencies. Our model replaces the error function term in the original fuzzy …

2014

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

Page 1. arXiv:1407.7245v2 [math.DG] 10 Aug 2014 ON TANGENT CONES AND

PARALLEL TRANSPORT IN WASSERSTEIN SPACE JOHN LOTT Abstract. If M

is a smooth compact Riemannian manifold, let P(M) denote the …

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

Page 1. Technische Universität München Department of Mathematics Master's Thesis Phase

retrieval on the quadratic Wasserstein space Arseniy Tsipenyuk Supervisor: Gero Friesecke

Advisor: Dominik Jüstel Submission Date: 22.12.2014 Page 2 …

Fast computation of Wasserstein barycenters

M Cuturi, A Doucet - International conference on machine …, 2014 - proceedings.mlr.press

We present new algorithms to compute the mean of a set of N empirical probability

measures under the optimal transport metric. This mean, known as the Wasserstein

barycenter\citepagueh2011barycenters, rabin2012, is the measure that minimizes the sum …

[CITATION] Fast computation of Wasserstein barycenters.(2014)

M Cuturi, A Doucet - 2014

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Page 1. arXiv:1404.0145v2 [math.OC] 1 Jul 2015 Consensus in the Wasserstein Metric Space

of Probability Measures ∗ Adrian N. Bishop † Arnaud Doucet ‡ Abstract Distributed consensus

in the Wasserstein metric space of probability measures is intro- duced in this work …

2014 [PDF] kyoto-u.ac.jp

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 数理解析研究所講究録, 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

<——2014—— 2014——— - 190—

Nonlinear diffusion: geodesic convexity is equivalent to Wasserstein contraction

F Bolley, JA Carrillo - Communications in Partial Differential …, 2014 - Taylor & Francis

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the

space of probability measures equipped with the Euclidean Wasserstein distance. Under

suitable convexity conditions on the nonlinearity, due to McCann, the associated entropy is …

2014

[PDF] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J Wangb - arXiv preprint arXiv:1407.1986, 2014 - Citeseer

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential contractivity of diffusion semigroups (Pt) t≥ 0 with

respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that …

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

2014

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 数理解析研究所講究録, 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

Gradient flows in general metric and Wasserstein spaces

DL Forkert - 2014 - repositum.tuwien.at

In this thesis we approach gradient flows in metric spaces which are not necessarily

endowed with a natural linear structure. The first part is an introduction to the theory in

abstract metric spaces: We present three possible generalizations of gradient flows to the …

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

We consider the issue of estimating a deformation operator acting on measures. For this we

consider a parametric warping model on an empirical sample and provide a new matching

criterion for cloud points based on a generalization of the registration criterion used in …

PDF] arxiv.org

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2014 - IET

Colour image enhancement is an important preprocessing phase of many image analysis tasks such as image segmentation, pattern recognition and so on. This study presents a new local brightness adaptive variational model using Wasserstein distance for colour image …

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

We develop a new method for showing that a given sequence of random variables verifies

an appropriate law of the iterated logarithm. Our tools involve the use of general estimates

on multidimensional Wasserstein distances, that are in turn based on recently developed …

2014

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

H Lescornel - 2014 - theses.fr

Résumé La première partie de cette thèse est consacrée à l'estimation de covariance de processus stochastiques non stationnaires. Le modèle étudié amène à estimer la covariance du processus dans différents espaces vectoriels de matrices. Nous étudions …

<-—— 2014——— — 2014——— - 200—

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

We consider the issue of estimating a deformation operator acting on measures. For this we consider a parametric warping model on an empirical sample and provide a new matching criterion for cloud points based on a generalization of the registration criterion used in …

Estimation of deformations between distributions by minimal ...

hal.archives-ouvertes.fr › hal-00749519

by H Lescornel · 2014 · Cited by 2 — Estimation of deformations between distributions by minimal Wasserstein distance. Hélène Lescornel ¹ Jean-Michel Loubes ¹. Détails. 1 IMT - Institut de ...

[CITATION] Estimation of Deformations between Distributions with the Wasserstein Distance

H Lescornel, JM Loubes

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

We develop a new method for showing that a given sequence of random variables verifies an appropriate law of the iterated logarithm. Our tools involve the use of general estimates on multidimensional Wasserstein distances, that are in turn based on recently developed …

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

[PDF] bmj.com

Relation between surgeon volume and risk of complications after total hip arthroplasty: propensity score matched cohort study

…, R Jenkinson, PC Austin, R Croxford, D Wasserstein… - Bmj, 2014 - bmj.com

… -10-CA diagnostic code for intra-articular infection, with a confirmatory code for an irrigation

… of an healthplan’s code for a spacer insertion; and/or occurrence of a procedure code for a …

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation

for ions with massless thermalized electrons. We prove new weak-strong stability estimates

in the Wasserstein metric that allow us to extend and improve previously known …

2014 [PDF] inria.fr

Transport equation with source and generalized Wasserstein distance

B Piccoli - NETCO 2014-New Trends in Optimal Control, 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc..

Such models were successfully employed in traffic monitoring projects. Then we will pass to …

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a …

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution and subgeometric rates of convergence in the Wasserstein distance for general state-space Markov chains which are not phi-irreducible. Our approach is based on a coupling …

2014

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

M Giovanna Mora, M Peletier, L Scardia - arXiv e-prints, 2014 - ui.adsabs.harvard.edu

We consider systems of $ n $ parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations, and …

<——2014—— 2014——— - 210—

2014

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a …

2014

The derivation of swarming models: mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order models for swarming. We …

2014

[PDF] Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - global-sci.org

We present a multi-phase image segmentation method based on the histogram of the Gabor feature space, which consists of a set of Gabor-filter responses with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy …

2014 Technische Universit¨at München master thesis

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

X-ray crystallography is the main tool for the structural analysis of molecules today. One of its main subtasks is the phase retrieval problem. In this thesis, the phase retrieval problem is discussed in the context of the optimal transport. Phase retrieval is formulated as an energy …

URL: http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-149614

2014

Kell, Martin. On curvature conditions using Wasserstein spaces.

Degree: PhD, Mathematik und Informatik, 2014, Universität Leipzig

► This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature… (more)

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University of Waterloo

Kell

2014

Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow

by Bowles, Malcolm

In this thesis, we study a linear fractional Fokker-Planck equation that models non-local (`fractional') diffusion in the presence of a potential field. The...

Dissertation/ThesisCheck Library

2014

On curvature conditions using Wasserstein spaces

by Kell, Martin

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature...

Dissertation/ThesisCitation Online

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

2014

Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

A Irpino, R Verde, FAT De Carvalho - Expert Systems with Applications, 2014 - Elsevier

This paper presents a Dynamic Clustering Algorithm for histogram data with an automatic weighting step of the variables by using adaptive distances. The Dynamic Clustering Algorithm is a k-means-like algorithm for clustering a set of objects into a predefined number …

2014

[PDF] ucla.edu

Weak KAM theory on the Wasserstein torus with multidimensional underlying space

W Gangbo, A Tudorascu - … on Pure and Applied Mathematics, 2014 - Wiley Online Library

The study of asymptotic behavior of minimizing trajectories on the Wasserstein space ( d) has so far been limited to the case d= 1 as all prior studies heavily relied on the isometric identification of ( ) with a subset of the Hilbert space L2 (0, 1). There is no known …

<——2014—— 2014——— - 220—

2014

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

2014

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional analog. We show that simple finite-volume discretizations of the linear Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for reversible …

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the

empirical measure in the law of large numbers, in Wasserstein distance. We also consider

occupation measures of ergodic Markov chains. One motivation is the approximation of a …

2014

On curvature conditions using Wasserstein spaces

M Kell - 2014 - oatd.org

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure spaces is defined. In the second part of the thesis a proof of the identification of the q-heat …

2014

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

2014

Optimality of the triangular lattice for a particle system with Wasserstein interaction

DP Bourne, MA Peletier, F Theil - Communications in Mathematical …, 2014 - Springer

We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of two terms; the first term is the sum …

[PDF] puc-rio.br

[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.puc-rio.br

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the Wasserstein Metric. Rio de Janeiro, 2014. 89p. Dissertaçao de Mestrado—Departamento de Matemática, Pontifıcia Universidade Católica do Rio de Janeiro. In this work, we study the so …

2014

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

[HTML] On the non-injectivity of the Vaserstein symbol in dimension three

DR Rao, N Gupta - Journal of Algebra, 2014 - Elsevier

LN Vaserstein proved over a two dimensional ring that the orbit space of unimodular rows of length three modulo elementary action has a Witt group structure. RA Rao and W. van der Kallen showed that the Vaserstein symbol need not be injective over three dimensional …

H Lescornel - 2014 - theses.fr

[PDF] Etude de modeles de déformations entre distributions avec la distance de Wasserstein

2014 [PDF] sfds.asso.fr

H Lescornel, JM Loubes - Nous - papersjds14.sfds.asso.fr

Etude de mod`eles de déformations entre distributions avec la distance de Wasserstein … Hél`ene Lescornel 1 & Jean-Michel Loubes 2 … 1 Institut de Mathématiques de Toulouse 118 route de Narbonne 31000 Toulouse helene.lescornel@math.univ-toulouse.fr 2 Institut de Mathématiques …

<——2014—— 2014——— - 230—

2014 [PDF] arxiv.org

Nonlinear diffusion: geodesic convexity is equivalent to Wasserstein contraction

F Bolley, JA Carrillo - Communications in Partial Differential …, 2014 - Taylor & Francis

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance. Under suitable convexity conditions on the nonlinearity, due to McCann, the associated entropy is …

Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

AN Bishop - 17th International Conference on Information …, 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Distributed consensus in the Wasserstein metric space of probability measures is introduced

in this work. Convergence of each agent's measure to a common measure value is proven

under a weak network connectivity condition. The common measure reached at each agent …

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 数理解析研究所講究録, 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

Estimation of deformations between distributions by minimal Wasserstein distance

H Lescornel, JM Loubes - 2014 - hal.archives-ouvertes.fr

We consider the issue of estimating a deformation operator acting on measures. For this we

consider a parametric warping model on an empirical sample and provide a new matching

criterion for cloud points based on a generalization of the registration criterion used in …

[CITATION] Estimation of Deformations between Distributions with the Wasserstein Distance

H Lescornel, JM Loubes

[PDF] sfds.asso.fr

[PDF] Etude de modeles de déformations entre distributions avec la distance de Wasserstein

H Lescornel, JM Loubes - Nous - papersjds14.sfds.asso.fr

Etude de mod`eles de déformations entre distributions avec la distance de Wasserstein …

Hél`ene Lescornel 1 & Jean-Michel Loubes 2 … 1 Institut de Mathématiques de Toulouse 118

route de Narbonne 31000 Toulouse helene.lescornel@math.univ-toulouse.fr 2 Institut de Mathématiques …

Wasserstein propagation for semi-supervised learning

J Solomon, R Rustamov, L Guibas… - … on Machine Learning, 2014 - proceedings.mlr.press

Probability distributions and histograms are natural representations for product ratings, traffic

measurements, and other data considered in many machine learning applications. Thus,

this paper introduces a technique for graph-based semi-supervised learning of histograms …

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

M Giovanna Mora, M Peletier, L Scardia - arXiv e-prints, 2014 - ui.adsabs.harvard.edu

We consider systems of $ n $ parallel edge dislocations in a single slip system, represented

by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We

formulate the energy of this system in terms of the empirical measure of the dislocations, and …

Decomposition of geodesics in the Wasserstein space and the globalization problem

F Cavalletti - Geometric and Functional Analysis, 2014 - Springer

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m)

be a non-branching metric measure space verifying CD _ loc (K, N) CD loc (K, N) or

equivalently CD^*(K, N) CD∗(K, N). We prove that every geodesic t μ t in the L 2 …

2014

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

<——2014—— 2014——— - 240—

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

2014

[PDF] global-sci.org

[PDF] Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - global-sci.org

We present a multi-phase image segmentation method based on the histogram of the Gabor

feature space, which consists of a set of Gabor-filter responses with various orientations,

scales and frequencies. Our model replaces the error function term in the original fuzzy …

2014

M Kell - 2014 - oatd.org

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics

in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure

spaces is defined. In the second part of the thesis a proof of the identification of the q-heat …

Wasserstein Metric Based Adaptive Fuzzy Clustering Methods ...

2014

www.semanticscholar.org › paper › Wasserstein-Metric-B...

SDA (Symbolic Data Analysis) is a new research field in knowledge discovery and data management, and is closely ... Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data ... H. Li; Published 2014; Mathematics.

[CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

H Li - 2014

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 数理解析研究所講究録, 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

2014

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the

empirical measure in the law of large numbers, in Wasserstein distance. We also consider

occupation measures of ergodic Markov chains. One motivation is the approximation of a …

2014

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

2014

Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities

Y Ding - Statistics & Probability Letters, 2014 - Elsevier

In this paper, we study Wasserstein-Divergence transportation inequalities which are the

generalization of classical transportation inequalities. We present sufficient and necessary

conditions for them separately, which coincide in the limit case. Using this kind of …

2014

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of

probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely

continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

2014

Transport equation with source and generalized Wasserstein distance

B Piccoli - NETCO 2014-New Trends in Optimal Control, 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc..

Such models were successfully employed in traffic monitoring projects. Then we will pass to …

<——2014—— 2014——— - 250—

[PDF] puc-rio.br

[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.puc-rio.br

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the

Wasserstein Metric. Rio de Janeiro, 2014. 89p. Dissertaçao de Mestrado—Departamento de

Matemática, Pontifıcia Universidade Católica do Rio de Janeiro. In this work, we study the so …

Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

2014

A Irpino, R Verde, FAT De Carvalho - Expert Systems with Applications, 2014 - Elsevier

This paper presents a Dynamic Clustering Algorithm for histogram data with an automatic

weighting step of the variables by using adaptive distances. The Dynamic Clustering

Algorithm is a k-means-like algorithm for clustering a set of objects into a predefined number …

2014

[PDF] Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - global-sci.org

We present a multi-phase image segmentation method based on the histogram of the Gabor

feature space, which consists of a set of Gabor-filter responses with various orientations,

scales and frequencies. Our model replaces the error function term in the original fuzzy …

2014

MR3144594 Rao, Dhvanita R.; Gupta, Neena On the non-injectivity of the Vaserstein symbol in dimension three. J. Algebra 399 (2014), 378–388. (Reviewer: L. N. Vaserstein) 13C10 (19B14 19G12) 1 Citation

[HTML] On the non-injectivity of the Vaserstein symbol in dimension three

DR Rao, N Gupta - Journal of Algebra, 2014 - Elsevier

LN Vaserstein proved over a two dimensional ring that the orbit space of unimodular rows of

length three modulo elementary action has a Witt group structure. RA Rao and W. van der

Kallen showed that the Vaserstein symbol need not be injective over three dimensional …

The derivation of swarming models: mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of

interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We …

2014

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

H Lescornel - 2014 - theses.fr

Résumé La première partie de cette thèse est consacrée à l'estimation de covariance de

processus stochastiques non stationnaires. Le modèle étudié amène à estimer la

covariance du processus dans différents espaces vectoriels de matrices. Nous étudions …

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

Decomposition of geodesics in the Wasserstein space and the globalization problem

F Cavalletti - Geometric and Functional Analysis, 2014 - Springer

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m)

be a non-branching metric measure space verifying CD _ loc (K, N) CD loc (K, N) or

equivalently CD^*(K, N) CD∗(K, N). We prove that every geodesic t μ t in the L 2 …

2014

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem | SpringerLink

https://link.springer.com › article

Jan 29, 2014 — We will prove a decomposition for Wasserstein geodesics in the following sense: ... Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem ... Structure of level sets and sard-type properties of lipschitz maps. ... Communications in Mathematical Physics, 318, 615–673 (2013).

<——2014—— 2014——— - 260—

2014

[HTML] On the non-injectivity of the Vaserstein symbol in dimension three

DR Rao, N Gupta - Journal of Algebra, 2014 - Elsevier

LN Vaserstein proved over a two dimensional ring that the orbit space of unimodular rows of

length three modulo elementary action has a Witt group structure. RA Rao and W. van der

Kallen showed that the Vaserstein symbol need not be injective over three dimensional …

2014

An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker–Planck equation is gradient flow for the entropy

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

2014

Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

AN Bishop - 17th International Conference on Information …, 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

2014

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Distributed consensus in the Wasserstein metric space of probability measures is introduced

in this work. Convergence of each agent's measure to a common measure value is proven

under a weak network connectivity condition. The common measure reached at each agent …

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2014 - IET

Colour image enhancement is an important preprocessing phase of many image analysis

tasks such as image segmentation, pattern recognition and so on. This study presents a new

local brightness adaptive variational model using Wasserstein distance for colour image …

2014

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and subgeometric rates of convergence in the Wasserstein distance for general state-space

Markov chains which are not phi-irreducible. Our approach is based on a coupling …

2014

M Kell - 2014 - oatd.org

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics

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Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

2014

H Lescornel - 2014 - theses.fr

Résumé La première partie de cette thèse est consacrée à l'estimation de covariance de

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O Butkovsky - Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

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and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

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<——2014—— 2014——— - 280—

Covariance estimation and study of models of deformations between distributions with the Wasserstein distance

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Estimation of deformations between distributions by minimal ...

https://hal.archives-ouvertes.fr › document

PDF

by H Lescornel · 2014 · Cited by 2 — MSC 2010 subject classifications: Primary 62F12, 62F12; secondary. 62E20. Keywords and phrases: Wasserstein distance, M estimation, Density.

[CITATION] Estimation of Deformations between Distributions with the Wasserstein Distance

H Lescornel, JM Loubes

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

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2014

Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities

Y Ding - Statistics & Probability Letters, 2014 - Elsevier

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J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

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2014

[PDF] kobv.de

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

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Transport equation with source and generalized Wasserstein distance

B Piccoli - NETCO 2014-New Trends in Optimal Control, 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

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[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.puc-rio.br

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the

Wasserstein Metric. Rio de Janeiro, 2014. 89p. Dissertaçao de Mestrado—Departamento de

Matemática, Pontifıcia Universidade Católica do Rio de Janeiro. In this work, we study the so …

Gradient flows in general metric and Wasserstein spaces

<——2014—— 2014——— - 290—

[PDF] tuwien.at

DL Forkert - 2014 - repositum.tuwien.at

In this thesis we approach gradient flows in metric spaces which are not necessarily

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Weak KAM theory on the Wasserstein torus with multidimensional underlying space

W Gangbo, A Tudorascu - Communications on Pure and …, 2014 - Wiley Online Library

The study of asymptotic behavior of minimizing trajectories on the Wasserstein space (

d) has so far been limited to the case d= 1 as all prior studies heavily relied on the isometric

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KT Sturm - Singular phenomena and scaling in mathematical …, 2014 - Springer

Abstract The Wasserstein space P (M) on an Euclidean or Riemannian space M–ie the

space of probability measures on M equipped with the L 2-Wasserstein distance d W–offers

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2013

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

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equation exhibit the recently established entropic gradient-flow structure for reversible …

[PDF] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J Wangb - arXiv preprint arXiv:1407.1986, 2014 - Citeseer

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential contractivity of diffusion semigroups (Pt) t≥ 0 with

respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that …

2014

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

X-ray crystallography is the main tool for the structural analysis of molecules today. One of its

main subtasks is the phase retrieval problem. In this thesis, the phase retrieval problem is

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[PDF] Optimal Transport and the Wasserstein Metric

PN Orenstein - 2014 - mat.puc-rio.br

Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the

Wasserstein Metric. Rio de Janeiro, 2014. 89p. Dissertaçao de Mestrado—Departamento de

Matemática, Pontifıcia Universidade Católica do Rio de Janeiro. In this work, we study the so …

Wasserstein propagation for semi-supervised learning

2014

J Solomon, R Rustamov, L Guibas… - … on Machine Learning, 2014 - proceedings.mlr.press

Probability distributions and histograms are natural representations for product ratings, traffic

measurements, and other data considered in many machine learning applications. Thus,

this paper introduces a technique for graph-based semi-supervised learning of histograms …

2014

Wasserstein Metric Based Adaptive Fuzzy Clustering Methods ...

https://www.semanticscholar.org › paper › Wasserstein-M...

[CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

H Li - 2014

[CITATION] Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Data

H Li - 2014

Gradient flows in general metric and Wasserstein spaces

DL Forkert - 2014 - repositum.tuwien.at

In this thesis we approach gradient flows in metric spaces which are not necessarily

endowed with a natural linear structure. The first part is an introduction to the theory in

abstract metric spaces: We present three possible generalizations of gradient flows to the …

<——2014—— 2014——— - 300—

Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer

In this article, we generalize the Wasserstein distance to measures with different masses.

We study the properties of this distance. In particular, we show that it metrizes weak

convergence for tight sequences. We use this generalized Wasserstein distance to study a …

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

In this work, we provide non-asymptotic bounds for the average speed of convergence of the

empirical measure in the law of large numbers, in Wasserstein distance. We also consider

occupation measures of ergodic Markov chains. One motivation is the approximation of a …

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition

and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

Decomposition of geodesics in the Wasserstein space and the globalization problem

F Cavalletti - Geometric and Functional Analysis, 2014 - Springer

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m)

be a non-branching metric measure space verifying CD _ loc (K, N) CD loc (K, N) or

equivalently CD^*(K, N) CD∗(K, N). We prove that every geodesic t μ t in the L 2 …

An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker–Planck equation is gradient flow for the entropy

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

2014

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation

for ions with massless thermalized electrons. We prove new weak-strong stability estimates

in the Wasserstein metric that allow us to extend and improve previously known …

2014 [PDF] dtic.mil

Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

AN Bishop - 17th International Conference on Information …, 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

Nonlinear diffusion: geodesic convexity is equivalent to Wasserstein contraction

F Bolley, JA Carrillo - … in Partial Differential Equations, 2014 - Taylor & Francis

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the

space of probability measures equipped with the Euclidean Wasserstein distance. Under

suitable convexity conditions on the nonlinearity, due to McCann, the associated entropy is …

A monotone approximation to the Wasserstein diffusion

KT Sturm - Singular phenomena and scaling in mathematical …, 2014 - Springer

Abstract The Wasserstein space P (M) on an Euclidean or Riemannian space M–ie the

space of probability measures on M equipped with the L 2-Wasserstein distance d W–offers

a rich geometric structure. This allows to develop a far reaching first order calculus, with …

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Distributed consensus in the Wasserstein metric space of probability measures is introduced

in this work. Convergence of each agent's measure to a common measure value is proven

under a weak network connectivity condition. The common measure reached at each agent …

<——2014—— 2014——— - 310—

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of

probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely

continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and subgeometric rates of convergence in the Wasserstein distance for general state-space

Markov chains which are not phi-irreducible. Our approach is based on a coupling …

2014

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

[PDF] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J Wangb - arXiv preprint arXiv:1407.1986, 2014 - Citeseer

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential contractivity of diffusion semigroups (Pt) t≥ 0 with

respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that …

Evolution in Measure Spaces with Wasserstein Distance

E Cristiani, B Piccoli, A Tosin - Multiscale Modeling of Pedestrian …, 2014 - Springer

In this chapter, we provide a fairly general mathematical setting for the nonlinear transport

equation analyzed in Chap. 6 (namely Eqs.(5.1) and (6.6)). More precisely, we study the

evolution of solutions in measures spaces endowed with the Wasserstein distance and its …

An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker–Planck equation is gradient flow for the entropy

2014

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

Nonlinear diffusion: geodesic convexity is equivalent to Wasserstein contraction

F Bolley, JA Carrillo - Communications in Partial Differential …, 2014 - Taylor & Francis

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the

space of probability measures equipped with the Euclidean Wasserstein distance. Under

suitable convexity conditions on the nonlinearity, due to McCann, the associated entropy is …

Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

AN Bishop - 17th International Conference on Information …, 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

2014

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition

and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

2014

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and subgeometric rates of convergence in the Wasserstein distance for general state-space

Markov chains which are not phi-irreducible. Our approach is based on a coupling …

<——2014—— 2014——— -320—

2014

OD matrix structural similarity: Wasserstein metric

A Ruiz de Villa, J Casas, M Breen - 2014 - trid.trb.org

In this paper the authors introduce a metric and a method, considering the spatial structure,

for comparing OD matrices. It is based on mass transportation techniques, in particular the

notion of Wasserstein distance. The result of the comparison is measured in total travel time …

2014

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and subgeometric rates of convergence in the Wasserstein distance for general state-space

Markov chains which are not phi-irreducible. Our approach is based on a coupling …

year 2014

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

X-ray crystallography is the main tool for the structural analysis of molecules today. One of its

main subtasks is the phase retrieval problem. In this thesis, the phase retrieval problem is

discussed in the context of the optimal transport. Phase retrieval is formulated as an energy …

A monotone approximation to the Wasserstein diffusion

KT Sturm - Singular phenomena and scaling in mathematical …, 2014 - Springer

Abstract The Wasserstein space P (M) on an Euclidean or Riemannian space M–ie the

space of probability measures on M equipped with the L 2-Wasserstein distance d W–offers

a rich geometric structure. This allows to develop a far reaching first order calculus, with …

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

2014

… fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown correlation

AN Bishop - … Conference on Information Fusion (FUSION), 2014 - ieeexplore.ieee.org

In this work, a general information fusion problem is formulated as an optimisation protocol

in the space of probability measures (ie the so-called Wasserstein metric space). The

highlevel idea is to consider the data fusion result as the probability measure that is closest …

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 数理解析研究所講究録, 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

[PDF] Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

A Takatsu - 数理解析研究所講究録, 2014 - repository.kulib.kyoto-u.ac.jp

In the workshop, $ I $ demonstrated that a certain evolution equation on a weighted

Riemannian manifold can be considered as a Wasserstein gradient flow (the talk was based

on [7], where we usedthe notions of the information geometry). In this note, I discuss …

Wasserstein propagation for semi-supervised learning

J Solomon, R Rustamov, L Guibas… - … on Machine Learning, 2014 - proceedings.mlr.press

Probability distributions and histograms are natural representations for product ratings, traffic

measurements, and other data considered in many machine learning applications. Thus,

this paper introduces a technique for graph-based semi-supervised learning of histograms …

2014 [PDF] arxiv.org

Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

A Irpino, R Verde, FAT De Carvalho - Expert Systems with Applications, 2014 - Elsevier

This paper presents a Dynamic Clustering Algorithm for histogram data with an automatic

weighting step of the variables by using adaptive distances. The Dynamic Clustering

Algorithm is a k-means-like algorithm for clustering a set of objects into a predefined number …

<——2014—— 2014——— - 330 —

2014 Full View

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2014 - ieeexplore.ieee.org

Colour image enhancement is an important preprocessing phase of many image analysis

tasks such as image segmentation, pattern recognition and so on. This study presents a new

local brightness adaptive variational model using Wasserstein distance for colour image …

2014

[PDF] A Parametric Registration model for warped distributions with Wasserstein's distance

MA Antolín, JAC Albertos, H Lescornel, JM Loubes - personales.unican.es

… For this, a natural distance to measure the deformation cost to align two distributions is given

by the 2-Wasserstein distance which is at the heart of warping issues between probabilities …

[CITATION] A Parametric Registration model for warped distributions with Wasserstein's distance

M Agullo, JA Cuesta, H Lescornel, JM Loubes - J. Multivariate Anal., to ap pear, 2014

Multi-scale non-rigid point cloud registration using robust sliced-Wasserstein distance via Laplace-Beltrami eigenmap

R Lai, H Zhao - arXiv preprint arXiv:1406.3758, 2014 - arxiv.org

In this work, we propose computational models and algorithms for point cloud registration

with non-rigid transformation. First, point clouds sampled from manifolds originally

embedded in some Euclidean space $\mathbb {R}^ D $ are transformed to new point clouds …

2014 [PDF] global-sci.org

Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - cambridge.org

We present a multi-phase image segmentation method based on the histogram of the Gabor

feature space, which consists of a set of Gabor-filter responses with various orientations,

scales and frequencies. Our model replaces the error function term in the original fuzzy …

OD matrix structural similarity: Wasserstein metric

A Ruiz de Villa, J Casas, M Breen - 2014 - trid.trb.org

In this paper the authors introduce a metric and a method, considering the spatial structure,

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notion of Wasserstein distance. The result of the comparison is measured in total travel time …

Fast Computation of Wasserstein Barycenters

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482 citations* for all

456 citations*

2014 INTERNATIONAL CONFERENCE ON MACHINE LEARNING

Marco Cuturi ¹,Arnaud Doucet ²

¹ Kyoto University ,² University of Oxford

Subgradient method

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Epidemiology of primary anterior shoulder dislocation requiring closed reduction in Ontario, Canada.

156 citations*

2014 AMERICAN JOURNAL OF SPORTS MEDICINE

Timothy Leroux ¹,David Wasserstein ²,Christian Veillette ^1,3,Amir Khoshbin ¹,Patrick Henry ¹ see all 9 authors

¹ University of Toronto ,² Sunnybrook Health Sciences Centre ,³ University Health Network

Anterior shoulder

Population

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Background:There is a lack of high-quality population-based literature describing the epidemiology of primary anterior shoulder dislocation.Purpose:To (1) calculate the incidence density rate (IDR) of primary anterior shoulder dislocation requiring closed reduction (CR; “index event”) in the general... View Full Abstract

The derivation of swarming models: mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of

30interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We …

2014 [PDF] inria.fr

Transport equation with source and generalized Wasserstein distance

B Piccoli - NETCO 2014-New Trends in Optimal Control, 2014 - hal.inria.fr

We will start by revising some macroscopic model, based on systems of conservation (or

balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc..

Such models were successfully employed in traffic monitoring projects. Then we will pass to …

The derivation of swarming models: mean-field limit and Wasserstein distances

<——2014—— 2014——— - 340—

2014 [PDF] arxiv.org

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of

interacting particles with applications in swarming models. We first make a summary of the

kinetic models derived as continuum versions of second order models for swarming. We …

2014 [PDF] arxiv.org

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation

for ions with massless thermalized electrons. We prove new weak-strong stability estimates

in the Wasserstein metric that allow us to extend and improve previously known …

2014 [PDF] arxiv.org

Consensus in the wasserstein metric space of probability measures

AN Bishop, A Doucet - arXiv preprint arXiv:1404.0145, 2014 - arxiv.org

Distributed consensus in the Wasserstein metric space of probability measures is introduced

in this work. Convergence of each agent's measure to a common measure value is proven

under a weak network connectivity condition. The common measure reached at each agent …

2014 [HTML] mdpi.com

[HTML] The Gromov–Wasserstein distance: A brief overview

F Mémoli - Axioms, 2014 - mdpi.com

… Need Help? Support. Find support for a specific problem in the support section of our website.

Get Support. Feedback. Please let us know what you think of our products and services. Give

Feedback. Information. Visit our dedicated information section to learn more about MDPI. Get …

2014 [PDF] arxiv.org

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

We develop a new method for showing that a given sequence of random variables verifies

an appropriate law of the iterated logarithm. Our tools involve the use of general estimates

on multidimensional Wasserstein distances, that are in turn based on recently developed …

2014

2014 [PDF] projecteuclid.org

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - The Annals of Applied Probability, 2014 - projecteuclid.org

We establish subgeometric bounds on convergence rate of general Markov processes in the

Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition

and the existence of a “good” $ d $-small set imply subgeometric convergence to the …

2014 [PDF] arxiv.org

An analog of the 2-Wasserstein metric in non-commutative probability under which the Fermionic Fokker–Planck equation is gradient flow for the entropy

EA Carlen, J Maas - Communications in mathematical physics, 2014 - Springer

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra

generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation

relations, Q i Q j+ Q j Q i= 2δ ij I, and let τ denote the normalized trace on C C. This algebra …

[CITATION] … 2-Wasserstein metric in non-commutative probability under which the Fermionic Fokker-Planck equation is gradient flow for the entropy. vol. 331, issue 3

2014 [PDF] psu.edu

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of

probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely

continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

2014 [PDF] psu.edu

[PDF] New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains

A Durmus, E Moulines, G Fort - arXiv preprint arXiv:1402.4577, 2014 - Citeseer

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and subgeometric rates of convergence in the Wasserstein distance for general state-space

Markov chains which are not phi-irreducible. Our approach is based on a coupling …

2014 [PDF] ucla.edu

Weak KAM theory on the Wasserstein torus with multidimensional underlying space

W Gangbo, A Tudorascu - Communications on Pure and …, 2014 - Wiley Online Library

The study of asymptotic behavior of minimizing trajectories on the Wasserstein space (

d) has so far been limited to the case d= 1 as all prior studies heavily relied on the isometric …

<——2014—— 2014——— - 350—

OD matrix structural similarity: Wasserstein metric

A Ruiz de Villa, J Casas, M Breen - 2014 - trid.trb.org

In this paper the authors introduce a metric and a method, considering the spatial structure,

for comparing OD matrices. It is based on mass transportation techniques, in particular the …

2014 [PDF] arxiv.org
The derivation of swarming models: mean-field limit and Wasserstein distances

JA Carrillo, YP Choi, M Hauray - Collective dynamics from bacteria to …, 2014 - Springer

These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order models for swarming. We …

2014 [PDF] psu.edu

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein space of

probability measures on M. If S is an embedded submanifold of M, and µ is an absolutely

continuous measure on S, we compute the tangent cone of P (M) at µ. We describe a …

2014

Exponential Convergence in $L^p$-Wasserstein Distance for ...

https://www.semanticscholar.org › paper › Exponential-C...

Jul 8, 2014 — Exponential Convergence in $L^p$-Wasserstein Distance for Diffusion Processes without Uniformly Dissipative Drift.

[CITATION] Exponential Contractivity in the L p-Wasserstein Distance for Diffusion Processes

D Luoa, J

2014 [PDF] global-sci.org

Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - cambridge.org

… We developed a multi-phase segmentation model using the squared 2−Wasserstein …

segmentation. The computational time are shorten due to that the closed form solution of Fi(l)

is to take the mean value instead of the weighted median in the case of using linear 1−Wasserstein …

2014

Contraction in the Wasserstein metric for some Markov chains ...

Fast Computation of Wasserstein Barycenters - Proceedings ...

by B Kloeckner · 2014 · Cited by 17 — ... Markov chains, and applications to the dynamics of expanding maps ... set of probability measures on M with the 1-Wasserstein metric.

2014

http://proceedings.mlr.press › cuturi14

by M Cuturi · 2014 · Cited by 554 — We present new algorithms to compute the mean of a set of N empirical probability measures under the optimal transport metric. This mean, known as the ...

DISSERTATION

The exponential formula for the Wasserstein metric

Craig, Katy ; 2014

The exponential formula for the Wasserstein metric

Online Access Available

2014 video

Wasserstein Metric from Transport Theory and Ri... - NSF Math Institutes

NSF Media Library | Wasserstein Metric from Transport Theory and Riemannian Structure of Dens

Jun 12, 2014

2014 video

What is … a Wasserstein distance? on Vimeo

- Uploaded by Berlin Mathematical School

A special subclass is formed by gradient flows with respect to the Wasserstein distance. This class was first ...

Oct 7, 2014

<——2014———— 2014—————360—

2014 Computer Program,
Subgeometric rates of convergence of Markov processes in the Wasserstein metricAuthor:Butkovsky, Oleg (Creator)
Summary:We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a “good” $d$-small set imply subgeometric convergence to the invariant measure. In the continuous time setting we obtain the same convergence rate provided that there exists a “good” $d$-small set and the Douc–Fort–Guillin supermartingale condition holds. As an application of our results, we prove that the Veretennikov–Khasminskii condition is sufficient for subexponential convergence of strong solutions of stochastic delay differential equationsShow more
Computer Program, 2014-04
English
Publisher:The Institute of Mathematical Statistics, 2014-04
Access Free

2014 Computer Program,
On the mean speed of convergence of empirical and occupation measures in Wasserstein distanceAuthors:Boissard, Emmanuel (Creator), Le Gouic, Thibaut (Creator)
Summary:In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably highlighted in the example of infinite-dimensional Gaussian measuresShow more
Computer Program, 2014-05
English
Publisher:Institut Henri Poincaré, 2014-05
Access Free

2014 see 2010

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

Authors:Boissard, Emmanuel (Creator), Le Gouic, Thibaut (Creator)
Summary:In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably highlighted in the example of infinite-dimensional Gaussian measuresShow more
Computer Program, 2014-05
English
Publisher:Institut Henri Poincaré, 2014-05

2014 see 2013 2015 Peer-reviewed
On the rate of convergence in Wasserstein distance of the empirical measure

Authors:Nicolas Fournier, Arnaud Guillin
Summary:Abstract: Let be the empirical measure associated to a -sample of a given probability distribution on . We are interested in the rate of convergence of to , when measured in the Wasserstein distance of order . We provide some satisfying non-asymptotic -bounds and concentration inequalities, for any values of and . We extend also the non asymptotic -bounds to stationary -mixing sequences, Markov chains, and to some interacting particle systemsShow more
Article, 2014
Publication:Probability Theory and Related Fields, 162, 20141018, 707
Publisher:2014

2014 SEE 2012 Peer-reviewed
An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy

Authors:Eric A. Carlen, Jan Maas
Summary:Let C denote the Clifford algebra over R n , which is the von Neumann algebra generated by n self-adjoint operators Q j , j = 1,…,n satisfying the canonical anticommutation relations, Q i Q j + Q j Q i = 2δ ij I, and let τ denote the normalized trace on C . This algebra arises in quantum mechanics as the algebra of observables generated by n fermionic degrees of freedom. Let P denote the set of all positive operators ρ ∈ C such that τ(ρ) = 1; these are the non-commutative analogs of probability densities in the non-commutative probability space ( C , τ ) . The fermionic Fokker-Planck equation is a quantum-mechanical analog of the classical Fokker-Planck equation with which it has much in common, such as the same optimal hypercontractivity properties. In this paper we construct a Riemannian metric on P that we show to be a natural analog of the classical 2-Wasserstein metric, and we show that, in analogy with the classical case, the fermionic Fokker-Planck equation is gradient flow in this metric for the relative entropy with respect to the ground state. We derive a number of consequences of this, such as a sharp Talagrand inequality for this metric, and we prove a number of results pertaining to this metric. Several open problems are raisedShow more
Article, 2014
Publication:Communications in Mathematical Physics, 331, 201411, 887
Publisher:2014

2014

P2014 see 2013 2015 eer-reviewed
Sliced and Radon Wasserstein Barycenters of Measures

Authors:Bonneel N., Pfister H., Rabin J., Peyre G.
Article, 2014
Publication:Journal of Mathematical Imaging and Vision, 51, 2014, 22
Publisher:2014

2014 comp pr see 2013 thesis
Localisation de masse et espaces de Wasserstein

Authors:Thibaut Le Gouic, Philippe Berthet, Université Toulouse 3 Paul Sabatier (1969-....).
Summary:Le travail de cette thèse est basé sur deux outils : le packing d'un ensemble et les espaces de Wasserstein. Une première partie s'intéresse à la localisation de la masse d'une mesure de probabilité Mu. Lorsque Mu est régulière, les ensembles de niveau de sa densité fournissent une bonne notion pour localiser les zones "denses" de masse, mais perdent leur sens pour les mesures à support fini, comme dans le cas de la mesure empirique. Nous définissons alors une fonction Tau dite de taille, sur les fermés d'un espace métrique, basée sur leur packing. Les ensembles de plus petite Tau-taille ayant une masse 1 - alpha donnée permettent de localiser les zones denses de Mu, même dans les cas irréguliers. Nous montrons que les ensembles de plus petite Tau-taille pour Mu et alpha fixés dépendent continuement de Mu et de alpha, pour la distance de Hausdorff. Nous en tirons une nouvelle méthode de quantification de Mu, robuste et stable. Une seconde partie s'intéresse à la distance de Wasserstein entre une probabilité mu et la mesure empirique associée. Nous obtenons une majoration non asymptotique de l'espérance de cette distance, dans la cadre d'un espace métrique quelconque. Une particularisation aux espaces de dimension finie permet de mettre en valeur la précision de cette majoration. Nous obtenons aussi dans le cas des mesures gaussiennes sur les espaces de Banach, de nouvelles majorations qui coïncident asymptotiquement avec celles des meilleurs quantifieurs possibles. À l'aide d'inégalités de concentration, nous établissons des bornes de déviations. Enfin, nous utilisons ces résultats pour définir des tests statistiques non asymptotiques et non paramétriques d'adéquation à une famille de lois. Une troisième partie s'intéresse au barycentre d'une famille finie de mesures de probabilité. La moyenne de Fréchet fournit une extension de la notion de barycentre aux espaces métriques, nous permettant de le définir sur les espaces de Wasserstein. Nous montrons son existence, puis, en étudions les propriétés de continuité en les mesures de probabilité. Nous discutons enfin de l'application pratique de ces résultats en agrégation de mesures empiriques et en mélange d'imagesShow more
Computer Program, 2014
French
Publisher:Université Paul Sabatier, Toulouse 3, Toulouse, 2014

2014 thesis
Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow

Author:Malcolm Bowles
Abstract:In this thesis, we study a linear fractional Fokker-Planck equation that models non-local (`fractional') diffusion in the presence of a potential field. The non-locality is due to the appearance of the `fractional Laplacian' in the corresponding PDE, in place of the classical Laplacian which distinguishes the case of regular (Gaussian) diffusion. Motivated by the observation that, in contrast to the classical Fokker-Planck equation (describing regular diffusion in the presence of a potential field), there is no natural gradient flow formulation for its fractional counterpart, we prove existence of weak solutions to this fractional Fokker-Planck equation by combining a splitting technique together with a Wasserstein gradient flow formulation. An explicit iterative construction is given, which we prove weakly converges to a weak solution of this PDEShow more
Thesis, Dissertation, 2014
English
Publisher:University of Victoria, Victoria, 2014

014 thesis
Some linear and non-linear structures in Wasserstein geometry

Author:高津, 飛鳥 (Creator)
Thesis, Dissertation, 2014-02-26T01:28:27Z
English
Publisher:2014-02-26T01:28:27Z

014 see 2013 2015 Peer-reviewed
Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates

Authors:Kazumasa Kuwada, SpringerLink (Online service)
Downloadable Article, 2014
English
Publication:Calculus of variations and partial differential equations.
Publisher:2014

<——2014———— 2014—————370—

The Gromov-Wasserstein distance: A brief overview

Author:Memoli F.
Article, 2014
Publication:Axioms, 3, 2014 09 01, 335
Publisher:2014

Wasserstein Distance
Encyclopedia Article, 2014
Publication:Wiley StatsRef: Statistics Reference Online, 20140929
Publisher:2014

<——2014———— 2014—————372— end 2014

Including 3 titles with Vaserstein

start 2015

Snowflake universality of Wasserstein spaces arXiv published in 2018

Alexandr Andoni, Assaf Naor, Ofer Neiman

(Submitted on 29 Sep 2015)

For p∈(1,∞) let 𝒫p(ℝ3) denote the metric space of all p-integrable Borel probability measures on ℝ3, equipped with the Wasserstein p metric 𝖶p. We prove that for every ε>0, every θ∈(0,1/p] and every finite metric space (X,dX), the metric space (X,dθX) embeds into 𝒫p(ℝ3) with distortion at most 1+ε. We show that this is sharp when p∈(1,2] in the sense that the exponent 1/p cannot be replaced by any larger number. In fact, for arbitrarily large n∈ℕ there exists an n-point metric space (Xn,dn) such that for every α∈(1/p,1] any embedding of the metric space (Xn,dαn) into 𝒫p(ℝ3) incurs distortion that is at least a constant multiple of (logn)α−1/p. These statements establish that there exists an Alexandrov space of nonnegative curvature, namely 𝒫2(ℝ3), with respect to which there does not exist a sequence of bounded degree expander graphs. It also follows that 𝒫2(ℝ3) does not admit a uniform, coarse, or quasisymmetric embedding into any Banach space of nontrivial type. Links to several longstanding open questions in metric geometry are discussed, including the characterization of subsets of Alexandrov spaces, existence of expanders, the universality problem for 𝒫2(ℝk), and the metric cotype dichotomy problem.

[PDF] " A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

Abstract The fair placement of a facility often depends on other existing players and on an

optimal assignment map of clients to these facilities. This problem arises in various contexts

in decision mathematics such as, for instance, location theory in operational research and ...

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes arXiv

Scalable Bayes via Barycenter in Wasserstein Space arXiv

S Srivastava, C Li, DB Dunson - arXiv preprint arXiv:1508.05880, 2015 - arxiv.org

Abstract: We propose a novel approach WASP for Bayesian inference when massive size of

the data prohibits posterior computations. WASP is estimated in three steps. First, data are

divided into smaller computationally tractable subsets. Second, posterior draws of ...

Modified Arratia flow and Wasserstein diffusion arXiv

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1504.00559, 2015 - arxiv.org

Abstract: Extending previous work~[arXiv: 1408.0628] by the first author we present a variant

of the Arratia flow of a field of coalescing Brownian motions starting from every point of the

unit interval. The important new feature of the model is that individual particles carry mass ...

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Abstract: We consider $ L^ p $-Wasserstein distances on a subset of probability measures. If

the subset of interest appears to be a simplex, these distances are determined by their

values on extreme points of the simplex. We show that this fact is a corollary of the ...

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

arXivJ Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

Abstract: When the Ricci curvature of a Riemannian manifold is not lower bounded by a

constant, but lower bounded by a continuous function, we give a new characterization of this

lower bound through the convexity of relative entropy on the probability space over the ...

Evolution variational inequality and Wasserstein control in variable curvature context arXiv

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

Abstract: In this note we continue the analysis of metric measure space with variable ricci

curvature bounds. First, we study $(\ kappa, N) $-convex functions on metric spaces where

$\ kappa $ is a lower semi-continuous function, and gradient flow curves in the sense of a ...

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

Abstract In this chapter we use the minimal value of transport problems between two

probabilities in order to define a distance on the space of probabilities. We mainly consider

costs of the form c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\ varOmega ⊂ R^ d. We ...

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions arXiv

K Craig - arXiv preprint arXiv:1512.07255, 2015 - arxiv.org

Abstract: Over the past fifteen years, the theory of Wasserstein gradient flows of convex (or,

more generally, semiconvex) energies has led to advances in several areas of partial

differential equations and analysis. In this work, we extend the well-posedness theory for ...

Uniform contractivity in Wasserstein metric for the original 1D Kac's model arXiv

M Hauray - arXiv preprint arXiv:1512.01986, 2015 - arxiv.org

Abstract: We study here a very popular 1D jump model introduced by Kac: it consists of $ N $

velocities encountering random binary collisions at which they randomly exchange energy.

We show the uniform (in $ N $) exponential contractivity of the dynamics in a non-standard ...

On the Wasserstein-Fisher-Rao metric

FX Vialard - MATH ON THE ROCKS - researchgate.net

Abstract This note gives a summary of the presentation that I gave at the workshop on shape

analysis1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to

measures that have different total masses. This generalization enjoys most of the ...

Sliced Wasserstein Kernels for Probability Distributions arXiv

S Kolouri, Y Zou, GK Rohde - arXiv preprint arXiv:1511.03198, 2015 - arxiv.org

Abstract: Optimal transport distances, otherwise known as Wasserstein distances, have

recently drawn ample attention in computer vision and machine learning as a powerful

discrepancy measure for probability distributions. The recent developments on alternative ...

2016 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) Book Series: IEEE Conference on Computer Vision and Pattern Recognition Pages: 5258-5267 Published: 2016

An augmented Lagrangian approach to Wasserstein gradient flows and applications

JD Benamou, G Carlier, M Laborde - 2015 - hal.archives-ouvertes.fr

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ...

ESAIM: PROCEEDINGS AND SURVEYS, June 2016, Vol. 54, p. 1-17

] Learning in Wasserstein Space

J Ye - personal.psu.edu

ABSTRACT Learning from probability measures is an emerging problem that has potential

benefiting multiple domains. Different from previous computational learning concentrated on

neural representations and parametric statistical models, my research focuses on ...

Modified October 1, 2017 Penn State Information and Technology

MR3442190 Le Gouic, Thibaut; Loubes, Jean-Michel Barycenter in Wasserstein spaces: existence and consistency. Geometric science of information, 104–108, Lecture Notes in Comput. Sci., 9389, Springer, Cham, 2015. (Reviewer: Sławomir Kolasiński) 60B05 (49Q20 60B10 62H11 94A15)

Barycenter in Wasserstein Spaces: Existence and Consistency

T Le Gouic, JM Loubes - Geometric Science of Information, 2015 - Springer

Abstract We study barycenters in the Wasserstein space P_p(E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure ℙ on P_p(E)

as its Fréchet mean. The paper establishes its existence and states consistency with ...Fuzzy clustering of distribution-valued data using an adaptive L 2 Wasserstein distance IEEE

FAT de Carvalho, A Irpino… - Fuzzy Systems (FUZZ-IEEE …, 2015 - ieeexplore.ieee.org

Abstract—In this paper, a fuzzy c-means algorithm based on an adaptive L2-Wasserstein

distance for histogram-valued data is proposed. The adaptive distance induces a set of

weights associated with the components of histogram-valued data and thus of the ...

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

Peer-reviewed
Barycenter in Wasserstein spaces: Existence and consistency
Authors:Le Gouic T., Loubes J.-M., 2nd International Conference on Geometric Science of Information, GSI 2015
Article, 2015
Publication:Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 9389, 2015, 104
Publisher:2015

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

arXiv

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

Abstract: The curvature-dimension condition is a generalization of the Bochner inequality to

weighted Riemannian manifolds and general metric measure spaces. It is now known to be

equivalent to evolution variational inequalities for the heat semigroup, and quadratic ...

Accelerated Discrete Distribution Clustering under Wasserstein Distance ResearchGate Sep 2015

In a variety of research areas, the bag of weighted vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich-Wasserstein metric.

arXive 2015

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps pdf

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2015 - hal-pjse.archives-ouvertes.fr

Abstract This paper is concerned by the study of barycenters for random probability

measures in the Wasserstein space. Using a duality argument, we give a precise

characterization of the population barycenter for various parametric classes of random ...

[PDF] Problemes d'adéquations entre distributions: une approche par un modele de déformations et la distance de Wasserstein.

H Lescornel, E del Barrio, JM Loubes - papersjds15.sfds.asso.fr

1 INRIA Saclay, 1 rue Honoré d'Estienne d'Orves, 91 120 Palaiseau.

helene.lescornel@inria.fr 2 Universitad de Valladolid, Facultad de Sciencas, C/ Prado de la Magdalena

s/n, 47005 Valladolid, ESPAGNE. tasio@eio.uva.es 3 Institut de Mathématiques de ...

<——2015————2015—— 20—

基于 Wasserstein 距离和改进 K-medoids 聚类的风电/光伏经典场景集生成算法

[ Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and Revised K-methods Clusters ]

WANG Qun, DONG Wenlue, YANG Li

王群，董文略，杨莉 - 中国电机工程学报, 2015

On some non linear evolution systems which are perturbations of Wasserstein gradient flows arXiv

M Laborde - arXiv preprint arXiv:1506.00126, 2015 - arxiv.org

Abstract: This paper presents existence and uniqueness results for a class of parabolic

systems with non linear diffusion and nonlocal interaction. These systems can be viewed as

regular perturbations of Wasserstein gradient flows. Here we extend results known in the ...

On Wasserstein Barycenters and MMOSPA Estimation - IEEE Journals ...

by M Baum - ‎2015 Cited by 12- ‎ - ‎Related articles

Mar 4, 2015 - Abstract: The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for example, suggest the best ...

calable Bayes via Barycenter in Wasserstein Space arXiv

S Srivastava, C Li, DB Dunson - arXiv preprint arXiv:1508.05880, 2015 - arxiv.org

Abstract: We propose a novel approach WASP for Bayesian inference when massive size of

the data prohibits posterior computations. WASP is estimated in three steps. First, data are

divided into smaller computationally tractable subsets. Second, posterior draws of ...

Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in higher dimension arXiv

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1503.06097, 2015 - arxiv.org

Abstract: This work is concerned with the quasineutral limit of the Vlasov-Poisson system in

two and three dimensions. We justify the formal limit for very small but rough perturbations of

analytic initial data, generalizing the results of\ cite {HI} to higher dimension.

Quasineutral limit for Vlasov-Poisson via ... - NASA/ADS

https://ui.adsabs.harvard.edu › abs › abstract

by D Han-Kwan · 2015 · Cited by 23 — We justify the formal limit for very small but rough perturbations of analytic initial ... Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in ...

MR3399536 Pending Jin, Chunyin Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space. Nonlinear Anal. 128 (2015), 412–422. 35Q31 (35B30 35L45 76N10)

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

C Jin - Nonlinear Analysis: Theory, Methods & Applications, 2015 - Elsevier

Abstract We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the ...

Learning with a Wasserstein Loss arXiv

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - arXiv preprint arXiv: …, 2015 - arxiv.org Advances in Neural …, 2015 -

Abstract: Learning to predict multi-label outputs is challenging, but in many problems there is

a natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The ...

Cited by 54

Learning with a Wasserstein Loss - Poggio Lab - MIT

Learning with a Wasserstein Loss - CSAIL People - MIT

Evolution variational inequality and Wasserstein control in variable curvature context arXiv

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

Abstract: In this note we continue the analysis of metric measure space with variable ricci

curvature bounds. First, we study $(\ kappa, N) $-convex functions on metric spaces where

$\ kappa $ is a lower semi-continuous function, and gradient flow curves in the sense of a ...

Learning with a Wasserstein loss

C Frogner, C Zhang, H Mobahi, M Araya… - Advances in Neural …, 2015 - papers.nips.cc

Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The …

Geodesic PCA in the Wasserstein space by Convex PCA

J Bigot, R Gouet, T Klein, A López - 2015 - math.u-bordeaux1.fr

Abstract We introduce the method of Geodesic Principal Component Analysis (GPCA) on the

space of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard ...

Nonpositive curvature, the variance functional, and the Wasserstein barycenter arXiv

<—-2015— —————2015- ————30—

YH Kim, B Pass - arXiv preprint arXiv:1503.06460, 2015 - arxiv.org

Abstract: This paper connects nonpositive sectional curvature of a Riemannian manifold with

the displacement convexity of the variance functional on the space $ P (M) $ of probability

measures over $ M $. We show that $ M $ has nonpositive sectional curvature and has ...

All 2 versions [PDF] arxiv.org

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test arXiv

E Del Barrio, L Hélène, L Jean-Michel - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

Abstract: We propose a study of a distribution registration model for general deformation

functions. In this framework, we provide estimators of the deformations as well as a

goodness of fit test of the model. For this, we consider a criterion which studies the Fr {\'e} ...

Limit laws of the empirical Wasserstein distance: Gaussian distributions arXiv

T Rippl, A Munk, A Sturm - arXiv preprint arXiv:1507.04090, 2015 - arxiv.org

Abstract: We derive central limit theorems for the Wasserstein distance between the

empirical distributions of Gaussian samples. The cases are distinguished whether the

underlying laws are the same or different. Results are based on the (quadratic) Fr\'echet ...

Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data arXiv

E Anderes, S Borgwardt, J Miller - arXiv preprint arXiv:1507.07218, 2015 - arxiv.org

Abstract: Wasserstein barycenters correspond to optimal solutions of transport problems for

several marginals, and as such are at the core of applications ranging from economics to

statistics and computer science. The corresponding theory for data in the form of ...

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure arXiv

D Loibl, D Matthes, J Zinsl - arXiv preprint arXiv:1507.05507, 2015 - arxiv.org

Abstract: We prove the global-in-time existence of nonnegative weak solutions to a class of

fourth order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with ...

An Algorithmic Approach to Compute Principal Geodesics in the Wasserstein Space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015 - arxiv.org

Abstract: We consider in this work the space of probability measures P (X) on a Hilbert space

X endowed with the 2-Wasserstein metric. Given a family of probability measures in P (X),

we propose an algorithm to compute curves that summarize efficiently that family in the 2- ...
[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - Preprint, 2015

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

MR3453299 Döbler, Christian New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods. ALEA Lat. Am. J. Probab. Math. Stat. 12 (2015), no. 2, 863–902. (Reviewer: N. C. Weber) 60F05 (60G50)

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

Abstract: We prove abstract bounds on the Wasserstein and Kolmogorov distances between

non-randomly centered random sums of real iid random variables with a finite third moment

and the standard normal distribution. Except for the case of mean zero summands, these ...

$ L^ p $-Wasserstein distances on state and quasi-state spaces of $ C^* $-algebras

D Zaev - arXiv preprint arXiv:1505.06061, 2015 - arxiv.org

Abstract: We construct an analogue of the classical $ L^ p $-Wasserstein distance for the

state space of a $ C^* $-algebra. Given an abstract Lipschitz gauge on a $ C^* $-algebra $\

mathcal {A} $ in the sense of Rieffel, one can define the classical $ L^ p $-Wasserstein ...

[PDF] Regularizing Image Intensity Transformations Using the Wasserstein Metric

M Oskarsson - maths.lth.se

Abstract. In this paper we direct our attention to the problem of discretization effects in

intensity transformations of images. We propose to use the Wasserstein metric (also known

as the Earth mover distance) to bootstrap the transformation process. The Wasserstein ...

2015 eBook
From large deviations to Wasserstein gradient flows in multiple dimensions

Authors:Matthias Erbar, Jan Maas, D. R. Michiel Renger, Weierstraß-Institut für Angewandte Analysis und Stochastik
Summary:We study the large deviation rate functional for the empirical measure of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer [ADPZ11] that this functional is asymptotically equivalent (in the sense of 񖉖񖌠-convergence) to the Jordan-Kinderlehrer-Otto functional arising in the Wasserstein gradient flow structure of the Fokker-Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof in [DLR13] relies on regularity properties of optimal transport maps that are restricted to one dimension. In this note we present a new proof of the upper bound, thereby generalising the result of [ADPZ11] to arbitrary dimensionsShow more
eBook, 2015
English
Publisher:Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V, Berlin, 2015
From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - arXiv preprint arXiv:1505.05712, 2015 - arxiv.org

Abstract: We study the large deviation rate functional for the empirical distribution of

independent Brownian particles with drift. In one dimension, it has been shown by Adams,

Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\ ...

<—-2015——————2015—— -40—

Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - Information Processing in Medical …, 2015 - Springer

Abstract Brain morphometry study plays a fundamental role in medical imaging analysis and

diagnosis. This work proposes a novel framework for brain cortical surface classification

using Wasserstein distance, based on uniformization theory and Riemannian optimal ...

DF] A Hitchhiker's guide to Wasserstein distances

G Basso - 2015 - n.ethz.ch

The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions

we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric

space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a ...

On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests

A Ramdas, N Garcia, M Cuturi - arXiv preprint arXiv:1509.02237, 2015 - arxiv.org

Abstract: Nonparametric two sample or homogeneity testing is a decision theoretic problem

that involves identifying differences between two random variables without making

parametric assumptions about their underlying distributions. The literature is old and rich, ...

Wasserstein Training of Boltzmann Machines

G Montavon, KR Müller, M Cuturi - arXiv preprint arXiv:1507.01972, 2015 - arxiv.org

Abstract: The Boltzmann machine provides a useful framework to learn highly complex,

multimodal and multiscale data distributions that occur in the real world. The default method

to learn its parameters consists of minimizing the Kullback-Leibler (KL) divergence from ...

Generalized Wasserstein distance and weak convergence of sublinear expectations

X Li, Y Lin - arXiv preprint arXiv:1505.04954, 2015 - arxiv.org

Abstract: In this paper, we define the generalized Wasserstein distance for sets of Borel

probability measures and demonstrate that the weak convergence of sublinear expectations

can be characterized by means of this distance.

Scalable Bayes via Barycenter in Wasserstein Space

14 citations*

2015 ARXIV: METHODOLOGY

Wasserstein continuity of entropy and outer bounds for interference channels

Y Polyanskiy, Y Wu - arXiv preprint arXiv:1504.04419, 2015 - arxiv.org

Abstract: It is shown that under suitable regularity conditions, differential entropy is a

Lipschitz functional on the space of distributions on $ n $-dimensional Euclidean space with

respect to the quadratic Wasserstein distance. Under similar conditions,(discrete) ...

2015 see 2013 Peer-reviewed
Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates
Author:Kazumasa Kuwada
Summary:The duality in Bakry-Émery’s gradient estimates and Wasserstein controls for heat distributions is extended to that in refined estimates in a high generality. As a result, we find an equivalent condition to Bakry-Ledoux’s refined gradient estimate involving an upper dimension bound. This new condition is described as a L 2 -Wasserstein control for heat distributions at different times. The L p -version of those estimates are studied on Riemannian manifolds via coupling methodShow more
Article, 2015
Publication:Calculus of Variations and Partial Differential Equations, 54, 201509, 127
Publisher:2015

Existence and consistency of Wasserstein barycenters

TL Gouic, JM Loubes - arXiv preprint arXiv:1506.04153, 2015 - arxiv.org

Abstract: In this paper, based on the Fr\'echet mean, we define a notion of barycenter

corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein

barycenters of random distributions defined on a geodesic space (E, d). We also prove the ...

version 2 2016

2015 arXiv150302533C

Cuturi, Marco; Peyré, Gabriel; Rolet, Antoine

A Smoothed Dual Approach for Variational Wasserstein Problems

Abstract: Variational problems that involve Wasserstein distances have been recently

proposed as a mean to summarize and learn from probability measures. Despite being

conceptually simple, such problems are computationally challenging because they ...

<——2015————2015- ———50—

2015arXiv150300113D

Dedecker, Jérôme; Merlevède, Florence

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $alpha$-dependent sequences

Abstract: We study the Wasserstein distance of order 1 between the empirical distribution

and the marginal distribution of stationary $\ alpha $-dependent sequences. We prove some

moments inequalities of order p for any p $\ ge $1, and we give some conditions under ...

2015arXiv150206216P

Peyré, Gabriel

Entropic Wasserstein Gradient Flows

Abstract: This article details a novel numerical scheme to approximate gradient flows for

optimal transport (ie Wasserstein) metrics. These flows have proved useful to tackle

theoretically and numerically non-linear diffusion equations that model for instance porous ...

2015arXiv150202336B

Bhattacharya, Anirban; Pati, Debdeep

Bernstein von Mises Theorems in Wasserstein distance

Abstract: We study the Bernstein von-Mises (BvM) phenomenon in Gaussian process

regression models by retaining the leading terms of the induced Karhunen--Loeve

expansion. A recent related result by Bontemps, 2011 in a sieve prior context necessitates ...

2015 see 2017 arXiv150104437K

2015arXiv150107820B

Berman, Robert J.; Onnheim, Magnus

Propagation of chaos, Wasserstein gradient flows and toric Kahler-Einstein metrics

Abstract: Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a

general non-equlibrium statistical mechanics model in Euclidean space consisting of the

stochastic gradient flow of a given quasi-convex N particle interaction energy. We show ... MR

Kinderlehrer, David; Monsaingeon, Léonard; Xu, Xiang

A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations

Abstract: The Poisson-Nernst-Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and ...

2015arXiv150101498J

Jourdain, Benjamin; Reygner, Julien

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

Abstract: This article is dedicated to the study of diagonal hyperbolic systems in one space

dimension, with cumulative distribution functions, or more generally nonconstant monotonic

bounded functions, as initial data. Under a uniform strict hyperbolicity assumption on the ...

MR3284787 Indexed Lee, Kooktae; Halder, Abhishek; Bhattacharya, Raktim Performance and robustness analysis of stochastic jump linear systems using Wasserstein metric. Automatica J. IFAC 51 (2015), 341–347. 93E03 (93B35)

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

Abstract This paper focuses on the performance and robustness analysis of stochastic jump

linear systems. In the presence of stochastic jumps, state variables evolve as random

process, with associated time varying probability density functions. Consequently, system ...
Cited by 27 Related articles All 9 versions

Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

Abstract We study a linear fractional Fokker–Planck equation that models non-local diffusion

in the presence of a potential field. The non-locality is due to the appearance of the

'fractional Laplacian'in the corresponding PDE, in place of the classical Laplacian which ...

2015 see 2014 Peer-reviewed
On local well-posedness of the thin-film equation via the Wasserstein gradient flow
Author:Ehsan Kamalinejad
Summary:A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on the Wasserstein space is proved. The proofs are based on a relaxation of displacement convexity in the Wasserstein space and can be applied to a family of higher order energy functionals which are not displacement convex in the standard sense. As the result a local well-posedness of the corresponding nonlinear evolution equations including the thin-film equation and the quantum drift diffusion equation are provedShow more
Article, 2015
Publication:Calculus of Variations and Partial Differential Equations, 52, 201503, 547
Publisher:2015

Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains pdf

J Solomon, F de Goes, PA Studios… - … on Graphics (Proc. …, 2015 - iip.ist.i.kyoto-u.ac.jp

Abstract This paper introduces a new class of algorithms for optimization problems involving

optimal transportation over geometric domains. Our main contribution is to show that optimal

transportation can be made tractable over large domains used in graphics, such as ...

"Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains." pdf

SIGGRAPH 2015, Los Angeles.

(supplemental document; code; slides)

Solomon, Justin, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas.

ZCM DL

<——2015———2015———60—

Wassersen continuity of entropy and outer bounds for interference ...

by Y Polyanskiy - ‎2015 - ‎Cited by 49 - ‎Related articles

Apr 17, 2015 - Under similar conditions, (discrete) Shannon entropy is shown to be ... with respect to Ornstein's -distance (Wasserstein distance corresponding ...

MR3535537 Ma, Ming; Lei, Na; Su, Kehua; Zhang, Junwei; Wen, Chengfeng; Cui, Li; Fan, Xin; Gu, Xianfeng Surface-based shape classification using Wasserstein distance. Geom. Imaging Comput. 2 (2015), no. 4, 237–255. 49Q20 (53A05 68T10 68U05)

Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical imaging. In this work, we proposes a novel method for shape classification of brain's hippocampus using Wasserstein distance based on optimal mass transport theory. In comparison with the conventional method based on Monge–Kantorovich theory, our proposed method employs Monge–Brenier theory for the computation of the optimal mass transport map, which remarkably ameliorates the efficiency by reducing computational …

On the Lagrangian Description of Absolutely Continuous Curves in the ...

MR3436238 Amsaad, Mohamed; Tudorascu, Adrian On the Lagrangian description of absolutely continuouscurves in the Wasserstein space on the line; well-posedness for the continuity equation. Indiana Univ. Math. J. 64 (2015), no. 6, 1835–1877. (Reviewer: Alpár Richárd Mészáros) 35L65 (35B30 35F20 37C10 37J99 49Q20 60A10)

Whereas each such curve admits a Lagrangian description as a well-defined flow ... the Wasserstein Space on the Line; Well-Posedness for the Continuity Equation ... of absolutely continuous curves of probability measures on the real line is ...

MR3434297 Fraser, Jonathan M. First and second moments for self-similar couplings and Wasserstein distances. Math. Nachr. 288 (2015), no. 17-18, 2028–2041. (Reviewer: Balázs Bárány) 28A33 (28A80 42A85 60B05)

First and second moments for self‐similar couplings and Wasserstein ...

by JM Fraser - ‎2015 - ‎Cited by 5 - ‎Related articles

Jun 29, 2015 - We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves ...

MR3434206 Erbar, Matthias; Maas, Jan; Renger, D. R. Michiel From large deviations to Wassersteigradient flows in multiple dimensions. Electron. Commun. Probab. 20 (2015), no. 89, 12 pp. 60F10 (35A15 35B27 35Q84 35R60 60B10)

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma $-convergence) to the Jordan-Kinderlehrer-Otto functional arising in the Wasserstein gradient flow structure of the Fokker-Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper …

MR3424906 Kloeckner, Benoît R.; Lopes, Artur O.; Stadlbauer, Manuel Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps. Nonlinearity 28 (2015), no. 11, 4117–4137. (Reviewer: Diogo Pinheiro) 37A50 (49K45 49Q10)

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

… While we stick here to the more standard case of Hölder potentials, we take a more geomet- ric point of view that allows us first to handle a much broader family of dynamical systems and second to derive a number of corollaries. Namely, the contraction in the Wasserstein metric easily implies a spectral gap and decay of correlations, but also the stability results alluded to above. Our main result and method of proof are also similar to a recent result of the third named author for some random Markov shifts [Sta13]; again the present result is less general in some aspects and more …

MR3423268 Carlier, Guillaume (F-PARIS9-A); Oberman, Adam (3-MGL); Oudet, Edouard (F-GREN-LJK)

Numerical methods for matching for teams and Wasserstein barycenters. (English summary)

ESAIM Math. Model. Numer. Anal. 49 (2015), no. 6, 1621–1642. 90C05 (49M29 49Q20)

Numerical methods for matching for teams and Wasserstein barycenters

by G Carlier - ‎2015 - ‎Cited by 47 - ‎Related articles

Numerical methods for matching for teams and Wasserstein barycenters. Guillaume Carlier¹, Adam Oberman² and Edouard Oudet³. ¹ CEREMADE, UMR ...

MR3413589 Pending Peyré, Gabriel Entropic approximation of Wasserstein gradient flows. SIAM J. Imaging Sci. 8 (2015), no. 4, 2323–2351. 94A08 (49Q20 68U10 90C25 90C48)

Entropic Wasserstein Gradient Flows

by G Peyré - ‎2015 - ‎Cited by 36 - ‎Related articles

Feb 22, 2015 - Entropic Wasserstein Gradient Flows. ... These gradient flows define a suitable notion of weak solutions for these evolutions and they can be approximated in a stable way using discrete flows. These discrete flows are implicit Euler time stepping according to the Wasserstein metric.

2015

MR3383341 Fournier, Nicolas; Guillin, Arnaud; On the rate of convergence in Wasserstein distance of the empirical measure. Probab. Theory Related Fields 162 (2015), no. 3-4, 707–738.

On the rate of convergence in Wasserstein distance of ... - Springer Link

by N Fournier - ‎2015 - ‎Cited by 209 - ‎Related articles

We are interested in the rate of convergence of $\mu _N$ to $\mu $, when measured in the Wasserstein distance of order $p>0$. We provide some satisfying ...

On the rate of convergence in Wasserstein distance of the ...

Distribution function estimates by Wasserstein metric and Bernstein ...

by N Fournier · 2015 · Cited by 497 — On the rate of convergence in Wasserstein distance of the empirical measure ... Let \mu _N be the empirical measure associated to a N-sample of a given ... Concerning concentration estimates, only few results are available.

MR3377899 Wu, Zong-min; Tian, Zheng; Distribution function estimates by Wasserstein metric and Bernstein approximation for C−1 functions. Appl. Math. J. Chinese Univ. Ser. B 30 (2015), no. 2, 141–150.

by Z Wu - ‎2015 - ‎Cited by 1 - ‎Related articles

Jun 9, 2015 - The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presente

ein metric in our study. … the statistical distance called Wasserstein metric [1] for density …

Save Cite Cited by 2 Related articles All 5 versions

ein metric in our study. … the statistical distance called Wasserstein metric [1] for density …

<---2015——2015- ————70—

MR3356496 Pending Disser, Karoline; Liero, Matthias On gradient structures for Markov chains and the passage to Wasserstein gradient flows. Netw. Heterog. Media 10 (2015), no. 2, 233–253. 35K10 (35K20 35Q84 37L05 49Q20 60J27 65M08)

On gradient structures for Markov chains and the passage to ...

by K Disser - ‎2015 - ‎Cited by 9 - ‎Related articles

We study the approximation of Wasserstein gradient structures by their finite-dimensional analog. We show that simple finite-volume discretizations of the linear ...

MR3352761 Hynd, Ryan; Kim, Hwa Kil Value functions in the Wasserstein spaces: finite time horizons. J. Funct. Anal. 269 (2015), no. 4, 968–997. (Reviewer: Luca Granieri) 49Q20 (35D40 35F25 49L25)

Value functions in the Wasserstein spaces: finite time horizons ...

by R Hynd - ‎2015 - ‎Cited by 5 - ‎Related articles

Aug 15, 2015 - We study analogs of value functions arising in classical mechanics in the space of probability measures endowed with the Wasserstein metric ...

2015 see 2017
Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support
Authors:Ye, Jianbo (Creator), Wu, Panruo (Creator), Wang, James Z. (Creator), Li, Jia (Creator)
Summary:In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich-Wasserstein metric. D2-clustering has a severe scalability issue, the bottleneck being the computation of a centroid distribution, called Wasserstein barycenter, that minimizes its sum of squared distances to the cluster members. In this paper, we develop a modified Bregman ADMM approach for computing the approximate discrete Wasserstein barycenter of large clusters. In the case when the support points of the barycenters are unknown and have low cardinality, our method achieves high accuracy empirically at a much reduced computational cost. The strengths and weaknesses of our method and its alternatives are examined through experiments, and we recommend scenarios for their respective usage. Moreover, we develop both serial and parallelized versions of the algorithm. By experimenting with large-scale data, we demonstrate the computational efficiency of the new methods and investigate their convergence properties and numerical stability. The clustering results obtained on several datasets in different domains are highly competitive in comparison with some widely used methods in the corresponding areasShow more
Downloadable Archival Material, 2015-09-30
Undefined
Publisher:2015-09-30

MR3345406 Schmitzer, Bernhard; Schnörr, Christoph Globally optimal joint image segmentation and shape matching based on Wasserstein modes. J. Math. Imaging Vision 52 (2015), no. 3, 436–458. 94A08

Globally Optimal Joint Image Segmentation and Shape Matching ...

by B Schmitzer - ‎2015 - ‎Cited by 8 - ‎Related articles

Jul 1, 2015 - Globally Optimal Joint Image Segmentation and Shape Matching ... A functional for joint variational object segmentation and shape matching is developed. ..... by computing short signatures for database vectors while roughly ...

MR3339225 Pending Gentil, Ivan Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold. Potential Anal. 42 (2015), no. 4, 861–873. 58J65 (53B21 58J35)

Dimensional Contraction in Wasserstein Distance for Diffusion ...

by I Gentil - ‎2015 - ‎Cited by 5 - ‎Related articles

Jan 17, 2015 - Dimensional Contraction in Wasserstein Distance for Diffusion Semigroups on a ... It is proved by using a dimensional coercive estimate for the ...

MR3338654 Barbour, A. D.; Gan, H. L.; Xia, A. Stein factors for negative binomial approximation in Wasserstein distance. Bernoulli 21 (2015), no. 2, 1002–1013. (Reviewer: Fraser Alexander Daly) 60E05 (62E10 62P10)

Stein factors for negative binomial approximation in Wasserstein ...

by AD Barbour - ‎2015 - ‎Cited by 11 - ‎Related articles

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the ...

MR3338645 Pending Boissard, Emmanuel; Le Gouic, Thibaut; Loubes, Jean-Michel Distribution's template estimate with Wasserstein metrics. Bernoulli 21 (2015), no. 2, 740–759. 60A10 (60E05

Distribution's template estimate with Wasserstein metrics - Project Euclid

by E Boissard - ‎2015 - ‎Cited by 43 - ‎Related articles

Distribution's template estimate with Wasserstein metrics. Emmanuel Boissard, Thibaut Le Gouic, and Jean-Michel Loubes ...

MR3325471 Pending Duong, Manh Hong Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation. Asymptot. Anal. 92 (2015), no. 1-2, 85–106. 35K57 (35B27 35K15 49J45)

Asymptotic equivalence of the discrete variational functional and a rate ...

by MH Duong - ‎2015 - ‎Related articles

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium ...

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

MH Duong - Asymptotic Analysis, 2015 - content.iospress.com

In this paper, we study the Wasserstein gradient flow structure of the porous medium

equation restricted to q-Gaussians. The JKO-formulation of the porous medium equation

gives a variational functional K h, which is the sum of the (scaled-) Wasserstein distance and …

A geometric study of Wasserstein spaces: ultrametrics - Hal

MR3333967 Pending Kloeckner, Benoît R. A geometric study of Wasserstein spaces: ultrametrics. Mathematika 61 (2015), no. 1, 162–178. 30L05 (37F35 49Q20)

by B Kloeckner - ‎2015 - ‎Cited by 7 - ‎Related articles

Jan 10, 2014 - Abstract. — We study the geometry of the space of measures of a compact ultrametric space X, endowed with the Lp Wasserstein distance from optimal transportation. We show that the power p of this distance makes this Wasserstein space affinely isometric to a convex subset of l1.

MR3317894 Irpino, Antonio; Verde, Rosanna Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein distance. Adv. Data Anal. Classif. 9 (2015), no. 1, 81–106. 62J05 (46F10 62G30)

Linear regression for numeric symbolic variables: a least squares ...

by A Irpino - ‎2015 - ‎Cited by 9 - ‎Related articles

Linear regression for numeric symbolic variables: a least squares approach based on ... We propose solving the linear regression problem by starting from a ...

Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein Distance

A Irpino, R Verde - Advances in Data Analysis and Classification, 2015 - Springer

In this paper we present a new linear regression technique for distributional symbolic variables,

ie, variables whose realizations can be histograms, empirical distributions or empirical estimates...

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Wang, Qun; Dong, Wenlue

Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering

2015 v. 35 no. 11 pp. 2654–2661

Journal Article

<——2015—————2015———— -80 —

MR3304898 Pending Durmus, Alain; Moulines, Éric Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm. Stat. Comput. 25 (2015), no. 1, 5–19. 60J99 (62M05)

Quantitative bounds of convergence for geometrically ergodic Markov ...

by A Durmus - ‎2015 - ‎Cited by 8 - ‎Related articles

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis Adjusted Langevin ...

MR3304897 Indexed Haario, Heikki Introduction to "Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm'' by A. Durmus, É. Moulines [MR3304898]. Stat. Comput. 25 (2015), no. 1, 3. 60J99 (62M05)

Introduction to "Quantitative bounds of convergence for geometrically ...

Introduction to "Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis ...

MR3311904 Pending Kamalinejad, Ehsan On local well-posedness of the thin-film equation via the sserstein gradient flow. Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 547–564. 49Q20 (35B30 35K25 35K59 49J52 49K40 76A20)

On local well-posedness of the thin-film equation via the Wasserstein ...

by E Kamalinejad - ‎2015 - ‎Related articles

The best-studied example is the thin-film equation \(\partial _t u =- \nabla \cdot (u ... Hence the gradient flow of the Dirichlet energy is locally well-posed and the ...

MR3306430 Agulló-Antolín, Marina; Cuesta-Albertos, J. A.; Lescornel, Hélène; Loubes, Jean-Michel A parametric registration model for warped distributions with Wasserstein's distance. J. Multivariate Anal. 135 (2015), 117–130. 62H10 (62F10)

A parametric registration model for warped ... - Science Direct

by M Agulló-Antolín - ‎2015 - ‎Cited by 10 - ‎Related articles

In this paper we focus on the issue of registering measures warped by a parametric deformation operator. When confronted to large data sample, the data may ...

[PDF]

MR3300482 Bonneel, Nicolas; Rabin, Julien; Peyré, Gabriel; Pfister, Hanspeter Sliced and Radon Wasserstein barycenters of measures. J. Math. Imaging Vision 51 (2015), no. 1, 22–45. 94A08

Sliced and Radon Wasserstein Barycenters of Measures | SpringerLink

by N Bonneel - ‎2015 - ‎Cited by 76 - ‎Related articles

This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures.

MR3314482 Pending Dedecker, Jérôme; Fischer, Aurélie; Michel, Bertrand Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one. Electron. J. Stat. 9 (2015), 234–265. 62G05 (62C20)

Improved rates for Wasserstein deconvolution with ... - Project Euclid

by J Dedecker - ‎2015 - ‎Cited by 2 - ‎Related articles

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one. Jérôme Dedecker, Aurélie Fischer, and Bertrand Michel ...

MR3302526 Pending Hynd, Ryan; Kim, Hwa Kil Infinite horizon value functions in the Wasserstein spaces. J. Differential Equations 258 (2015), no. 6, 1933–1966. 49L20 (35D40 35F21)

Infinite horizon value functions in the Wasserstein spaces ...

by R Hynd - ‎2015 - ‎Related articles

Mar 15, 2015 - In our prior study [18], we considered value functions on a finite horizon in the Wasserstein spaces. This current work addresses the analogous ...MR3294365 Bowles, Malcolm; Agueh, Martial Weak solutions to a fractional Fokker-Planck equation via splitting and Wasserstein gradient flow. Appl. Math. Lett. 42 (2015), 30–35. 35R11 (35D30 35Q84 82C31)

Peer-reviewed
Distribution???s template estimate with Wasserstein metrics
Authors:Emmanuel Boissard, Thibaut Le Gouic, Jean-Michel Loubes
Summary:In this paper, we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a centered random operator, then the barycenter enables to recover this distribution templateShow more

Posterior contraction in Gaussian process regression using Wasserstein approximations.

by A Bhattacharya - ‎2015 - ‎Cited by 1 - ‎Related articles

Feb 9, 2015 - ... posterior rates of contraction in Gaussian process regression with ... Our argument relies on developing a Gaussian approximation to the ...

[PDF]

Posterior contraction in Gaussian process regression using using Wasserstein approximations.

by A Bhattacharya - ‎2015 - ‎Cited by 1 - ‎Related articles

Oct 2, 2015 - We study posterior rates of contraction in Gaussian process regression with unbounded covariate domain. Our argument relies on developing a ...

FUSION 2015 SPECIAL SESSIONS July 6-9, Washington, DC

FUSION 2015 : SS Data Mining and Knowledge Discover - Fusion ...

Fusion 2015 » Special Sessions

SS5: Averaging Measures: Wasserstein Barycenters, MMOSPA, and more

Description: Summarizing the information encoded in (one or more) probability measures is a fundamental problem in many areas such as signal processing, machine learning, computer vision, and data fusion. In this context, the concept of an “average” measure has recently gained significant interest: Wasserstein Barycenters are used, for example, for texture mixing and fusing (empirical) probability densities. In multi-target tracking with missing target identities, the mean square error (MSE) cannot be used to calculate expected target states. Hence, instead of the MSE the Mean Optimum Subpattern Assignment (MOSPA) distance is employed, which is closely related to the Wasserstein distance. This leads to Minimum MOPSPA estimates instead of MMSE estimates. This Special Session addresses all recent research results that involve the calculation of an “average” of (one or more) probability measures in all its variants. This includes both new theoretical results and applications.

Organizers: Marcus Baum, Karlsruhe Institute of Technology; Peter Willett; and Uwe Hanebeck, Karlsruhe Institute of Technology.

<——2015—————2015————— -90 —

[PDF]

Fast Discrete Distribution Clustering Using Wasserstein Barycenter ...

by J Ye - ‎2015 - ‎Cited by 30 - ‎Related articles

1. Fast Discrete Distribution Clustering Using. Wasserstein Barycenter with Sparse Support. Jianbo Ye, Panruo Wu, James Z. Wang and Jia Li Senior Member, ...

[PDF] uclouvain.be

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal

assignment map of clients to these facilities. This problem arises in various contexts in

decision mathematics such as, for instance, location theory in operational research and the …

Related articles All 2 versions
University of Victoria

Data-driven Distributionally Robust Optimization Using the ...

May 19, 2015 - Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations. Authors: ...

by PM Esfahani - ‎2015 - ‎Cited by 425 - ‎Related articles

Cited by 19 Related articles

Distribution function estimates by Wasserstein metric and Bernstein approximation for C −1 functions
Authors:Zong-min Wu, Zheng Tian
Summary:The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L 1 norm of the Bernstein approximation for monotone C −1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distanceShow more
Article, 2015

A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations

David Kinderlehrer, Léonard Monsaingeon, Xiang Xu

2015

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and nonlinear diffusion. The proof of the main results relies on the derivation of extra estimates based on the flow interchange technique developed by Matthes, McCann, and Savaré.

Comments:	updated version (proof of the main theorem fixed), accepted in ESAIM: Control, Optimisation and Calculus of Variations
Subjects:	Analysis of PDEs (math.AP)
MSC classes:	35K15, 35K55, 35K65
Cite as:	arXiv:1501.04437 [math.AP]
	(or arXiv:1501.04437v3 [math.AP] for this version)

Submission history

From: Leonard Monsaingeon Mr. [view email]

[v1] Mon, 19 Jan 2015 10:08:58 UTC (39 KB)

[v2] Wed, 21 Jan 2015 17:22:32 UTC (42 KB)

[v3] Sun, 6 Sep 2015 10:50:33 UTC (38 KB)

[PDF] Gram-Schmidt-Vaserstein generators for odd sized elementary groups

P Chattopadhyay, RA Rao - arXiv preprint arXiv:1511.08688, 2015 - arxiv.org

The Gram-Schmidt process of LN Vaserstein for making an elementary matrix symplectic

yields a nice set of generators for the odd sized elementary group. Subjects: Commutative

Algebra (math. AC) Cite as: arXiv: 1511.08688 [math. AC](or arXiv: 1511.08688 v1 [math …

Snowflake universality of Wasserstein spaces

A Andoni, A Naor, O Neiman - arXiv preprint arXiv:1509.08677, 2015 - arxiv.org

For $ p\in (1,\infty) $ let $\mathscr {P} _p (\mathbb {R}^ 3) $ denote the metric space of all $ p

$-integrable Borel probability measures on $\mathbb {R}^ 3$, equipped with the

Wasserstein $ p $ metric $\mathsf {W} _p $. We prove that for every $\varepsilon> 0$, every …

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein

distance. Compared to the more classical total variation bounds, the proposed rate of

convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

A geometric study of Wasserstein spaces: ultrametrics

BR Kloeckner - Mathematika, 2015 - cambridge.org

We study the geometry of the space of measures of a compact ultrametric space $ X $,

endowed with the $ L^{p} $ Wasserstein distance from optimal transportation. We show that

the power $ p $ of this distance makes this Wasserstein space affinely isometric to a convex …

<—-2015—2015- ————— 100 ——

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

A wind power/photovoltaic typical scenario set generation algorithm based on wasserstein distance metric and revised k-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and

solar power, power system operations face new challenges as the supply uncertainty

increases dramatically. Scenario analysis is widely used because it explicitly incorporates a …

CITATION] … Engineering, Zhejiang University;; A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and …

Q WANG, W DONG, L YANG - 中国电机工程学报, 2015

On Wasserstein barycenters and MMOSPA estimation

M Baum, PK Willett… - IEEE Signal Processing …, 2015 - ieeexplore.ieee.org

The two title concepts have been evolving rather rapidly, but independent of each other. The

Wasserstein barycenter, on one hand, has mostly made its appearance in image processing

as it can describe a measure of similarity between images. Its minimization might, for …

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to

justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily …

Shape classification using Wasserstein distance for brain morphometry analysis

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - International Conference on …, 2015 - Springer

Brain morphometry study plays a fundamental role in medical imaging analysis and

diagnosis. This work proposes a novel framework for brain cortical surface classification

using Wasserstein distance, based on uniformization theory and Riemannian optimal mass …

2015

On the rate of convergence in Wasserstein distance of the empirical measure

C Frogner, C Zhang, H Mobahi, M Araya… - Advances in neural …, 2015 - papers.nips.cc

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

2015 [PDF] arxiv.org

N Fournier, A Guillin - Probability Theory and Related Fields, 2015 - Springer

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability

distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ,

when measured in the Wasserstein distance of order p> 0 p> 0. We provide some satisfying …

On the rate of convergence in Wasserstein distance of the empirical measure

2015 [PDF] archives-ouvertes.fr

Convolutional wasserstein distances: Efficient optimal transportation on geometric domains

J Solomon, F De Goes, G Peyré, M Cuturi… - ACM Transactions on …, 2015 - dl.acm.org

This paper introduces a new class of algorithms for optimization problems involving optimal

transportation over geometric domains. Our main contribution is to show that optimal

transportation can be made tractable over large domains used in graphics, such as images …

Entropic Approximation of Wasserstein Gradient Flows

Gabriel Peyré

SIAM Journal on Imaging Sciences Vol. 8, No. 4, pp. 2323–23512015

Entropic approximation of Wasserstein gradient flows

G Peyré - SIAM Journal on Imaging Sciences, 2015 - SIAM

This article details a novel numerical scheme to approximate gradient flows for optimal

transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically

and numerically nonlinear diffusion equations that model, for instance, porous media or …

Sliced and radon wasserstein barycenters of measures

N Bonneel, J Rabin, G Peyré, H Pfister - Journal of Mathematical Imaging …, 2015 - Springer

This article details two approaches to compute barycenters of measures using 1-D

Wasserstein distances along radial projections of the input measures. The first method

makes use of the Radon transform of the measures, and the second is the solution of a …

<—-2015—2015—— ——110—

Numerical methods for matching for teams and Wasserstein barycenters

G Carlier, A Oberman, E Oudet - ESAIM: Mathematical Modelling …, 2015 - esaim-m2an.org

Equilibrium multi-population matching (matching for teams) is a problem from mathematical

economics which is related to multi-marginal optimal transport. A special but important case

is the Wasserstein barycenter problem, which has applications in image processing and …

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia - Bernoulli, 2015 - projecteuclid.org

The paper gives the bounds on the solutions to a Stein equation for the negative binomial

distribution that are needed for approximation in terms of the Wasserstein metric. The proofs

are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 …

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

We propose a study of a distribution registration model for general deformation functions. In

this framework, we provide estimators of the deformations as well as a goodness of fit test of

the model. For this, we consider a criterion which studies the Fr {é} chet mean (or …

Wasserstein training of Boltzmann machines

G Montavon, KR Müller, M Cuturi - arXiv preprint arXiv:1507.01972, 2015 - arxiv.org

The Boltzmann machine provides a useful framework to learn highly complex, multimodal

and multiscale data distributions that occur in the real world. The default method to learn its

parameters consists of minimizing the Kullback-Leibler (KL) divergence from training …

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

2015

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

Page 1. Nonlinearity PAPER Contraction in the Wasserstein metric for some Markov chains, and

applications to the dynamics of expanding maps To cite this article: Benoît R Kloeckner et al 2015

Nonlinearity 28 4117 View the article online for updates and enhancements. Related content …

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry–Ledoux's refined gradient estimate involving an upper …

Distribution's template estimate with Wasserstein metrics

E Boissard, T Le Gouic, JM Loubes - Bernoulli, 2015 - projecteuclid.org

In this paper, we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

[HTML] Value functions in the Wasserstein spaces: finite time hhorizons

R Hynd, HK Kim - Journal of Functional Analysis, 2015 - Elsevier

We study analogs of value functions arising in classical mechanics in the space of

probability measures endowed with the Wasserstein metric W p, for 1< p<∞. Our main result

is that each of these generalized value functions is a type of viscosity solution of an …

<—-2015———————2015—— —— 120—

基于 Wasserstein 距离和改进 K-medoids 聚类的风电/光伏经典场景集生成算法

王群，董文略，杨莉 - 中国电机工程学报, 2015 - cqvip.com

随着风电, 光伏等可再生能源发电渗透率的增加, 电力系统运行需要考虑随之而来的不确定性.

场景分析法因为可明确体现不确定性因素的概率特征而被广泛采用, 但是由于大规模场景会降低

随机规划的求解效率, 实用性受到限制. 针对该问题, 提出一种经典场景集生成算法 …

[Chinese Collection of wind power/photovoltaic classic scenarios based on Wasserstein distance and improved K-medoids clustering]

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-

randomly centered random sums of real iid random variables with a finite third moment and

the standard normal distribution. Except for the case of mean zero summands, these bounds …

Barycenter in Wasserstein spaces: Existence and consistency

T Le Gouic, JM Loubes - … Conference on Geometric Science of Information, 2015 - Springer

We study barycenters in the Wasserstein space P _p (E) P p (E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure PP on P _p

(E) P p (E) as its Fréchet mean. The paper establishes its existence and states consistency …

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

[PDF] Modified Arratia flow and Wasserstein diffusion

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1504.00559, 2015 - researchgate.net

Extending previous work [20] by the first author we present a variant of the Arratia flow of a

field of coalescing Brownian motions starting from every point of the unit interval. The

important new feature of the model is that individual particles carry mass which aggregated …

[PDF] Convolutional wasserstein distances

J Solomon, F De Goes, G Peyré, M Cuturi… - ACM Trans … - researchgate.net

This paper introduces a new class of algorithms for optimization problems involving optimal

transportation over geometric domains. Our main contribution is to show that optimal

transportation can be made tractable over large domains used in graphics, such as images …

Regularizing image intensity transformations using the wasserstein metric

[PDF] A Hitchhiker's guide to Wasserstein distances

G Basso - 2015 - n.ethz.ch

The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions

we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric

space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a signed …

M Oskarsson - Scandinavian Conference on Image Analysis, 2015 - Springer

In this paper we direct our attention to the problem of discretization effects in intensity

transformations of images. We propose to use the Wasserstein metric (also known as the

Earth mover distance) to bootstrap the transformation process. The Wasserstein metric gives …

[PDF] Geodesic kriging in the Wasserstein space

R Gouet, A López, JM Ortiz - … of the 17th annual Conference of the …, 2015 - researchgate.net

We introduce the method of Geodesic Kriging for spatially-dependent functional data, not

supported by a linear space. We present the theory for Hadamard metric spaces and provide

more detailed analysis for particular cases such the Hilbert and Wasserstein spaces …

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

<—-2015—2015—— 130 ——

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one

J Dedecker, A Fischer, B Michel - Electronic journal of statistics, 2015 - projecteuclid.org

This paper deals with the estimation of a probability measure on the real line from data

observed with an additive noise. We are interested in rates of convergence for the

Wasserstein metric of order $ p\geq1 $. The distribution of the errors is assumed to be …

[HTML] Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - Journal of Differential Equations, 2015 - Elsevier

We perform a systematic study of optimization problems in the Wasserstein spaces that are

analogs of infinite horizon, deterministic control problems. We derive necessary conditions

on action minimizing paths and present a sufficient condition for their existence. We also …

-Wasserstein distances on state and quasi-state spaces of -algebras

D Zaev - arXiv preprint arXiv:1505.06061, 2015 - arxiv.org

We construct an analogue of the classical $ L^ p $-Wasserstein distance for the state space

of a $ C^* $-algebra. Given an abstract Lipschitz gauge on a $ C^* $-algebra $\mathcal {A} $

in the sense of Rieffel, one can define the classical $ L^ p $-Wasserstein distance on the …

Evolution variational inequality and wasserstein control in variable curvature context

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

In this note we continue the analysis of metric measure space with variable ricci curvature

bounds. First, we study $(\kappa, N) $-convex functions on metric spaces where $\kappa $ is

a lower semi-continuous function, and gradient flow curves in the sense of a new evolution …

Entropic approximation of Wasserstein gradient flows

G Peyré - SIAM Journal on Imaging Sciences, 2015 - SIAM

This article details a novel numerical scheme to approximate gradient flows for optimal

transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically

and numerically nonlinear diffusion equations that model, for instance, porous media or …

2015

Distribution's template estimate with Wasserstein metrics

E Boissard, T Le Gouic, JM Loubes - Bernoulli, 2015 - projecteuclid.org

In this paper, we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

The Wasserstein Loss Function - Jeevana Priya Inala

https://jinala.github.io › assets › papers

by P Dhariwal — One such loss function is the Wasserstein Loss function, which provides a notion of the distance between two measures on a target label space with a particular ...

7 pages PDF

[CITATION] The Wasserstein Loss Function

P Dhariwal, J Inala

A Review of Wasserstein Barycenter Algorithms, with a New One

G Peyré - 2015 - pdfs.semanticscholar.org

The computation of Wasserstein barycenters is the cornerstone that allows to unleash the

power of optimal transport (OT) methods to applications such a imaging sciences and

machine learning. Indeed, it enables to extend traditional problems in these fields, such as …

[ Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical

imaging. In this work, we proposes a novel method for shape classification of brain's

hippocampus using Wasserstein distance based on optimal mass transport theory. In …

All 2 versions
<—-2015—————2015—— —— 140—

[PDF] On the Wasserstein-Fisher-Rao metric

FX Vialard - MATH ON THE ROCKS, 2015 - pdfs.semanticscholar.org

This note gives a summary of the presentation that I gave at the workshop on shape analysis

1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to

measures that have different total masses. This generalization enjoys most of the properties …

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

… (Wasserstein distances) that are themselves hard to compute. We show that the dual

formulation of Wasserstein variational problems introduced recently by [13] can be regularized

using an entropic smoothing, which leads to smooth, differentiable, convex optimization problems …

[CITATION] A Smoothed Dual Formulation for Variational Wasserstein Problems

M Cuturi, G Peyré, A Rolet - arXiv preprint arXiv:1503.02533, 2015 - e-print

[PDF] Bernstein von Mises Theorems in Wasserstein distance

A Bhattacharya, D Pati - arXiv preprint arXiv:1502.02336, 2015 - researchgate.net

We study the Bernstein von-Mises (BvM) phenomenon in Gaussian process regression

models by retaining the leading terms of the induced Karhunen–Loeve expansion. A recent

related result by [9] in a sieve prior context necessitates the prior to be flat, ruling out …

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear

systems. In the presence of stochastic jumps, state variables evolve as random process, with

associated time varying probability density functions. Consequently, system analysis is …

2015

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $

X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm

{Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

[PDF] uclouvain.be

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal

assignment map of clients to these facilities. This problem arises in various contexts in

decision mathematics such as, for instance, location theory in operational research and the …

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on …

<—-2015———2015—— —— 140

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

2015

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - arXiv preprint arXiv …, 2015 - arxiv.org

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

[CITATION] Learning with a Wasserstein Loss Advances in Neural Information Processing Systems (NIPS)

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - 2015

[PDF] mit.edu

M Araya-Polo, CA Frogner, C Zhang, H Mobahi… - 2015 - dspace.mit.edu

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

We develop a gradient-flow theory for time-dependent functionals in abstract metric spaces.

Results about global well-posedness and asymptotic behavior of solutions are obtained.

Conditions on functionals and metric spaces allow to consider the Wasserstein space P2 …

A Smoothed Dual Approach for Variational Wasserstein Problems

2015 ARXIV: MACHINE LEARNING

Fast Discrete Distribution Clustering Using Wasserstein Barycenter With Sparse Support

95 citations* for all

95 citations*

2017 IEEE TRANSACTIONS ON SIGNAL PROCESSING

Jianbo Ye ¹,Panruo Wu ²,James Z. Wang ¹,Jia Li ³

¹ Penn State College of Information Sciences and Technology ,² University of California, Riverside ,³ Pennsylvania State University

Cluster analysis

View More (7+)

In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorov... View Full Abstrac

[CITATION] A Smoothed Dual Approach for Variational Wasserstein Problems. arXiv. org

M Cuturi, G Peyré, A Rolet - 2015 - March

Existence and Consistency of Wasserstein Barycenters

2015 see2017

12 citations*

2015 ARXIV: STATISTICS THEORY

Wasserstein Distance and the Rectifiability of Doubling Measures: Part I

22 citations* for all

5 citations*

2017 MATHEMATISCHE ZEITSCHRIFT

Jonas Azzam ¹,Guy David ²,Tatiana Toro ³

¹ University of Edinburgh ,² University of Paris-Sud ,³ University of Washington

Carleson measure

Lebesgue measure

View More (6+)

Let $\mu $ be a doubling measure in ${\mathbb {R}}^n$. We investigate quantitative relations between the rectifiability of $\mu $ and its distance to flat measures. More precisely, for $x$ in the support $\Sigma $ of $\mu $ and $r > 0$, we introduce a number $\alpha (x,r)\in (0,1]$ t... View Full Abstract

[CITATION] Existence and consistency of wasserstein barycenters. 2015

T Le Gouic, JM Loubes - URL: http://arXiv. org/abs/1506.04153, 2015

[CITATION] Data-driven risk-averse stochastic optimization with wasserstein metric, Optim

C Zhao, Y Guan - 2015 - Online

[CITATION] Existence and consistency of Wasserstein barycenters.< hal-01163262>

T Le Gouic, JM Loubes - 2015

MENUJU MEKANIKA KUANTUM DALAM RUANG WASSERSTEIN

K WAHYUNINGSIH - 2015 - etd.repository.ugm.ac.id

Perluasan ruang keadaan bagi mekanika kuantum dalam ruang Wasserstein telah

dilakukan. Kajian yang dilakukan yakni merumuskan peluang dalam mekanika kuantum

secara klasik. Ruang keadaan ruang Wasserstein memuat keadaan murni dan keadaan …

[Indonesian TOWARDS A QUANTUM MECHANICS IN A WASSERSTEIN SPACE]

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

… (Some figures may appear in colour only in the online journal) 1. Introduction and statement of

the main results It has already been noticed that the 1-Wasserstein distance issued from optimal

transporta- tion theory is very convenient to prove exponential contraction properties for Markov …

…

<—-2015————2015- ————150—

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on …

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein

distance. Compared to the more classical total variation bounds, the proposed rate of

convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

On gradient structures for Markov chains and the passage to ...

www.aimsciences.org › article › doi › nhm.2015.10.233

On gradient structures for Markov chains and the passage to Wasserstein gradient ... established entropic gradient-flow structure for reversible Markov chains.

by K Disser · ‎2015 · ‎Cited by 23 · ‎Related articles

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

Wasserstein Barycenters over Riemannian manifolds

Oct 2, 2015 — As applications, we prove versions of Jensen's inequality on Wasserstein space and a generalized Brunn-Minkowski inequality for a random measurable set on a Riemannian manifold. ...

by YH Kim · ‎2014 · ‎Cited by 44 · ‎Related articles

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $

X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm

{Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

2015

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the

presence of a potential field. The non-locality is due to the appearance of the 'fractional

Laplacian'in the corresponding PDE, in place of the classical Laplacian which distinguishes …

2015

[PDF] A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

U Gianazza, G Savaré, G Toscani - Preprint, Universita di Pavia …, 2004 - www-dimat.unipv.it

Page 1. A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein

spaces Giuseppe Savar ´e Department of Mathematics - University of Pavia and Institute of Applied

Mathematics and Information Technology, CNR, Pavia in collaboration with Ugo Gianazza …

PDF] semanticscholar.org

[PDF] On the Wasserstein-Fisher-Rao metric

FX Vialard - MATH ON THE ROCKS, 2015 - pdfs.semanticscholar.org

This note gives a summary of the presentation that I gave at the workshop on shape analysis

1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to

measures that have different total masses. This generalization enjoys most of the properties …

2015

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

<—-2015———————2015—— —— 160

2015

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

The Lagrangian description of absolutely continnous curves of probability measures on the

real line is analyzed. Whereas each such curve admits a Lagrangian description as a well-

defined flow of its velocity field, further conditions on the curve and/or its velocity are …

2015

Propagation of chaos, Wasserstein gradient flows and toric Kahler-Einstein metrics

RJ Berman, M Onnheim - arXiv preprint arXiv:1501.07820, 2015 - arxiv.org

Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-

equilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We …

2015

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry–Ledoux's refined gradient estimate involving an upper …

2015

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation (with M. Amsaad), Indiana University Mathematics J., Vol. 64 (2015), 1835-1877.

2015

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

The Lagrangian description of absolutely continnous curves of probability measures on the real line is analyzed. Whereas each such curve admits a Lagrangian description as a well-defined flow of its velocity field, further conditions on the curve and/or its velocity are …

2015

C Frogner, C Zhang, H Mobahi, M Araya… - Advances in neural …, 2015 - papers.nips.cc

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

[CITATION] Learning with a Wasserstein Loss Advances in Neural Information Processing Systems (NIPS)

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - 2015

Learning with a Wasserstein loss

M Araya-Polo, CA Frogner, C Zhang, H Mobahi… - 2015 - dspace.mit.edu

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

[PDF] Learning with a Wasserstein Loss

C Frogner, C Zhang, H Mobahi, M Araya… - Advances in Neural …, 2015 - papers.nips.cc

By the definition of L, E [✓]= R (h✓) and ÊS [✓]= ˆRS [h✓]. Therefore, this theorem provides a

uniform control for the deviation of the empirical risk from the risk. Theorem B. 4

(McDiarmid's Inequality). Let S={X1,..., XN}⇢ X be N iid random variables. Assume there …

[PDF] Learning with a Wasserstein Loss

C Frogner, C Zhang, H Mobahi, M Araya… - Advances in Neural …, 2015 - papers.nips.cc

By the definition of L, E [✓]= R (h✓) and ÊS [✓]= ˆRS [h✓]. Therefore, this theorem provides a

uniform control for the deviation of the empirical risk from the risk. Theorem B. 4

(McDiarmid's Inequality). Let S={X1,..., XN}⇢ X be N iid random variables. Assume there …

2015

Wasserstein training of Boltzmann machines

G Montavon, KR Müller, M Cuturi - arXiv preprint arXiv:1507.01972, 2015 - arxiv.org

The Boltzmann machine provides a useful framework to learn highly complex, multimodal

and multiscale data distributions that occur in the real world. The default method to learn its

parameters consists of minimizing the Kullback-Leibler (KL) divergence from training …

2015

Nonpositive curvature, the variance functional, and the Wasserstein barycenter

YH Kim, B Pass - arXiv preprint arXiv, 2015 - ams.org

We show that a Riemannian manifold M has nonpositive sectional curvature and is simply

connected if and only if the variance functional on the space P (M) of probability measures

over M is displacement convex. We then establish convexity over Wasserstein barycenters …

2015

A Review of Wasserstein Barycenter Algorithms, with a New One

G Peyré - 2015 - pdfs.semanticscholar.org

The computation of Wasserstein barycenters is the cornerstone that allows to unleash the

power of optimal transport (OT) methods to applications such a imaging sciences and

machine learning. Indeed, it enables to extend traditional problems in these fields, such as …

Existence and Consistency of Wasserstein Barycenters

2015

by TL Gouic · ‎2015 · ‎Cited by 85 · ‎Related articles

Jun 12, 2015 — We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the distributions or of a growing set of distributions.

[CITATION] Existence and consistency of wasserstein barycenters. 2015

T Le Gouic, JM Loubes - URL: http://arXiv. org/abs/1506.04153, 2015

[CITATION] Existence and consistency of wasserstein barycenters.

T Le Gouic, JM Loubes - URL: http://arXiv. org/abs/1506.04153, 2015

2015

Sliced and radon wasserstein barycenters of measures

N Bonneel, J Rabin, G Peyré, H Pfister - Journal of Mathematical Imaging …, 2015 - Springer

This article details two approaches to compute barycenters of measures using 1-D

Wasserstein distances along radial projections of the input measures. The first method

makes use of the Radon transform of the measures, and the second is the solution of a …

<—-2015———————2015—— —— 170

2015

Numerical methods for matching for teams and Wasserstein barycenters

G Carlier, A Oberman, E Oudet - ESAIM: Mathematical Modelling …, 2015 - esaim-m2an.org

Equilibrium multi-population matching (matching for teams) is a problem from mathematical

economics which is related to multi-marginal optimal transport. A special but important case

is the Wasserstein barycenter problem, which has a

pplications in image processing and …

2015

[PDF] A note on the computation of Wasserstein barycenters

PC Álvarez-Esteban, E Del Barrio, JA Cuesta-Albertos… - Preprint, 2015 - Citeseer

We consider the problem of finding the barycenter of a finite set of probabilities on Rd with

respect to the Wasserstein metric. We introduce an iterative procedure which consistenly

approximates the barycenter under general conditions. These cover the case of probabilities …

2015

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

We propose a study of a distribution registration model for general deformation functions. In

this framework, we provide estimators of the deformations as well as a goodness of fit test of

the model. For this, we consider a criterion which studies the Fr {é} chet mean (or …

2015

On Wasserstein barycenters and MMOSPA estimation

M Baum, PK Willett… - IEEE Signal Processing …, 2015 - ieeexplore.ieee.org

The two title concepts have been evolving rather rapidly, but independent of each other. The

Wasserstein barycenter, on one hand, has mostly made its appearance in image processing

as it can describe a measure of similarity between images. Its minimization might, for …

[CITATION] On Wasserstein Barycenters and MMOSPA Estimation...................... M. Baum, PK Willett, and UD Hanebeck 1511 Objective Consumer Device Photo …

S Imani, SA Ghorashi, T Bouchoucha, MFA Ahmed… - ieeexplore.ieee.org

…

LETTERS On Wasserstein Barycenters and MMOSPA Estimation ...................... M. Baum, PK

Willett, and UD Hanebeck … Objective Consumer Device Photo Quality Evaluation ................

............ MA Saad, P. Corriveau, and R. Jaladi … Transmit Signal and Receive Filter Design in

<—5

2015

[PDF] Geodesic kriging in the Wasserstein space

R Gouet, A López, JM Ortiz - … of the 17th annual Conference of the …, 2015 - researchgate.net

We introduce the method of Geodesic Kriging for spatially-dependent functional data, not supported by a linear space. We present the theory for Hadamard metric spaces and provide more detailed analysis for particular cases such the Hilbert and Wasserstein spaces …

[PDF] Modified Arratia flow and Wasserstein diffusion

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1504.00559, 2015 - researchgate.net

Extending previous work [20] by the first author we present a variant of the Arratia flow of a

field of coalescing Brownian motions starting from every point of the unit interval. The

important new feature of the model is that individual particles carry mass which aggregated …

-Wasserstein distances on state and quasi-state spaces of -algebras

D Zaev - arXiv preprint arXiv:1505.06061, 2015 - arxiv.org

We construct an analogue of the classical $ L^ p $-Wasserstein distance for the state space

of a $ C^* $-algebra. Given an abstract Lipschitz gauge on a $ C^* $-algebra $\mathcal {A} $

in the sense of Rieffel, one can define the classical $ L^ p $-Wasserstein distance on the …

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

∑ ∑ - arXiv.org

arxiv.org › pdf PDF

Вассерштейна (на наш взгляд исторически более правильно это расстояние называть расстоянием. Монжа–Канторовича–Добрушина), как это можно ...

by A Gasnikov · ‎2015 · ‎Cited by 12 · ‎Related articles
<—-2015———————2015—— —— 180—

[PDF] Bernstein von Mises Theorems in Wasserstein distance

A Bhattacharya, D Pati - arXiv preprint arXiv:1502.02336, 2015 - researchgate.net

We study the Bernstein von-Mises (BvM) phenomenon in Gaussian process regression

models by retaining the leading terms of the induced Karhunen–Loeve expansion. A recent

related result by [9] in a sieve prior context necessitates the prior to be flat, ruling out …

A geometric study of Wasserstein spaces: ultrametrics

BR Kloeckner - Mathematika, 2015 - cambridge.org

We study the geometry of the space of measures of a compact ultrametric space $ X $,

endowed with the $ L^{p} $ Wasserstein distance from optimal transportation. We show that

the power $ p $ of this distance makes this Wasserstein space affinely isometric to a convex …

2015

Snowflake universality of Wasserstein spaces

[HTML] Value functions in the Wasserstein spaces: finite time horizons

R Hynd, HK Kim - Journal of Functional Analysis, 2015 - Elsevier

We study analogs of value functions arising in classical mechanics in the space of

probability measures endowed with the Wasserstein metric W p, for 1< p<∞. Our main result

is that each of these generalized value functions is a type of viscosity solution of an …

2015

A Andoni, A Naor, O Neiman - arXiv preprint arXiv:1509.08677, 2015 - arxiv.org

For $ p\in (1,\infty) $ let $\mathscr {P} _p (\mathbb {R}^ 3) $ denote the metric space of all $ p

$-integrable Borel probability measures on $\mathbb {R}^ 3$, equipped with the

Wasserstein $ p $ metric $\mathsf {W} _p $. We prove that for every $\varepsilon> 0$, every …

2015

Barycenter in Wasserstein spaces: Existence and consistency

T Le Gouic, JM Loubes - … Conference on Geometric Science of Information, 2015 - Springer

We study barycenters in the Wasserstein space P _p (E) P p (E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure PP on P _p

(E) P p (E) as its Fréchet mean. The paper establishes its existence and states consistency …

2015

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

2015

Regularizing image intensity transformations using the wasserstein metric

[HTML] Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - Journal of Differential Equations, 2015 - Elsevier

We perform a systematic study of optimization problems in the Wasserstein spaces that are

analogs of infinite horizon, deterministic control problems. We derive necessary conditions

on action minimizing paths and present a sufficient condition for their existence. We also …

2015 [PDF] springer.com

M Oskarsson - Scandinavian Conference on Image Analysis, 2015 - Springer

In this paper we direct our attention to the problem of discretization effects in intensity transformations of images. We propose to use the Wasserstein metric (also known as the Earth mover distance) to bootstrap the transformation process. The Wasserstein metric gives …

Distribution's template estimate with Wasserstein metrics

E Boissard, T Le Gouic, JM Loubes - Bernoulli, 2015 - projecteuclid.org

In this paper, we tackle the problem of comparing distributions of random variables and

defining a mean pattern between a sample of random events. Using barycenters of

measures in the Wasserstein space, we propose an iterative version as an estimation of the …

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

We propose a study of a distribution registration model for general deformation functions. In

this framework, we provide estimators of the deformations as well as a goodness of fit test of

the model. For this, we consider a criterion which studies the Fr {é} chet mean (or …

<—–2015———————2015————190-

2015 PDF

Data-Driven Risk-Averse Two-Stage Stochastic Program with ...http://www.optimization-online.org › 2015/07

by C Zhao · 2015 · Cited by 55 — In this paper, we develop a data-driven stochastic optimization framework to provide a risk

averse decision making under uncertainty. In our approach, starting ...

[CITATION] Data-driven risk-averse stochastic optimization with wasserstein metric, Optim

C Zhao, Y Guan - 2015 - Online

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-

randomly centered random sums of real iid random variables with a finite third moment and

the standard normal distribution. Except for the case of mean zero summands, these bounds …

2015 gradient

Entropic approximation of Wasserstein gradient flows

G Peyré - SIAM Journal on Imaging Sciences, 2015 - SIAM

This article details a novel numerical scheme to approximate gradient flows for optimal

transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically

and numerically nonlinear diffusion equations that model, for instance, porous media or …

2015 gradient

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

2015 gradient

Propagation of chaos, Wasserstein gradient flows and toric Kahler-Einstein metrics

RJ Berman, M Onnheim - arXiv preprint arXiv:1501.07820, 2015 - arxiv.org

Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-

equilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We …

2015 gradient

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the

presence of a potential field. The non-locality is due to the appearance of the 'fractional

Laplacian'in the corresponding PDE, in place of the classical Laplacian which distinguishes …

2015 gradient

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

Convolutional wasserstein distances: Efficient optimal transportation on geometric domains

J Solomon, F De Goes, G Peyré, M Cuturi… - ACM Transactions on …, 2015 - dl.acm.org

This paper introduces a new class of algorithms for optimization problems involving optimal

transportation over geometric domains. Our main contribution is to show that optimal

transportation can be made tractable over large domains used in graphics, such as images …

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to

justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily …

[PDF] A Hitchhiker's guide to Wasserstein distances

G Basso - 2015 - n.ethz.ch

The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions

we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric

space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a signed …

<—-2015———————2015—— —— 200

First and second moments for self‐similar couplings and Wasserstein distances

JM Fraser - Mathematische Nachrichten, 2015 - Wiley Online Library

We study aspects of the Wasserstein distance in the context of self‐similar measures.

Computing this distance between two measures involves minimising certain moment

integrals over the space of couplings, which are measures on the product space with the …

Wasserstein distances and curves in the Wasserstein spaces

[PDF] Convolutional wasserstein distances

J Solomon, F De Goes, G Peyré, M Cuturi… - ACM Trans … - researchgate.net

This paper introduces a new class of algorithms for optimization problems involving optimal

transportation over geometric domains. Our main contribution is to show that optimal

transportation can be made tractable over large domains used in graphics, such as images …

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

-Wasserstein distances on state and quasi-state spaces of -algebras

D Zaev - arXiv preprint arXiv:1505.06061, 2015 - arxiv.org

We construct an analogue of the classical $ L^ p $-Wasserstein distance for the state space

of a $ C^* $-algebra. Given an abstract Lipschitz gauge on a $ C^* $-algebra $\mathcal {A} $

in the sense of Rieffel, one can define the classical $ L^ p $-Wasserstein distance on the …

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $

X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm

{Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

On the rate of convergence in Wasserstein distance of the empirical measure

N Fournier, A Guillin - Probability Theory and Related Fields, 2015 - Springer

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability

distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ,

when measured in the Wasserstein distance of order p> 0 p> 0. We provide some satisfying …

Shape classification using Wasserstein distance for brain morphometry analysis

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - International Conference on …, 2015 - Springer

Brain morphometry study plays a fundamental role in medical imaging analysis and

diagnosis. This work proposes a novel framework for brain cortical surface classification

using Wasserstein distance, based on uniformization theory and Riemannian optimal mass …

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein

distance. Compared to the more classical total variation bounds, the proposed rate of

convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia - Bernoulli, 2015 - projecteuclid.org

The paper gives the bounds on the solutions to a Stein equation for the negative binomial

distribution that are needed for approximation in terms of the Wasserstein metric. The proofs

<—-2015———————2015—— —— 210—

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein Distance

A Irpino, R Verde - Advances in Data Analysis and Classification, 2015 - Springer

In this paper we present a new linear regression technique for distributional symbolic

variables, ie, variables whose realizations can be histograms, empirical distributions or

empirical estimates of parametric distributions. Such data are known as numerical modal …

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical

imaging. In this work, we proposes a novel method for shape classification of brain's

hippocampus using Wasserstein distance based on optimal mass transport theory. In …

[PDF] Bernstein von Mises Theorems in Wasserstein distance

A Bhattacharya, D Pati - arXiv preprint arXiv:1502.02336, 2015 - researchgate.net

We study the Bernstein von-Mises (BvM) phenomenon in Gaussian process regression

models by retaining the leading terms of the induced Karhunen–Loeve expansion. A recent

related result by [9] in a sieve prior context necessitates the prior to be flat, ruling out …

2015

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal

assignment map of clients to these facilities. This problem arises in various contexts in

decision mathematics such as, for instance, location theory in operational research and the …

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia - Bernoulli, 2015 - projecteuclid.org

The paper gives the bounds on the solutions to a Stein equation for the negative binomial

distribution that are needed for approximation in terms of the Wasserstein metric. The proofs

are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 …

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear

systems. In the presence of stochastic jumps, state variables evolve as random process, with

associated time varying probability density functions. Consequently, system analysis is …

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

Page 1. Nonlinearity PAPER Contraction in the Wasserstein metric for some Markov chains, and

applications to the dynamics of expanding maps To cite this article: Benoît R Kloeckner et al 2015

Nonlinearity 28 4117 View the article online for updates and enhancements. Related content …

<—-2015———————2015—— —— 220—

Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

P Mohajerin Esfahani, D Kuhn - arXiv, 2015 - ui.adsabs.harvard.edu

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

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Regularizing image intensity transformations using the wasserstein metric

M Oskarsson - Scandinavian Conference on Image Analysis, 2015 - Springer

In this paper we direct our attention to the problem of discretization effects in intensity

transformations of images. We propose to use the Wasserstein metric (also known as the

Earth mover distance) to bootstrap the transformation process. The Wasserstein metric gives …

Distribution function estimates by Wasserstein metric and Bernstein approximation for C⁻¹ functions

Z Wu, Z Tian - Applied Mathematics-A Journal of Chinese Universities, 2015 - Springer

The aim of the paper is to estimate the density functions or distribution functions measured

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Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

… 1 1.2 Elements of optimal transport the Wasserstein metric and Otto's calculus … Wasserstein

metric and Otto's calculus In this section we present some preliminaries on the Wasserstein metric,

the Wasserstein space and Otto's calculus which will be needed later …

2015 [PDF] arxiv.org

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The

formulation is based on optimal transport wrt geometric distance and local feature similarity.

Geometric invariance and modelling of object-typical statistical variations is achieved by …

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

C Jin - Nonlinear Analysis, 2015 - Elsevier

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the …

2015 [PDF] arxiv.org

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

Numerical methods for matching for teams and Wasserstein barycenters

2015

G Carlier, A Oberman, E Oudet - ESAIM: Mathematical Modelling …, 2015 - esaim-m2an.org

Equilibrium multi-population matching (matching for teams) is a problem from mathematical

economics which is related to multi-marginal optimal transport. A special but important case

is the Wasserstein barycenter problem, which has applications in image processing and …

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on …

On the rate of convergence in Wasserstein distance of the empirical measure

2015

[PDF] A note on the computation of Wasserstein barycenters

PC Alvarez-Esteban, E Del Barrio, JA Cuesta-Albertos… - Preprint, 2015 - Citeseer

We consider the problem of finding the barycenter of a finite set of probabilities on Rd with

respect to the Wasserstein metric. We introduce an iterative procedure which consistenly

approximates the barycenter under general conditions. These cover the case of probabilities …

<—-2015———————2015—— —— 230—

N Fournier, A Guillin - Probability Theory and Related Fields, 2015 - Springer

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability

distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ,

when measured in the Wasserstein distance of order p> 0 p> 0. We provide some satisfying …

2015

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

MH Duong - Asymptotic Analysis, 2015 - content.iospress.com

In this paper, we study the Wasserstein gradient flow structure of the porous medium

equation restricted to q-Gaussians. The JKO-formulation of the porous medium equation

gives a variational functional K h, which is the sum of the (scaled-) Wasserstein distance and …

Distribution function estimates by Wasserstein metric and Bernstein approximation for C− 1 functions

2015

Z Wu, Z Tian - Applied Mathematics-A Journal of Chinese Universities, 2015 - Springer

The aim of the paper is to estimate the density functions or distribution functions measured

by Wasserstein metric, a typical kind of statistical distances, which is usually required in the

statistical learning. Based on the classical Bernstein approximation, a scheme is presented …

2015

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

On Wasserstein barycenters and MMOSPA estimation

M Baum, PK Willett… - IEEE Signal Processing …, 2015 - ieeexplore.ieee.org

The two title concepts have been evolving rather rapidly, but independent of each other. The

Wasserstein barycenter, on one hand, has mostly made its appearance in image processing

as it can describe a measure of similarity between images. Its minimization might, for …

[CITATION] On Wasserstein Barycenters and MMOSPA Estimation...................... M. Baum, PK Willett, and UD Hanebeck 1511 Objective Consumer Device Photo …

S Imani, SA Ghorashi, T Bouchoucha, MFA Ahmed… - ieeexplore.ieee.org

LETTERS On Wasserstein Barycenters and MMOSPA Estimation ...................... M. Baum, PK

Willett, and UD Hanebeck … Objective Consumer Device Photo Quality Evaluation ................

............ MA Saad, P. Corriveau, and R. Jaladi … Transmit Signal and Receive Filter Design in …

2015

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and

solar power, power system operations face new challenges as the supply uncertainty

increases dramatically. Scenario analysis is widely used because it explicitly incorporates a …

[CITATION] YANG Li. A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

W Qun, D Wenlue - Proceedings of the CSEE, 2015

[CITATION] … Engineering, Zhejiang University;; A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and …

Q WANG, W DONG, L YANG - 中国电机工程学报, 2015

2015

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

B Piccoli, F Rossi - Acta applicandae mathematicae, 2013 - Springer

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein

space. In particular, we consider the Cauchy problem for a transport equation, where the

velocity field depends on the measure itself. We deal with numerical schemes for this …

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The

formulation is based on optimal transport wrt geometric distance and local feature similarity.

Geometric invariance and modelling of object-typical statistical variations is achieved by …

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

Distribution function estimates by Wasserstein metric and Bernstein approximation for C− 1 functions

<—-2015———————2015—— —— 240 —

Z Wu, Z Tian - Applied Mathematics-A Journal of Chinese Universities, 2015 - Springer

The aim of the paper is to estimate the density functions or distribution functions measured

by Wasserstein metric, a typical kind of statistical distances, which is usually required in the

statistical learning. Based on the classical Bernstein approximation, a scheme is presented …

Entropic approximation of Wasserstein gradient flows

G Peyré - SIAM Journal on Imaging Sciences, 2015 - SIAM

This article details a novel numerical scheme to approximate gradient flows for optimal

transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically

and numerically nonlinear diffusion equations that model, for instance, porous media or …

A geometric study of Wasserstein spaces: ultrametrics

BR Kloeckner - Mathematika, 2015 - Wiley Online Library

We study the geometry of the space of measures of a compact ultrametric space, endowed

with the Wasserstein distance from optimal transportation. We show that the power of this

distance makes this Wasserstein space affinely isometric to a convex subset of. As a …

Snowflake universality of Wasserstein spaces

A Andoni, A Naor, O Neiman - arXiv preprint arXiv:1509.08677, 2015 - arxiv.org

For $ p\in (1,\infty) $ let $\mathscr {P} _p (\mathbb {R}^ 3) $ denote the metric space of all $ p

$-integrable Borel probability measures on $\mathbb {R}^ 3$, equipped with the

Wasserstein $ p $ metric $\mathsf {W} _p $. We prove that for every $\varepsilon> 0$, every …

MR3293301 Pending Shao, Jinghai Ergodicity of regime-switching diffusions in Wasserstein distances. Stochastic Process. Appl. 125 (2015), no. 2, 739–758. 60J60 (60B10 60J27)

Ergodicity of regime-switching diffusions in Wasserstein distances ...

by J Shao - ‎2015 - ‎Cited by 22 - ‎Related articles

The work [8] attracts us to studying the ergodicity of regime-switching diffusion processes in Wasserstein distance. ... When is finite, namely, is a Markov chain in a finite state space, we call ( X t , Λ t ) a regime-switching diffusion process in finite state space.

On properties of the generalized Wasserstein distance

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

JavaScript is disabled on your browser. Please enable JavaScript to use all

the features on this page. Skip to main content Skip to article …

2015

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2016 - Springer

The Wasserstein distances W p (p\geqq≧ 1), defined in terms of a solution to the Monge–

Kantorovich problem, are known to be a useful tool to investigate transport equations. In

particular, the Benamou–Brenier formula characterizes the square of the Wasserstein …

Propagation of chaos, Wasserstein gradient flows and toric Kahler-Einstein metrics

RJ Berman, M Onnheim - arXiv preprint arXiv:1501.07820, 2015 - arxiv.org

… 1.4. Organization. In Section 2 we start by recalling the general setup that we will need from

probability, the theory of Wasserstein spaces and weak gradient flows and then turn to the proof

of Theorem 1.1 in Section 2.6 (starting with the discretized situation) …

MR3342407 Pending Cacciafesta, Federico; de Suzzoni, Anne-Sophie Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure. J. Differential Equations 259 (2015), no. 3, 1024–1067. 35Q53

Continuity of the flow of KdV with regard to the Wasserstein metrics ...

Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure ... Two-dimensional Navier-Stokes equations 3.
[HTML] sciencedirect.com

[HTML] Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

F Cacciafesta, AS de Suzzoni - Journal of Differential Equations, 2015 - Elsevier

In this paper, we prove the continuity of the flow of KdV on spaces of probability measures

with respect to a combination of Wasserstein distances on H s, s> 0 and L 2. We are

motivated by the existence of an invariant measure belonging to the spaces onto which …

[HTML] Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

F Cacciafesta, AS de Suzzoni - Journal of Differential Equations, 2015 - Elsevier

… In this paper, we prove the continuity of the flow of KdV on spaces of probability measures with

respect to a combination of Wasserstein distances on H s , s > 0 and L 2 . We are motivated by

the existence of an invariant measure belonging to the spaces onto which these …

2015 [PDF] arxiv.org

First and second moments for self‐similar couplings and Wasserstein distances

JM Fraser - Mathematische Nachrichten, 2015 - Wiley Online Library

… and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein …

Cited by 11 Related article

Consistent estimation of a population barycenter in the Wasserstein space

Jérémie Bigot (DMIA), Thierry Klein (IMT)

We define a notion of barycenter for random probability measures in the Wasserstein space. We give a characterization of the population barycenter in terms of existence and uniqueness for compactly supported measures. Then, the problem of estimating this barycenter from n independent and identically distributed random probability measures is considered. We study the convergence of the empirical barycenter proposed in Agueh and Carlier (2011) to its population counterpart as the number of measures n tends to infinity. To illustrate the benefits of this approach for data analysis and statistics, we finally discuss the usefulness of barycenters in the Wasserstein space for curve and image warping.

Subjects:	Statistics Theory (math.ST)
Cite as:	arXiv:1212.2562 [math.ST]
	(or arXiv:1212.2562v1 [math.ST] for this version)

Submission history

From: Jeremie Bigot [view email] [via CCSD proxy]

[v1] Tue, 11 Dec 2012 17:58:28 UTC (23 KB)

[v2] Thu, 5 Dec 2013 07:37:44 UTC (29 KB)

[v3] Mon, 17 Mar 2014 18:33:37 UTC (29 KB)

[v4] Mon, 9 Mar 2015 17:23:33 UTC (24 KB)

[v5] Fri, 17 Jul 2015 16:14:10 UTC (25 KB)

[v6] Wed, 29 Nov 2017 15:07:20 UTC (27 KB)

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. ArXiv e-prints

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2015

Existence and Consistency of Wasserstein Barycenters

<——2015——2015———— 250—-

by TL Gouic · 2015 · Cited by 85 — [Submitted on 12 Jun 2015 (v1), last revised 12 Feb 2016 (this version, v2)] ... We prove the existence of Wasserstein barycenters of random distributions defined ...

[CITATION] Existence and consistency of wasserstein barycenters. 2015

T Le Gouic, JM Loubes - URL: http://arXiv. org/abs/1506.04153, 2015

[CITATION] Existence and consistency of Wasserstein barycenters.< hal-01163262>

T Le Gouic, JM Loubes - 2015

A Review of Wasserstein Barycenter Algorithms, with a New One

open.library.ubc.ca › ... › BIRS Workshop Lecture Videos

Feb 19, 2015 — Learning, knowledge, research, insight: welcome to the world of UBC Library, the second-largest academic research library in Canada.

[CITATION] A Review of Wasserstein Barycenter Algorithms, with a New One

G Peyré - 2015 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General

(Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

Page 1. Nonlinearity PAPER Contraction in the Wasserstein metric for some Markov chains, and

applications to the dynamics of expanding maps To cite this article: Benoît R Kloeckner et al 2015

Nonlinearity 28 4117 View the article online for updates and enhancements. Related content …

[CITATION] Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

2015

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

Entropic approximation of Wasserstein gradient flows

G Peyré - SIAM Journal on Imaging Sciences, 2015 - SIAM

This article details a novel numerical scheme to approximate gradient flows for optimal

transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically

and numerically nonlinear diffusion equations that model, for instance, porous media or …

2015

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - Networks & Heterogeneous Media, 2015 - aimsciences.org

We study the approximation of Wasserstein gradient structures by their finite-dimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

2015

Distance de Wasserstein d'une imagea une mesure quelconque

F de GOURNAY, L LEBRAT, J KHAN, P WEISS - smai.emath.fr

Mots-clés : Transport optimal, distance de Wasserstein, cellules de Laguerre Le calcul du transport

optimal entre deux mesures de probabilités i et ν a connu un spectaculaire développement durant

les derni`eres années. Il existe principalement 3 méthodes, les méthodes semi- discretes [1 …

Propagation of chaos, Wasserstein gradient flows and toric Kahler-Einstein metrics

RJ Berman, M Onnheim - arXiv preprint arXiv:1501.07820, 2015 - arxiv.org

Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-

equilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We …

<--—2015——2015—— —— 260—-

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the

presence of a potential field. The non-locality is due to the appearance of the 'fractional

Laplacian'in the corresponding PDE, in place of the classical Laplacian which distinguishes …

[PDF] Modified Arratia flow and Wasserstein diffusion

V Konarovskyi, M von Renesse - Communications on Pure and …, 2015 - researchgate.net

Extending previous work [20] by the first author we present a variant of the Arratia flow of a

field of coalescing Brownian motions starting from every point of the unit interval. The

important new feature of the model is that individual particles carry mass which aggregated …

[HTML] Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

F Cacciafesta, AS de Suzzoni - Journal of Differential Equations, 2015 - Elsevier

In this paper, we prove the continuity of the flow of KdV on spaces of probability measures

with respect to a combination of Wasserstein distances on H s, s> 0 and L 2. We are

motivated by the existence of an invariant measure belonging to the spaces onto which …

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

2015

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

We develop a gradient-flow theory for time-dependent functionals in abstract metric spaces.

Results about global well-posedness and asymptotic behavior of solutions are obtained.

Conditions on functionals and metric spaces allow to consider the Wasserstein space P2 …

Entropic approximation of Wasserstein gradient flows

G Peyré - SIAM Journal on Imaging Sciences, 2015 - SIAM

This article details a novel numerical scheme to approximate gradient flows for optimal

transport (ie, Wasserstein) metrics. These flows have proved useful to tackle theoretically

and numerically nonlinear diffusion equations that model, for instance, porous media or …

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

2015

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-

randomly centered random sums of real iid random variables with a finite third moment and

the standard normal distribution. Except for the case of mean zero summands, these bounds …

<——2015——2015—— —— 270—-

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia - Bernoulli, 2015 - projecteuclid.org

The paper gives the bounds on the solutions to a Stein equation for the negative binomial

distribution that are needed for approximation in terms of the Wasserstein metric. The proofs

are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 …

On Wasserstein Barycenters and MMOSPA Estimation

M Baum, P Willett, U Hanebeck - 2015 - ieeexplore.ieee.org

Abstract—The two title concepts have been evolving rather rapidly, but independent of each

other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image

processing as it can describe a measure of similarity between images. Its minimization ...

Cite Save [PDF] from arxiv.org Signal Processing Letters, …, 2

On Wasserstein Barycenters and MMOSPA Estimation - IEEE Xplore

ieeexplore.ieee.org › xpls › abs_all

The Wasserstein barycenter, on one hand, has mostly made its appearance in image ... On the other hand, MMOSPA estimation has been applied largely to multi-target tracking. ... Marcus Baum; Peter K. Willett; Uwe D. Hanebeck ... Y. Bar-Shalom, P. K. Willett and X. Tian, Tracking and Data Fusion: A Handbook of ...

[PDF] ieee.org OCTOBER 2015 VOLUME 22 NUMBER 10

[CITATION] On Wasserstein Barycenters and MMOSPA Estimation...................... M. Baum, PK Willett, and UD Hanebeck 1511 Objective Consumer Device Photo …

S Imani, SA Ghorashi, T Bouchoucha, MFA Ahmed… - ieeexplore.ieee.org

LETTERS On Wasserstein Barycenters and MMOSPA Estimation ...................... M. Baum, PK

Willett, and UD Hanebeck … Objective Consumer Device Photo Quality Evaluation ................

............ MA Saad, P. Corriveau, and R. Jaladi … Transmit Signal and Receive Filter Design in …
Cited by 29 Related articles All 3 versions

2015 Vaserstein

[PDF] Gram-Schmidt-Vaserstein generators for odd sized elementary groups

P Chattopadhyay, RA Rao - arXiv preprint arXiv:1511.08688, 2015 - arxiv.org

The Gram-Schmidt process of LN Vaserstein for making an elementary matrix symplectic

yields a nice set of generators for the odd sized elementary group. Subjects: Commutative

Algebra (math. AC) Cite as: arXiv: 1511.08688 [math. AC](or arXiv: 1511.08688 v1 [math …

Gram-Schmidt-Vaserstein generators for odd sized elementary groups

by Chattopadhyay, Pratyusha; Rao, Ravi A

(Submitted on 27 Nov 2015)

SciRate Published 30 Nov 2015 arXiv preprint arXiv:1511.08688, 2015

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

uzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

On Wasserstein barycenters and MMOSPA estimation

M Baum, PK Willett… - IEEE Signal Processing …, 2015 - ieeexplore.ieee.org

The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for …

[CITATION] On Wasserstein Barycenters and MMOSPA Estimation...................... M. Baum, PK Willett, and UD Hanebeck 1511 Objective Consumer Device Photo …

S Imani, SA Ghorashi, T Bouchoucha, MFA Ahmed… - ieeexplore.ieee.org

LETTERS On Wasserstein Barycenters and MMOSPA Estimation ...................... M. Baum, PK Willett, and UD Hanebeck … Objective Consumer Device Photo Quality Evaluation ................ ............ MA Saad, P. Corriveau, and R. Jaladi … Transmit Signal and Receive Filter Design in …

2015

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

We propose a study of a distribution registration model for general deformation functions. In this framework, we provide estimators of the deformations as well as a goodness of fit test of the model. For this, we consider a criterion which studies the Fr {é} chet mean (or …

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport wrt geometric distance and local feature similarity. Geometric invariance and modelling of object-typical statistical variations is achieved by …

Regularizing image intensity transformations using the wasserstein metric

M Oskarsson - Scandinavian Conference on Image Analysis, 2015 - Springer

[PDF] uclouvain.be

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal assignment map of clients to these facilities. This problem arises in various contexts in decision mathematics such as, for instance, location theory in operational research and the …

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-randomly centered random sums of real iid random variables with a finite third moment and the standard normal distribution. Except for the case of mean zero summands, these bounds …

2015

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein distance. Compared to the more classical total variation bounds, the proposed rate of convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

<——2015——2015--——— 280—-

2015

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but lower bounded by a continuous function, we give a new characterization of this lower bound through the convexity of relative entropy on the probability space over the Riemannian …

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

2015

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as a minimal effort required to map one distribution onto another. The concept has a long history with connections to optimal transport theory. However, the applications on …

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the

presence of a potential field. The non-locality is due to the appearance of the 'fractional

Laplacian'in the corresponding PDE, in place of the classical Laplacian which distinguishes …

2015

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

C Jin - Nonlinear Analysis, 2015 - Elsevier

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the …

2015

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

2915

2015

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $

X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm

{Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

2015

E Kamalinejad - … of Variations and Partial Differential Equations, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

2015 [PDF] uclouvain.be

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal

assignment map of clients to these facilities. This problem arises in various contexts in

decision mathematics such as, for instance, location theory in operational research and the …

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

2015

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and solar power, power system operations face new challenges as the supply uncertainty increases dramatically. Scenario analysis is widely used because it explicitly incorporates a … Cited by 28 Related articles

[CITATION] YANG Li. A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

W Qun, D Wenlue - Proceedings of the CSEE, 2015

[CITATION] Fast computation of Wasserstein barycenters.(2014)

M Cuturi, A Doucet - 2014

[CITATION] … Engineering, Zhejiang University;; A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and …

Q WANG, W DONG, L YANG - 中国电机工程学报, 2015

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities …

[CITATION] A Smoothed Dual Formulation for Variational Wasserstein Problems

M Cuturi, G Peyré, A Rolet - arXiv preprint arXiv:1503.02533, 2015 - e-print

[CITATION] A Smoothed Dual Approach for Variational Wasserstein Problems. arXiv. org

M Cuturi, G Peyré, A Rolet - 2015 - March

gradient Flows: In Metric Spaces and in the Space of ...

<——2015——2015--——— 290—-

2015 see 2004 2005 book

www2.stat.duke.edu › ~sayan › ambrosio

Jan 1, 2015 — II Gradient Flow in the Space of Probability Measures. 103 ... 7 The Wasserstein Distance and its Behaviour along Geodesics. 151. 7.1 The ... parts, the first one concerning gradient flows in metric spaces and the second one.

Cited by 3555 Related articles All 13 versions

2015

On the rate of convergence in Wasserstein distance of the empirical measure

N Fournier, A Guillin - Probability Theory and Related Fields, 2015 - Springer

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ, when measured in the Wasserstein distance of order p> 0 p> 0. We provide some satisfying …

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein distance. Compared to the more classical total variation bounds, the proposed rate of convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as a minimal effort required to map one distribution onto another. The concept has a long history with connections to optimal transport theory. However, the applications on …

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-randomly centered random sums of real iid random variables with a finite third moment and the standard normal distribution. Except for the case of mean zero summands, these bounds …

2015

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport wrt geometric distance and local feature similarity. Geometric invariance and modelling of object-typical statistical variations is achieved by …

2015

Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical imaging. In this work, we proposes a novel method for shape classification of brain's hippocampus using Wasserstein distance based on optimal mass transport theory. In …

Shape classification using Wasserstein distance for brain morphometry analysis

2015

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - International Conference on …, 2015 - Springer

Brain morphometry study plays a fundamental role in medical imaging analysis and diagnosis. This work proposes a novel framework for brain cortical surface classification using Wasserstein distance, based on uniformization theory and Riemannian optimal mass …

<——2015——2015—— —— 300—-

2015

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

E Boissard, T Le Gouic - Annales de l'IHP Probabilités et statistiques, 2014 - numdam.org

2015

Dynamic clustering of histogram data based on adaptive squared Wasserstein distances

A Irpino, R Verde, FAT De Carvalho - Expert Systems with Applications, 2014 - Elsevier

2015

[PDF] ucla.edu

Weak KAM theory on the Wasserstein torus with multidimensional underlying space

W Gangbo, A Tudorascu - … on Pure and Applied Mathematics, 2014 - Wiley Online Library

2015

[PDF] On tangent cones and parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1407.7245, 2014 - Citeseer

2015

[PDF] Multi-phase texture segmentation using gabor features histograms based on wasserstein distance

M Qiao, W Wang, M Ng - Communications in Computational Physics, 2014 - global-sci.org

We present a multi-phase image segmentation method based on the histogram of the Gabor feature space, which consists of a set of Gabor-filter responses with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy …

2015

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - 2014 - opus4.kobv.de

On the rate of convergence in Wasserstein distance of the empirical measure

N Fournier, A Guillin - Probability Theory and Related Fields, 2015 - Springer

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability

distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ,

when measured in the Wasserstein distance of order p> 0 p> 0. We provide some satisfying …

2015

On curvature conditions using Wasserstein spaces

M Kell - 2014 - oatd.org

2015

[PDF] Phase retrieval on the quadratic Wasserstein space

A Tsipenyuk - www-m7.ma.tum.de

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

<——2015——2015—— —— 310—-

[PDF] univ-mlv.fr

[PDF] On the Wasserstein-Fisher-Rao metric

FX Vialard - MATH ON THE ROCKS, 2015 - angkor.univ-mlv.fr

This note gives a summary of the presentation that I gave at the workshop on shape analysis 1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to measures that have different total masses. This generalization enjoys most of the properties …

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $ X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm {Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric points of view. We derive quantum mechanical models from Lagrangian principles on the so called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on the Wasserstein space is proved. The proofs are based on a relaxation of displacement convexity in the Wasserstein space and can be applied to a family of higher order energy …

2015 [PDF] umn.edu

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which minimizes a suitable action. We also study the relative entropy evolution between an …

2015 zzz 30

[CITATION] On the bi-Lipschitz structure of Wasserstein spaces

T Austin, A Naor - preprint, 2015

[CITATION] On the bi-Lipschitz structure of Wasserstein spaces

T Austin, A Naor - preprint, 2015

[CITATION] On the bi-Lipschitz structure of Wasserstein spaces

T Austin, A Naor - preprint, 2015

[CITATION] On the bi-Lipschitz structure of Wasserstein spaces

T Austin, A Naor - preprint, 2015

Convolutional wasserstein distances - Archive ouverte HAL

2015

https://hal.archives-ouvertes.fr › file › 2015-SIGG...

https://hal.archives-ouvertes.fr › file › 2015-SIGG...PDF

by J Solomon · 2015 · Cited by 501 — computation [Agueh and Carlier 2011], density propagation over ... (1). The 2-Wasserstein distance satisfies all metric axioms and has ..

2015 arxiv.org › math

On some non linear evolution systems which are perturbations ...

by M Laborde · 2015 · Cited by 17 — On some non linear evolution systems which are perturbations of Wasserstein gradient flows. This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows.

On some non linear evolution systems which are perturbations of Wasserstein gradient flows

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities …

[CITATION] A Smoothed Dual Approach for Variational Wasserstein Problems. arXiv. org

M Cuturi, G Peyré, A Rolet - 2015 - March

[CITATION] A Smoothed Dual Formulation for Variational Wasserstein Problems

M Cuturi, G Peyré, A Rolet - arXiv preprint arXiv:1503.02533, 2015 - e-print

2015

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

<——2015——2015—— —— 320—-

A Review of Wasserstein Barycenter Algorithms, with a New One

open.library.ubc.ca › ... › BIRS Workshop Lecture Videos

Feb 19, 2015 — Learning, knowledge, research, insight: welcome to the world of UBC Library, the second-largest academic research library in Canada.

[CITATION] A Review of Wasserstein Barycenter Algorithms, with a New One

G Peyré - 2015 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General (Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport wrt geometric distance and local feature similarity. Geometric invariance and modelling of object-typical statistical variations is achieved by …

2015

Convolutional wasserstein distances: Efficient optimal transportation on geometric domains

J Solomon, F De Goes, G Peyré, M Cuturi… - ACM Transactions on …, 2015 - dl.acm.org

This paper introduces a new class of algorithms for optimization problems involving optimal transportation over geometric domains. Our main contribution is to show that optimal transportation can be made tractable over large domains used in graphics, such as images …

[CITATION] Du, and Guibas. Solomon J, de Goes F, Peyré G, Cuturi M, Butscher A, Nguyen A, Du T, Guibas L (2015) Convolutional Wasserstein distances: Efficient …

G Solomon - ACM Transactions on Graphics

First and second moments for self‐similar couplings and Wasserstein distances

JM Fraser - Mathematische Nachrichten, 2015 - Wiley Online Library

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the …

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear systems. In the presence of stochastic jumps, state variables evolve as random process, with associated time varying probability density functions. Consequently, system analysis is …

2015

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry–Ledoux's refined gradient estimate involving an upper …

Barycenter in Wasserstein spaces: Existence and consistency

T Le Gouic, JM Loubes - … Conference on Geometric Science of Information, 2015 - Springer

We study barycenters in the Wasserstein space P _p (E) P p (E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure PP on P _p

(E) P p (E) as its Fréchet mean. The paper establishes its existence and states consistency …

20015

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. ArXiv e-prints

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2015

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

C Jin - Nonlinear Analysis, 2015 - Elsevier

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the …

<——2015——2015—— —— 330—-

2015

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

We develop a gradient-flow theory for time-dependent functionals in abstract metric spaces.

Results about global well-posedness and asymptotic behavior of solutions are obtained.

Conditions on functionals and metric spaces allow to consider the Wasserstein space P2 …

An Algorithmic Approach to Compute Principal Geodesics in ...

2015

www.researchgate.net › publication › 279310014_An_Al...

Download Citation | An Algorithmic Approach to Compute Principal Geodesics in the Wasserstein Space | We consider in this work the space of probability ...

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015

Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

23 citations*

2015 ARXIV: OPTIMIZATION AND CONTROL

Projection Robust Wasserstein Distance and Riemannian Optimization

10 citations* for all

10 citations*

2020 NEURAL INFORMATION PROCESSING SYSTEMS

Tianyi Lin ¹,Chenyou Fan ²,Nhat Ho ¹,Marco Cuturi ²,Michael I. Jordan ³

¹ University of California, Berkeley ,² Google ,³ Stanford University

Projection pursuit

Projection (linear algebra)

View More (8+)

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in particular when comparing probability measures in high-dimensions.... View Full Abstract

Clustering and Model Integration under the Wasserstein Metric

adapt.psu.edu › BigDataSymposium_Public › Jia_Li

Ye, P. Wu, J. Z. Wang, J. Li, “Accelerated Discrete Distribution Clustering under Wasserstein Distance,” manuscript, 2015.

PDF Distance,” manuscript, 2015.

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

[CITATION] A Smoothed Dual Approach for Variational Wasserstein Problems. arXiv. org

M Cuturi, G Peyré, A Rolet - 2015 - March

2015

Evolution variational inequality and wasserstein control in variable curvature context

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

In this note we continue the analysis of metric measure space with variable ricci curvature

bounds. First, we study $(\kappa, N) $-convex functions on metric spaces where $\kappa $ is

a lower semi-continuous function, and gradient flow curves in the sense of a new evolution …

2015

An Algorithmic Approach to Compute Principal Geodesics in ...

www.researchgate.net › publication › 279310014_An_Al...

Download Citation | An Algorithmic Approach to Compute Principal Geodesics in the Wasserstein Space | We consider in this work the space of probability ...

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015

Wasserstein distances and curves in the Wasserstein spaces

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

2015

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

We develop a gradient-flow theory for time-dependent functionals in abstract metric spaces.

Results about global well-posedness and asymptotic behavior of solutions are obtained.

Conditions on functionals and metric spaces allow to consider the Wasserstein space P2 …

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary -dependent sequences

J Dedecker, F Merlevede - arXiv preprint arXiv:1503.00113, 2015 - arxiv.org

We study the Wasserstein distance of order 1 between the empirical distribution and the

marginal distribution of stationary $\alpha $-dependent sequences. We prove some

moments inequalities of order p for any p $\ge $1, and we give some conditions under which …

<——2015——2015—— —— 340—-

2015 C Zhao, Y Guan[PDF] sfds.asso.fr

[PDF] Problemes d'adéquations entre distributions: une approche par un modele de déformations et la distance de Wasserstein.

H Lescornel, E del Barrio, JM Loubes - papersjds15.sfds.asso.fr

1 INRIA Saclay, 1 rue Honoré d'Estienne d'Orves, 91 120 Palaiseau.

helene.lescornel@inria.fr 2 Universitad de Valladolid, Facultad de Sciencas, C/ Prado de la Magdalena

s/n, 47005 Valladolid, ESPAGNE. tasio@eio.uva.es 3 Institut de Mathématiques de …

2015 Learning with a Wasserstein loss

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - arXiv preprint arXiv …, 2015 - arxiv.org

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

[PDF] mit.edu

M Araya-Polo, CA Frogner, C Zhang, H Mobahi… - 2015 - dspace.mit.edu

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

[CITATION] Learning with a Wasserstein Loss Advances in Neural Information Processing Systems (NIPS)

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - 2015

CITATION] Learning with a Wasserstein Loss Advances in Neural Information Processing Systems (NIPS)

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - 2015

Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

P Mohajerin Esfahani, D Kuhn - arXiv e-prints, 2015 - ui.adsabs.harvard.edu

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

WASP: Scalable Bayes via barycenters of subset posteriors

2015

S Srivastava, V Cevher, Q Dinh… - Artificial Intelligence …, 2015 - proceedings.mlr.press

… This section proposes to combine a collection of subset posteriors using their WB called

WASP. We prove that WASP is strongly consistent at the … We have presented the Wasserstein

Posterior (WASP) framework as a general approach for scalable Bayesian computations. The …

Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

P Mohajerin Esfahani, D Kuhn - arXiv e-prints, 2015 - ui.adsabs.harvard.edu

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

2015

[PDF] Bernstein von Mises Theorems in Wasserstein distance

A Bhattacharya, D Pati - arXiv preprint arXiv:1502.02336, 2015 - researchgate.net

We study the Bernstein von-Mises (BvM) phenomenon in Gaussian process regression

models by retaining the leading terms of the induced Karhunen–Loeve expansion. A recent

related result by [9] in a sieve prior context necessitates the prior to be flat, ruling out …

2015

Sliced and radon wasserstein barycenters of measures

N Bonneel, J Rabin, G Peyré, H Pfister - Journal of Mathematical Imaging …, 2015 - Springer

This article details two approaches to compute barycenters of measures using 1-D

Wasserstein distances along radial projections of the input measures. The first method

makes use of the Radon transform of the measures, and the second is the solution of a …

Sliced and radon wasserstein barycenters of measures

N Bonneel, J Rabin, G Peyré, H Pfister - Journal of Mathematical Imaging …, 2015 - Springer

This article details two approaches to compute barycenters of measures using 1-D

Wasserstein distances along radial projections of the input measures. The first method

makes use of the Radon transform of the measures, and the second is the solution of a …

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

Page 1. Nonlinearity PAPER Contraction in the Wasserstein metric for some Markov chains, and

applications to the dynamics of expanding maps To cite this article: Benoît R Kloeckner et al 2015

Nonlinearity 28 4117 View the article online for updates and enhancements. Related content …

[CITATION] Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

Shape classification using Wasserstein distance for brain morphometry analysis

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - International Conference on …, 2015 - Springer

Brain morphometry study plays a fundamental role in medical imaging analysis and

diagnosis. This work proposes a novel framework for brain cortical surface classification

using Wasserstein distance, based on uniformization theory and Riemannian optimal mass …

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear

systems. In the presence of stochastic jumps, state variables evolve as random process, with

associated time varying probability density functions. Consequently, system analysis is …

<——2015——2015—— —— 350—-

2015

Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

P Mohajerin Esfahani, D Kuhn - arXiv e-prints, 2015 - ui.adsabs.harvard.edu

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

Cited by 13 Related articles

Regularizing image intensity transformations using the wasserstein metric

M Oskarsson - Scandinavian Conference on Image Analysis, 2015 - Springer

In this paper we direct our attention to the problem of discretization effects in intensity

transformations of images. We propose to use the Wasserstein metric (also known as the

Earth mover distance) to bootstrap the transformation process. The Wasserstein metric gives …

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - … Fuzzy Systems (FUZZ-IEEE …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical

imaging. In this work, we proposes a novel method for shape classification of brain's

hippocampus using Wasserstein distance based on optimal mass transport theory. In …

2015

Convolutional wasserstein distances: Efficient optimal transportation on geometric domains

J Solomon, F De Goes, G Peyré, M Cuturi… - ACM Transactions on …, 2015 - dl.acm.org

This paper introduces a new class of algorithms for optimization problems involving optimal

transportation over geometric domains. Our main contribution is to show that optimal

transportation can be made tractable over large domains used in graphics, such as images …

2015

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and

solar power, power system operations face new challenges as the supply uncertainty

increases dramatically. Scenario analysis is widely used because it explicitly incorporates a …

[CITATION] A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015

Cited by 44 Related articles

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The

formulation is based on optimal transport wrt geometric distance and local feature similarity.

Geometric invariance and modelling of object-typical statistical variations is achieved by …

Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical

imaging. In this work, we proposes a novel method for shape classification of brain's

hippocampus using Wasserstein distance based on optimal mass transport theory. In …

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal

assignment map of clients to these facilities. This problem arises in various contexts in

decision mathematics such as, for instance, location theory in operational research and the …

Evolution variational inequality and wasserstein control in variable curvature context

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

In this note we continue the analysis of metric measure space with variable ricci curvature

bounds. First, we study $(\kappa, N) $-convex functions on metric spaces where $\kappa $ is

a lower semi-continuous function, and gradient flow curves in the sense of a new evolution …

<——2015——2015—— —— 360—-

[PDF] arxiv.or

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

MH Duong - Asymptotic Analysis, 2015 - content.iospress.com

In this paper, we study the Wasserstein gradient flow structure of the porous medium

equation restricted to q-Gaussians. The JKO-formulation of the porous medium equation

gives a variational functional K h, which is the sum of the (scaled-) Wasserstein distance and …

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and

solar power, power system operations face new challenges as the supply uncertainty

increases dramatically. Scenario analysis is widely used because it explicitly incorporates a …

[CITATION] … Engineering, Zhejiang University;; A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and …

Q WANG, W DONG, L YANG - 中国电机工程学报, 2015

[CITATION] YANG Li. A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

W Qun, D Wenlue - Proceedings of the CSEE, 2015

[HTML] A parametric registration model for warped distributions with Wasserstein's distance

M Agulló-Antolín, JA Cuesta-Albertos… - Journal of Multivariate …, 2015 - Elsevier

We consider a parametric deformation model for distributions. More precisely, we assume

we observe J samples of random variables which are warped from an unknown distribution

template. We tackle in this paper the problem of estimating the individual deformation …

[PDF] A Parametric Registration model for warped distributions with Wasserstein's distance

MA Antolín, JAC Albertos, H Lescornel, JM Loubes - personales.unican.es

We consider a parametric deformation model for distributions. More precisely, we assume

we observe J samples of random variables which are warped from an unknown distribution

template. We tackle in this paper the problem of estimating the individual deformation …

[CITATION] A Parametric Registration model for warped distributions with Wasserstein's distance

M Agullo, JA Cuesta, H Lescornel, JM Loubes - J. Multivariate Anal., to ap pear, 2014

[CITATION] A woman's world: Pam McKinnon on the decision to restore Wasserstein's cut dialogue to The Heidi Chronicles'

C Purcell - 2015 - Playbill

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

Evolution variational inequality and wasserstein control in variable curvature context

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

In this note we continue the analysis of metric measure space with variable ricci curvature

bounds. First, we study $(\kappa, N) $-convex functions on metric spaces where $\kappa $ is

a lower semi-continuous function, and gradient flow curves in the sense of a new evolution …

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear

systems. In the presence of stochastic jumps, state variables evolve as random process, with

associated time varying probability density functions. Consequently, system analysis is …

2015

Shape classification using Wasserstein distance for brain morphometry analysis

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - International Conference on …, 2015 - Springer

Brain morphometry study plays a fundamental role in medical imaging analysis and

diagnosis. This work proposes a novel framework for brain cortical surface classification

using Wasserstein distance, based on uniformization theory and Riemannian optimal mass …

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to

justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily …

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $

X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm

{Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

<——2015——2015—— —— 370—

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry–Ledoux's refined gradient estimate involving an upper …

2015 see 2018

Data-Driven Risk-Averse Stochastic Optimization with ...http://www.optimization-online.org › 2015/05

http://www.optimization-online.org › 2015/05
May 10, 2015 — We introduce the Wasserstein metric to construct the confidence set and by using this metric, we can successfully reformulate the risk-averse ...

[CITATION] Data-driven risk-averse stochastic optimization with wasserstein metric, Optim

C Zhao, Y Guan - 2015 - Online

[CITATION] Data-driven risk-averse stochastic optimization with wasserstein metric, Optim

C Zhao, Y Guan - 2015 - Online

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one

J Dedecker, A Fischer, B Michel - Electronic journal of statistics, 2015 - projecteuclid.org

This paper deals with the estimation of a probability measure on the real line from data

observed with an additive noise. We are interested in rates of convergence for the

Wasserstein metric of order $ p\geq1 $. The distribution of the errors is assumed to be …

[CITATION] Data-driven risk-averse stochastic optimization with wasserstein metric, Optim

C Zhao, Y Guan - 2015 - Online

[CITATION] Data-driven risk-averse stochastic optimization with wasserstein metric, Optim

C Zhao, Y Guan - 2015 - Online

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

2015

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

2015

Surface-based shape classification using Wasserstein distance

M Ma, N Lei, K Su, J Zhang, C Wen, L Cui… - Geometry, Imaging …, 2015 - intlpress.com

Surface based shape analysis plays a fundamental role in computer vision and medical

imaging. In this work, we proposes a novel method for shape classification of brain's

hippocampus using Wasserstein distance based on optimal mass transport theory. In …

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

MH Duong - Asymptotic Analysis, 2015 - content.iospress.com

In this paper, we study the Wasserstein gradient flow structure of the porous medium

equation restricted to q-Gaussians. The JKO-formulation of the porous medium equation

gives a variational functional K h, which is the sum of the (scaled-) Wasserstein distance and …

2015

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

2015

Nonpositive curvature, the variance functional, and the Wasserstein barycenter

YH Kim, B Pass - arXiv preprint arXiv:1503.06460, 2015 - arxiv.org

This paper connects nonpositive sectional curvature of a Riemannian manifold with the

displacement convexity of the variance functional on the space $ P (M) $ of probability

measures over $ M $. We show that $ M $ has nonpositive sectional curvature and has trivial …

Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

P Mohajerin Esfahani, D Kuhn - arXiv e-prints, 2015 - ui.adsabs.harvard.edu

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

Cited by 17 Related articles

<——2015——2015—— —— 380—-

2015

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

2015

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

The Lagrangian description of absolutely continnous curves of probability measures on the

real line is analyzed. Whereas each such curve admits a Lagrangian description as a well-

defined flow of its velocity field, further conditions on the curve and/or its velocity are …

[HTML] Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - Journal of Differential Equations, 2015 - Elsevier

We perform a systematic study of optimization problems in the Wasserstein spaces that are

analogs of infinite horizon, deterministic control problems. We derive necessary conditions

on action minimizing paths and present a sufficient condition for their existence. We also …

Sliced and radon wasserstein barycenters of measures

N Bonneel, J Rabin, G Peyré, H Pfister - … of Mathematical Imaging and …, 2015 - Springer

This article details two approaches to compute barycenters of measures using 1-D

Wasserstein distances along radial projections of the input measures. The first method

makes use of the Radon transform of the measures, and the second is the solution of a …

2015

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to

justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily …

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear

systems. In the presence of stochastic jumps, state variables evolve as random process, with

associated time varying probability density functions. Consequently, system analysis is …

Wasserstein training of Boltzmann machines

G Montavon, KR Müller, M Cuturi - arXiv preprint arXiv:1507.01972, 2015 - arxiv.org

The Boltzmann machine provides a useful framework to learn highly complex, multimodal

and multiscale data distributions that occur in the real world. The default method to learn its

parameters consists of minimizing the Kullback-Leibler (KL) divergence from training …

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein

distance. Compared to the more classical total variation bounds, the proposed rate of

convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on …

<——2015——2015—— —— 390—-

A statistical analysis of a deformation model with Wasserstein barycenters: estimation procedure and goodness of fit test

E Del Barrio, H Lescornel, JM Loubes - arXiv preprint arXiv:1508.06465, 2015 - arxiv.org

We propose a study of a distribution registration model for general deformation functions. In

this framework, we provide estimators of the deformations as well as a goodness of fit test of

the model. For this, we consider a criterion which studies the Fr {é} chet mean (or …

Propagation of chaos, Wasserstein gradient flows and toric Kahler-Einstein metrics

RJ Berman, M Onnheim - arXiv preprint arXiv:1501.07820, 2015 - arxiv.org

Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-

equilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We …

L^p-Wasserstein distances on state and quasi-state spaces of -algebras

D Zaev - arXiv preprint arXiv:1505.06061, 2015 - arxiv.org

We construct an analogue of the classical $ L^ p $-Wasserstein distance for the state space

of a $ C^* $-algebra. Given an abstract Lipschitz gauge on a $ C^* $-algebra $\mathcal {A} $

in the sense of Rieffel, one can define the classical $ L^ p $-Wasserstein distance on the …

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

The Lagrangian description of absolutely continnous curves of probability measures on the

real line is analyzed. Whereas each such curve admits a Lagrangian description as a well-

defined flow of its velocity field, further conditions on the curve and/or its velocity are …

[HTML] Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

F Cacciafesta, AS de Suzzoni - Journal of Differential Equations, 2015 - Elsevier

In this paper, we prove the continuity of the flow of KdV on spaces of probability measures

with respect to a combination of Wasserstein distances on H s, s> 0 and L 2. We are

motivated by the existence of an invariant measure belonging to the spaces onto which …

2015

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

D Zaev - arXiv preprint arXiv:1505.03721, 2015 - arxiv.org

Let $ X $ be a Polish space, $\mathcal {P}(X) $ be the set of Borel probability measures on $

X $, and $ T\colon X\to X $ be a homeomorphism. We prove that for the simplex $\mathrm

{Dom}\subseteq\mathcal {P}(X) $ of all $ T $-invariant measures, the Kantorovich metric on …

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

<——2015——2015—— —— 400—-

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

We develop a gradient-flow theory for time-dependent functionals in abstract metric spaces.

Results about global well-posedness and asymptotic behavior of solutions are obtained.

Conditions on functionals and metric spaces allow to consider the Wasserstein space P2 …

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

Numerical methods for matching for teams and Wasserstein barycenters

G Carlier, A Oberman, E Oudet - … : Mathematical Modelling and …, 2015 - esaim-m2an.org

Equilibrium multi-population matching (matching for teams) is a problem from mathematical

economics which is related to multi-marginal optimal transport. A special but important case

is the Wasserstein barycenter problem, which has applications in image processing and …

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - Networks & Heterogeneous Media, 2015 - aimsciences.org

We study the approximation of Wasserstein gradient structures by their finite-dimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

On Wasserstein barycenters and MMOSPA estimation

M Baum, PK Willett… - IEEE Signal Processing …, 2015 - ieeexplore.ieee.org

The two title concepts have been evolving rather rapidly, but independent of each other. The

Wasserstein barycenter, on one hand, has mostly made its appearance in image processing

as it can describe a measure of similarity between images. Its minimization might, for …

[CITATION] On Wasserstein Barycenters and MMOSPA Estimation...................... M. Baum, PK Willett, and UD Hanebeck 1511 Objective Consumer Device Photo …

S Imani, SA Ghorashi, T Bouchoucha, MFA Ahmed… - ieeexplore.ieee.org

LETTERS On Wasserstein Barycenters and MMOSPA Estimation ...................... M. Baum, PK

Willett, and UD Hanebeck … Objective Consumer Device Photo Quality Evaluation ................

............ MA Saad, P. Corriveau, and R. Jaladi …

2015

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-

randomly centered random sums of real iid random variables with a finite third moment and

the standard normal distribution. Except for the case of mean zero summands, these bounds …

First and second moments for self‐similar couplings and Wasserstein distances

JM Fraser - Mathematische Nachrichten, 2015 - Wiley Online Library

We study aspects of the Wasserstein distance in the context of self‐similar measures.

Computing this distance between two measures involves minimising certain moment

integrals over the space of couplings, which are measures on the product space with the …

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The

formulation is based on optimal transport wrt geometric distance and local feature similarity.

Geometric invariance and modelling of object-typical statistical variations is achieved by …

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry–Ledoux's refined gradient estimate involving an upper …

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

<——2015——2015—— —— 410—-

Nonpositive curvature, the variance functional, and the Wasserstein barycenter

YH Kim, B Pass - arXiv preprint arXiv:1503.06460, 2015 - arxiv.org

This paper connects nonpositive sectional curvature of a Riemannian manifold with the

displacement convexity of the variance functional on the space $ P (M) $ of probability

measures over $ M $. We show that $ M $ has nonpositive sectional curvature and has trivial …

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

Distribution function estimates by Wasserstein metric and Bernstein approximation for C− 1 functions

[PDF] Modified Arratia flow and Wasserstein diffusion

V Konarovskyi, M von Renesse - Communications on Pure and …, 2015 - researchgate.net

Extending previous work [20] by the first author we present a variant of the Arratia flow of a

field of coalescing Brownian motions starting from every point of the unit interval. The

important new feature of the model is that individual particles carry mass which aggregated …

Z Wu, Z Tian - Applied Mathematics-A Journal of Chinese Universities, 2015 - Springer

The aim of the paper is to estimate the density functions or distribution functions measured

by Wasserstein metric, a typical kind of statistical distances, which is usually required in the

statistical learning. Based on the classical Bernstein approximation, a scheme is presented …

Evolution variational inequality and wasserstein control in variable curvature context

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

In this note we continue the analysis of metric measure space with variable ricci curvature

bounds. First, we study $(\kappa, N) $-convex functions on metric spaces where $\kappa $ is

a lower semi-continuous function, and gradient flow curves in the sense of a new evolution …

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

Barycenter in Wasserstein spaces: Existence and consistency

T Le Gouic, JM Loubes - … Conference on Geometric Science of Information, 2015 - Springer

We study barycenters in the Wasserstein space P _p (E) P p (E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure PP on P _p

(E) P p (E) as its Fréchet mean. The paper establishes its existence and states consistency …

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

2015

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - Networks & Heterogeneous Media, 2015 - aimsciences.org

We study the approximation of Wasserstein gradient structures by their finite-dimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

<——2015——2015—— —— 420—-

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-

randomly centered random sums of real iid random variables with a finite third moment and

the standard normal distribution. Except for the case of mean zero summands, these bounds …

Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

[HTML] Value functions in the Wasserstein spaces: finite time horizons

R Hynd, HK Kim - Journal of Functional Analysis, 2015 - Elsevier

We study analogs of value functions arising in classical mechanics in the space of

probability measures endowed with the Wasserstein metric W p, for 1< p<∞. Our main result

is that each of these generalized value functions is a type of viscosity solution of an …

2015

P Mohajerin Esfahani, D Kuhn - arXiv e-prints, 2015 - ui.adsabs.harvard.edu

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

Cited by 14 Related articles

Nonpositive curvature, the variance functional, and the Wasserstein barycenter

YH Kim, B Pass - arXiv preprint arXiv:1503.06460, 2015 - arxiv.org

This paper connects nonpositive sectional curvature of a Riemannian manifold with the

displacement convexity of the variance functional on the space $ P (M) $ of probability

measures over $ M $. We show that $ M $ has nonpositive sectional curvature and has trivial …

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

2015

[HTML] Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - Journal of Differential Equations, 2015 - Elsevier

We perform a systematic study of optimization problems in the Wasserstein spaces that are

analogs of infinite horizon, deterministic control problems. We derive necessary conditions

on action minimizing paths and present a sufficient condition for their existence. We also …

Regularizing image intensity transformations using the wasserstein metric

M Oskarsson - Scandinavian Conference on Image Analysis, 2015 - Springer

In this paper we direct our attention to the problem of discretization effects in intensity

transformations of images. We propose to use the Wasserstein metric (also known as the

Earth mover distance) to bootstrap the transformation process. The Wasserstein metric gives …

[PDF] Geodesic kriging in the Wasserstein space

R Gouet, A López, JM Ortiz - … of the 17th annual Conference of the …, 2015 - researchgate.net

We introduce the method of Geodesic Kriging for spatially-dependent functional data, not

supported by a linear space. We present the theory for Hadamard metric spaces and provide

more detailed analysis for particular cases such the Hilbert and Wasserstein spaces …

[PDF] On the Wasserstein-Fisher-Rao metric

FX Vialard - MATH ON THE ROCKS, 2015 - angkor.univ-mlv.fr

This note gives a summary of the presentation that I gave at the workshop on shape analysis

1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to

measures that have different total masses. This generalization enjoys most of the properties …

[PDF] A random locational M-estimation problem based on the L2-Wasserstein distance

A Daouia, I Van Keilegom - 2015 - dial.uclouvain.be

The fair placement of a facility often depends on other existing players and on an optimal

assignment map of clients to these facilities. This problem arises in various contexts in

decision mathematics such as, for instance, location theory in operational research and the …

An Algorithmic Approach to Compute Principal Geodesics in the ...

<——2015——2015—— —— 430—-

https://www.researchgate.net › publication › 279310014_...

We onsider in this work the space of probability measures P(X) on a Hilbert space X endowed with the 2-Wasserstein metric. Given a family of probability ...

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015

Shape classification using Wasserstein distance for brain morphometry analysis

Z Su, W Zeng, Y Wang, ZL Lu, X Gu - International Conference on …, 2015 - Springer

Brain morphometry study plays a fundamental role in medical imaging analysis and

diagnosis. This work proposes a novel framework for brain cortical surface classification

using Wasserstein distance, based on uniformization theory and Riemannian optimal mass …

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia - Bernoulli, 2015 - projecteuclid.org

The paper gives the bounds on the solutions to a Stein equation for the negative binomial

distribution that are needed for approximation in terms of the Wasserstein metric. The proofs

are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 …

Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein Distance

A Irpino, R Verde - Advances in Data Analysis and Classification, 2015 - Springer

In this paper we present a new linear regression technique for distributional symbolic

variables, ie, variables whose realizations can be histograms, empirical distributions or

empirical estimates of parametric distributions. Such data are known as numerical modal …

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

CITATION] A Smoothed Dual Approach for Variational Wasserstein Problems. arXiv. org

M Cuturi, G Peyré, A Rolet - 2015 - March

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

C Jin - Nonlinear Analysis, 2015 - Elsevier

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the …

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one

J Dedecker, A Fischer, B Michel - Electronic journal of statistics, 2015 - projecteuclid.org

This paper deals with the estimation of a probability measure on the real line from data

observed with an additive noise. We are interested in rates of convergence for the

Wasserstein metric of order $ p\geq1 $. The distribution of the errors is assumed to be …

A Smoothed Dual Approach for ...

deepai.org

[CITATION] A Smoothed Dual Formulation for Variational Wasserstein Problems

M Cuturi, G Peyré, A Rolet - arXiv preprint arXiv:1503.02533, 2015 - e-print

Learning with a Wasserstein loss

2015

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - arXiv preprint arXiv …, 2015 - arxiv.org

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

<——2015——2015—— —— 440-—

[PDF] A Hitchhiker's guide to Wasserstein distances

G Basso - 2015 - people.math.ethz.ch

The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions

we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric

space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a signed …

Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein Distance

A Irpino, R Verde - Advances in Data Analysis and Classification, 2015 - Springer

In this paper we present a new linear regression technique for distributional symbolic

variables, ie, variables whose realizations can be histograms, empirical distributions or

empirical estimates of parametric distributions. Such data are known as numerical modal …

2015

A smoothed dual approach for variational wasserstein problems

M Cuturi, G Peyré - arXiv preprint arXiv:1503.02533, 2015 - arxiv.org

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

We develop a gradient-flow theory for time-dependent functionals in abstract metric spaces.

Results about global well-posedness and asymptotic behavior of solutions are obtained.

Conditions on functionals and metric spaces allow to consider the Wasserstein space P2 …

2015

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

J Shao, B Wu - arXiv preprint arXiv:1507.07995, 2015 - arxiv.org

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but

lower bounded by a continuous function, we give a new characterization of this lower bound

through the convexity of relative entropy on the probability space over the Riemannian …

https://papers.nips.cc › paper › 5679-learning-with-a-w...

by C Frogner · 2015 · Cited by 327 — Authors. Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya, Tomaso A. Poggio. Abstract. Learning to predict multi-label outputs is challenging, ...

[CITATION] Learning with a Wasserstein Loss Advances in Neural Information Processing Systems (NIPS)

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - 2015

An Algorithmic Approach to Compute Principal Geodesics in the ...

https://www.researchgate.net › publication › 279310014_...

We consider in this work the space of probability measures P(X) on a Hilbert space X endowed with the 2-Wasserstein metric. Given a family of probability ...

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015

2015 arXiv [v5] Fri, 17 Jul 2015 16:14:10 UTC (25 KB)

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. ArXiv e-prints

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2015

[PDF] Problemes d'adéquations entre distributions: une approche par un modele de déformations et la distance de Wasserstein.

[PDF] sfds.asso.fr

H Lescornel, E del Barrio, JM Loubes - papersjds15.sfds.asso.fr

1 INRIA Saclay, 1 rue Honoré d'Estienne d'Orves, 91 120 Palaiseau.

helene.lescornel@inria.fr 2 Universitad de Valladolid, Facultad de Sciencas, C/ Prado de la Magdalena

s/n, 47005 Valladolid, ESPAGNE. tasio@eio.uva.es 3 Institut de Mathématiques de …

<——2015——2015—— —— 450—-

2015

On the rate of convergence in Wasserstein distance of the empirical measure

N Fournier, A Guillin - Probability Theory and Related Fields, 2015 - Springer

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability

distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ,

when measured in the Wasserstein distance of order p> 0 p> 0. We provide some satisfying …

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to

justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily …

2015 [PDF] aimsciences.org

K Disser, M Liero - Networks & Heterogeneous Media, 2015 - aimsciences.org

We study the approximation of Wasserstein gradient structures by their finite-dimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia - Bernoulli, 2015 - projecteuclid.org

The paper gives the bounds on the solutions to a Stein equation for the negative binomial

distribution that are needed for approximation in terms of the Wasserstein metric. The proofs

are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 …

From large deviations to Wasserstein gradient flows in multiple dimensions

M Erbar, J Maas, M Renger - Electronic Communications in …, 2015 - projecteuclid.org

We study the large deviation rate functional for the empirical distribution of independent

Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier

and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma …

2015

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein

distance. Compared to the more classical total variation bounds, the proposed rate of

convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods

C Döbler - arXiv preprint arXiv:1504.05938, 2015 - arxiv.org

We prove abstract bounds on the Wasserstein and Kolmogorov distances between non-

randomly centered random sums of real iid random variables with a finite third moment and

the standard normal distribution. Except for the case of mean zero summands, these bounds …

2015 [PDF] arxiv.org

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

… ( ) ( ) Ω Ω α α α α − − W W W diam diam . 1 1 1 1 We only state our results with respect to

the Lipschitz regularity to avoid making the notation heavier. Note that the constants C and

λ are explicit, although convoluted (and λ may be much closer to 1 than θ). The Wasserstein …

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

[HTML] Value functions in the Wasserstein spaces: finite time horizons

R Hynd, HK Kim - Journal of Functional Analysis, 2015 - Elsevier

We study analogs of value functions arising in classical mechanics in the space of

probability measures endowed with the Wasserstein metric W p, for 1< p<∞. Our main result

is that each of these generalized value functions is a type of viscosity solution of an …

<——2015——2015—— —— 460—-

C Jin - Nonlinear Analysis, 2015 - Elsevier

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the …

Barycenter in Wasserstein spaces: Existence and consistency

T Le Gouic, JM Loubes - … Conference on Geometric Science of Information, 2015 - Springer

We study barycenters in the Wasserstein space P _p (E) P p (E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure PP on P _p

(E) P p (E) as its Fréchet mean. The paper establishes its existence and states consistency …

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

I Gentil - Potential Analysis, 2015 - Springer

We prove a refined contraction inequality for diffusion semigroups with respect to the

Wasserstein distance on a compact Riemannian manifold taking account of the dimension.

The result generalizes in a Riemannian context, the dimensional contraction established in …

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the

presence of a potential field. The non-locality is due to the appearance of the 'fractional

Laplacian'in the corresponding PDE, in place of the classical Laplacian which distinguishes …

Wasserstein distances and curves in the Wasserstein spaces

F Santambrogio - Optimal Transport for Applied Mathematicians, 2015 - Springer

In this chapter we use the minimal value of transport problems between two probabilities in

order to define a distance on the space of probabilities. We mainly consider costs of the form

c (x, y)=| x− y| pc (x, y)= | xy |^ p in Ω⊂ ℝ d\varOmega ⊂ R^ d. We analyze the properties of …

2015

[HTML] Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - Journal of Differential Equations, 2015 - Elsevier

We perform a systematic study of optimization problems in the Wasserstein spaces that are

analogs of infinite horizon, deterministic control problems. We derive necessary conditions

on action minimizing paths and present a sufficient condition for their existence. We also …

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

The Lagrangian description of absolutely continnous curves of probability measures on the

real line is analyzed. Whereas each such curve admits a Lagrangian description as a well-

defined flow of its velocity field, further conditions on the curve and/or its velocity are …

[PDF] Geodesic kriging in the Wasserstein space

R Gouet, A López, JM Ortiz - … of the 17th annual Conference of the …, 2015 - researchgate.net

We introduce the method of Geodesic Kriging for spatially-dependent functional data, not

supported by a linear space. We present the theory for Hadamard metric spaces and provide

more detailed analysis for particular cases such the Hilbert and Wasserstein spaces …

[HTML] Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

F Cacciafesta, AS de Suzzoni - Journal of Differential Equations, 2015 - Elsevier

In this paper, we prove the continuity of the flow of KdV on spaces of probability measures

with respect to a combination of Wasserstein distances on H s, s> 0 and L 2. We are

motivated by the existence of an invariant measure belonging to the spaces onto which …

On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

M Amsaad, A Tudorascu - Indiana University Mathematics Journal, 2015 - JSTOR

The Lagrangian description of absolutely continnous curves of probability measures on the

real line is analyzed. Whereas each such curve admits a Lagrangian description as a well-

defined flow of its velocity field, further conditions on the curve and/or its velocity are …

<——2015——2015—— —— 470—-

Evolution variational inequality and wasserstein control in variable curvature context

C Ketterer - arXiv preprint arXiv:1509.02178, 2015 - arxiv.org

In this note we continue the analysis of metric measure space with variable ricci curvature

bounds. First, we study $(\kappa, N) $-convex functions on metric spaces where $\kappa $ is

a lower semi-continuous function, and gradient flow curves in the sense of a new evolution …

[PDF] A Hitchhiker's guide to Wasserstein distances

G Basso - 2015 - people.math.ethz.ch

The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions

we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric

space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a signed …

[PDF] Bernstein von Mises Theorems in Wasserstein distance

A Bhattacharya, D Pati - arXiv preprint arXiv:1502.02336, 2015 - researchgate.net

We study the Bernstein von-Mises (BvM) phenomenon in Gaussian process regression

models by retaining the leading terms of the induced Karhunen–Loeve expansion. A recent

related result by [9] in a sieve prior context necessitates the prior to be flat, ruling out …

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on …

Cite Cited by 25 Related articles All 6 versions

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and

solar power, power system operations face new challenges as the supply uncertainty

increases dramatically. Scenario analysis is widely used because it explicitly incorporates a …

[CITATION] … Engineering, Zhejiang University;; A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and …

Q WANG, W DONG, L YANG - 中国电机工程学报, 2015

[CITATION] YANG Li. A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

W Qun, D Wenlue - Proceedings of the CSEE, 2015

Fuzzy clustering of distribution-valued data using an adaptive L₂ Wasserstein distance

2015

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

An Algorithmic Approach to Compute Principal Geodesics in the ...

https://www.researchgate.net › publication › 279310014_...

Download Citation | An Algorithmic Approach to Compute Principal Geodesics ... analysis in the Wasserstein space (Bigot et al., 2013; Seguy and Cuturi, 2015) .

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - arXiv preprint arXiv:1506.07944, 2015

2015

ÇÏ√smooth error in dimension one

J Dedecker, A Fischer, B Michel - Electronic journal of statistics, 2015 - projecteuclid.org

This paper deals with the estimation of a probability measure on the real line from data

observed with an additive noise. We are interested in rates of convergence for the

Wasserstein metric of order $ p\geq1 $. The distribution of the errors is assumed to be …

2015

Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

C Jin - Nonlinear Analysis, 2015 - Elsevier

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-

Wasserstein space with the initial mass and energy being finite. Our method is based on a

main observation pioneered by Brenier and Grenier that we can recover the solution of the …

2015

Barycenter in Wasserstein spaces: Existence and consistency

T Le Gouic, JM Loubes - … Conference on Geometric Science of Information, 2015 - Springer

We study barycenters in the Wasserstein space P _p (E) P p (E) of a locally compact

geodesic space (E, d). In this framework, we define the barycenter of a measure PP on P _p

(E) P p (E) as its Fréchet mean. The paper establishes its existence and states consistency …

<——2015——2015—— —— 480—-

2015

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

… To overcome it, we employ an approximation of the diffusion process by geodesic random

walks developed in [23, 25, 29, 41] … (1) (Space-time $( L^p, L^\beta )$-Wasserstein control)

For $\mu _0 , \mu _1 \in \fancyscript{P}(M)$ and $0 \le s < t$ …

2015

[HTML] Value functions in the Wasserstein spaces: finite time horizons

R Hynd, HK Kim - Journal of Functional Analysis, 2015 - Elsevier

… Download PDFDownload. Share. Export. Advanced. Elsevier. Journal of Functional Analysis.

Volume 269, Issue 4, 15 August 2015, Pages 968-997. Journal of Functional Analysis.

Value functions in the Wasserstein spaces: finite time horizons …

2015

[PDF] GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE

JC VALENCIA-GUEVARA, LCF FERREIRA - Livro de Resumos do IX ENAMA - core.ac.uk

… de Análise Matemática e Aplicaçoes UNIOESTE-Universidade Estadual do Oeste do Paraná

IX ENAMA-Novembro 2015 163–164 GRADIENT FLOWS OF TIME-DEPENDENT FUNCTIONALS

IN METRIC SPACES AND APPLICATIONS IN THE WASSERSTEIN SPACE JULIO C …

2015

[HTML] Value functions in the Wasserstein spaces: finite time horizons

R Hynd, HK Kim - Journal of Functional Analysis, 2015 - Elsevier

We study analogs of value functions arising in classical mechanics in the space of

probability measures endowed with the Wasserstein metric W p, for 1< p<∞. Our main result

is that each of these generalized value functions is a type of viscosity solution of an …

2015

Distribution function estimates by Wasserstein metric and Bernstein approximation for C− 1 functions

[HTML] Infinite horizon value functions in the Wasserstein spaces

R Hynd, HK Kim - Journal of Differential Equations, 2015 - Elsevier

We perform a systematic study of optimization problems in the Wasserstein spaces that are

analogs of infinite horizon, deterministic control problems. We derive necessary conditions

on action minimizing paths and present a sufficient condition for their existence. We also …

2015

Z Wu, Z Tian - Applied Mathematics-A Journal of Chinese Universities, 2015 - Springer

The aim of the paper is to estimate the density functions or distribution functions measured

by Wasserstein metric, a typical kind of statistical distances, which is usually required in the

statistical learning. Based on the classical Bernstein approximation, a scheme is presented …

2015

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

[PDF] A Hitchhiker's guide to Wasserstein distances

G Basso - 2015 - people.math.ethz.ch

The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions

we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric

space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a signed …

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

2015

On gradient structures for Markov chains and the passage to ...

https://www.aimsciences.org › doi › nhm.2015.10.233

by K Disser · 2015 · Cited by 20 — Keywords: evolutionary Γ-convergence, Markov chains., entropy/entropy- dissipation formulation, discrete gradient flow structures, Wasserstein gradient flow.

On gradient structures for reversible Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - wias-berlin.de

In this talk we discuss the limit passage from reversible, time-continuous Markov chains to

the one-dimensional Fokker–Planck equation with linear drift. In [Mie11] and [Maa11] it was

shown that Markov chains satisfying the reversibility condition (also called detailed balance …

Heterogeneous Media; Findings from Weierstrass Institute Update Knowledge of Heterogeneous Media

(On Gradient Structures For Markov Chains And The Passage To Wasserstein gradient flows)

Network weekly news, Jun 22, 2015, 170

According to news reporting out of Berlin, Germany, by VerticalNews editors, research stated, "We study the approximation of Wasserstein gradient structures by...

Newspaper ArticleCitation Online

<——2015——2015—— —— 490—-

Learning with a Wasserstein loss

C Frogner, C Zhang, H Mobahi, M Araya… - … information processing …, 2015 - papers.nips.cc

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The

Wasserstein distance provides a natural notion of dissimilarity for probability measures.

Although optimizing with respect to the exact Wasserstein distance is costly, recent work has

described a regularized approximation that is efficiently computed. We describe an efficient …

C Frogner, C Zhang, H Mobahi… - Advances in neural …, 2015 - proceedings.neurips.cc

… , based on the Wasserstein distance. The Wasserstein distance provides a natural notion of

… To our knowledge, this paper represents the first use of the Wasserstein distance as a loss …

[CITATION] Learning with a Wasserstein Loss Advances in Neural Information Processing Systems (NIPS)

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - 2015

C Cited by 453 Related articles All 16 versions

2015 [PDF] aimsciences.org

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - Networks & Heterogeneous Media, 2015 - aimsciences.org

We study the approximation of Wasserstein gradient structures by their finite-dimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

… While we stick here to the more standard case of Hölder potentials, we take a more geomet- ric

point of view that allows us first to handle a much broader family of dynamical systems and second

to derive a number of corollaries. Namely, the contraction in the Wasserstein metric easily implies …

[CITATION] Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

Underlying metric structures of some evolution equations with focus on the Wasserstein distance

2015 [PDF] tuwien.at

P Fuchs - 2015 - repositum.tuwien.at

This thesis is concerned with the investigation of evolution equations from different metric

points of view. We derive quantum mechanical models from Lagrangian principles on the so

called Wasserstein space. Futhermore we study the numerical treatment of gradient flows …

On local well-posedness of the thin-film equation via the Wasserstein gradient flow

E Kamalinejad - Calculus of Variations and Partial Differential …, 2015 - Springer

A local existence and uniquness of the gradient flow of one dimensional Dirichlet energy on

the Wasserstein space is proved. The proofs are based on a relaxation of displacement

convexity in the Wasserstein space and can be applied to a family of higher order energy …

2015

Findings in Mathematical Modelling Reported from University of Grenoble

(Numerical Methods For Matching For Teams And Wasserstein Barycenters)

Journal of Technology & Science, 12/2015

NewsletterFull Text Online

Mathematical Modelling; Findings in Mathematical Modelling Reported from University of Grenoble (Numerical Methods For Matching For Teams And Wasserstein...

Journal of technology & science, Dec 20, 2015, 106

According to news reporting out of Grenoble, France, by VerticalNews editors, research stated, "Equilibrium multi-population matching (matching for teams) is a...

Newspaper ArticleFull Text Online

Researchers from Autodesk Inc. Discuss Findings in Computer Graphics

(Convolutional Wasserstein...

Computer Weekly News, 09/2015

NewsletterFull Text Online

New Functional Analysis Findings from Seoul National University Outlined

(Value functions in the Wasserstein spaces: finite time horizons)

Journal of Technology & Science, 07/2015

NewsletterFull Text Online

Researchers' Work from Graduate School of Science Focuses on Differential Equations

(Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates)

Journal of Technology & Science, 09/2015

NewsletterFull Text Online

Reports Summarize Probability Research Study Results from Clermont Ferrand University

(On the rate of convergence in Wasserstein of the empirical measure)

Journal of Technology & Science, 09/2015

NewsletterFull Text Online

<——2015——2015—— —— 500—-

Reports from University of Melbourne Describe Recent Advances in Mathematical Statistics and Probability

(Stein factors for negative binomial approximation in Wasserstein. distance)

Journal of Mathematics, 06/2015

NewsletterCitation Online

Data on Potential Analysis Described by Researchers at University of Lyon

(Dimensional Contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold)

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

Journal of Mathematics, 05/2015

NewsletterCitation Online

Findings from Beijing Normal University in the Area of Stochastics and Dynamics Described

(Ergodicity of regime-switching diffusions in Wasserstein distances

Journal of Mathematics, 03/2015

NewsletterCitation Online

Findings in the Area of Applied Mathematics Reported from University of Victoria

(Weak solutions to a fractional Fokker-Planck equation via splitting and Wasserstein gradient flow(

Journal of Mathematics, 03/2015

New Control and Systems Engineering Study Findings Reported from Texas A&M University

(Performance and robustness analysis of stochastic jump linear systems using Wasserstein metric)

Journal of Engineering, 02/2015

NewsletterCitation Online

2015 see 2014 [PDF] wiley.com

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2015 - Wiley Online Library

… brightness adaptive contrast energy term and a Wasserstein dispersion energy term. In the

… we describe the Wasserstein dispersion energy term based on the Wasserstein distance [21], …

Findings in Image Processing Reported from Nanjing University of Science and Technology

(Local brightness adaptive image colour enhancement with Wasserstein distance)

Computer Weekly News, 01/2015

NewsletterFull Text Online

2015

Studies Conducted at Technical University on Asymptotic Analysis Recently Reported

(Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of yje porous medium equation)

Journal of Mathematics, 04/2015

NewsletterCitation Online

Functional Analysis; New Functional Analysis Findings from Seoul National University Outlined (Value functions in the Wasserstein gradient

Journal of technology & science, Jul 19, 2015, 299

According to news originating from Seoul, South Korea, by VerticalNews correspondents, research stated, "We study analogs of value functions arising in...

Newspaper ArticleFull Text Online

Probability Research; New Findings from M. Erbar and Co-Authors Describe Advances in Probability Research (From large deviations to Wasserstein gradient

Journal of robotics & machine learning, Dec 21, 2015, 92

According to news reporting out of Berlin, Germany, by VerticalNews editors, research stated, "We study the large deviation rate functional for the empirical...

Newspaper ArticleCitation Online

Differential Equations; Researchers' Work from Graduate School of Science Focuses on Differential Equations

(Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates)

Journal of technology & science, Sep 20, 2015, 423

According to news reporting originating from Tokyo, Japan, by VerticalNews editors, the research stated, "The duality in Bakry-A parts per thousand mery's...

Newspaper ArticleFull Text Online

<——2015——2015—— —— 510—-

Probability Research; Reports Summarize Probability Research Study Results from Clermont Ferrand University

(On the rate of convergence in Wasserstein distance of the empirical measure)

Journal of technology & science, Sep 13, 2015, 610

According to the news editors, the research concluded: "We extend also the non asymptotic -bounds to stationary -mixing sequences, Markov chains, and to some...

Newspaper ArticleFull Text Online

Computer Graphics; Researchers from Autodesk Inc. Discuss Findings in Computer Graphics (Convolutional Wasserstein...

Computer Weekly News, Sep 3, 2015, 501

According to the news editors, the research concluded: "We demonstrate the versatility and efficiency of our method on tasks including reflectance...

Newspaper ArticleCitation Online

June 2015

An Algorithmic Approach to Compute Principal Geodesics in ...

https://www.researchgate.net › publication › 279310014_...

We consider in this work the space of probability measures P(X) on a Hilbert space X endowed with the 2-Wasserstein metric. Given a family of probability ...

[CITATION] An algorithmic approach to compute principal geodesics in the Wasserstein space

V Seguy, M Cuturi - Preprint, 2015

Mathematical Statistics and Probability; Reports from University of Melbourne Describe Recent Advances in Mathematical Statistics and Probability

(Stein factors for negative binomial approximation in Wasserstein...

Journal of technology & science, Jun 7, 2015, 424

According to news reporting from Parkville, Australia, by VerticalNews journalists, research stated, "The paper gives the bounds on the solutions to a Stein...

Newspaper ArticleFull Text Online

Potential Analysis; Data on Potential Analysis Described by Researchers at University of Lyon

(Dimensional Contraction in Wasserstein...

Journal of technology & science, May 24, 2015, 141

According to news originating from Villeurbanne, France, by VerticalNews editors, the research stated, "We prove a refined contraction inequality for diffusion...

Newspaper ArticleFull Text Online

2015 newsletters newspapers from pennstate library

Stochastics and Dynamics; Findings from Beijing Normal University in the Area of Stochastics and Dynamics Described (Ergodicity of regime-switching diffusions in Wasserstein distances)

Journal of technology & science, Mar 22, 2015, 101

According to news originating from Beijing, People's Republic of China, by VerticalNews editors, the research stated, "Based on the theory of M-matrix and...

Newspaper ArticleFull Text Online

Applied Mathematics; Findings in the Area of Applied Mathematics Reported from University of Victoria

(Weak solutions to a fractional Fokker-Planck equation via splitting and Wasserstein gradient flow)

Journal of technology & science, Mar 8, 2015, 218

According to news originating from Victoria, Canada, by VerticalNews correspondents, research stated, "We study a linear fractional Fokker-Planck equation that...

Newspaper ArticleFull Text Online

Control and Systems Engineering; New Control and Systems Engineering Study Findings Reported from Texas A&M University (Performance and robustness analysis of stochastic jump linear systems using Wasserstein metric)

Journal of engineering (Atlanta, Ga.), Feb 25, 2015, 1088

According to news reporting originating in College Station, Texas, by VerticalNews journalists, research stated, "This paper focuses on the performance and...

Newspaper ArticleCitation Online
Cited by 26 Related articles All 10 versions

2015

] A parametric registration model for warped distributions with Wasserstein's distance

M Agulló-Antolín, JA Cuesta-Albertos… - Journal of Multivariate …, 2015 - Elsevier

… For this, we construct a registering criterion based on the Wasserstein distance to

quantify the alignment of the distributions. We prove consistency of the empirical estimators. …

Zbl 1329.62249

2015

Asymptotic Analysis; Studies Conducted at Technical University on Asymptotic Analysis Recently Reported

(Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wassersteingradient flow of the porous medium…)

Journal of technology & science, Apr 19, 2015, 520

According to news reporting out of Eindhoven, Netherlands, by VerticalNews editors, the research stated, "In this paper, we study the Wasserstein gradient flow...

<——2015——2015—— —— 520—-

year 2015

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

2015

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm

A Durmus, É Moulines - Statistics and Computing, 2015 - Springer

In this paper, we establish explicit convergence rates for Markov chains in Wasserstein

distance. Compared to the more classical total variation bounds, the proposed rate of

convergence leads to useful insights for the analysis of MCMC algorithms, and suggests …

2015

Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted …

H Haario - Statistics and Computing, 2015 - Springer

The Wasserstein distance between probability distributions might be intuitively described as

a minimal effort required to map one distribution onto another. The concept has a long

history with connections to optimal transport theory. However, the applications on …

A wind power/photovoltaic typical scenario set generation algorithm based on Wasserstein distance metric and revised K-medoids cluster

Q Wang, WL Dong, L Yang - Proceedings of the CSEE, 2015 - en.cnki.com.cn

With the higher penetration of renewable generation resources such as wind power and

solar power, power system operations face new challenges as the supply uncertainty

increases dramatically. Scenario analysis is widely used because it explicitly incorporates a …

[CITATION] … Engineering, Zhejiang University;; A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and …

Q WANG, W DONG, L YANG - 中国电机工程学报, 2015

2015

Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - arXiv preprint arXiv:1510.07793, 2015 - arxiv.org

The curvature-dimension condition is a generalization of the Bochner inequality to weighted

Riemannian manifolds and general metric measure spaces. It is now known to be equivalent

to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

2015

Globally optimal joint image segmentation and shape matching based on Wasserstein modes

B Schmitzer, C Schnörr - Journal of Mathematical Imaging and Vision, 2015 - Springer

A functional for joint variational object segmentation and shape matching is developed. The

formulation is based on optimal transport wrt geometric distance and local feature similarity.

Geometric invariance and modelling of object-typical statistical variations is achieved by …

[HTML] Ergodicity of regime-switching diffusions in Wasserstein distances

J Shao - Stochastic Processes and their Applications, 2015 - Elsevier

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to

justify the convergence of the regime-switching diffusion processes in Wasserstein

distances. The cost function we used to define the Wasserstein distance is not necessarily …

F] arxiv.org

First and second moments for self‐similar couplings and Wasserstein distances

JM Fraser - Mathematische Nachrichten, 2015 - Wiley Online Library

We study aspects of the Wasserstein distance in the context of self‐similar measures.

Computing this distance between two measures involves minimising certain moment

integrals over the space of couplings, which are measures on the product space with the …

2015

Numerical methods for matching for teams and Wasserstein barycenters

G Carlier, A Oberman, E Oudet - ESAIM: Mathematical Modelling …, 2015 - esaim-m2an.org

Equilibrium multi-population matching (matching for teams) is a problem from mathematical

economics which is related to multi-marginal optimal transport. A special but important case

is the Wasserstein barycenter problem, which has applications in image processing and …

2015

[CITATION] Consistent estimation of a population barycenter in the Wasserstein space. ArXiv e-prints

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2015

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one

<——2015——2015—— —— 530—-

J Dedecker, A Fischer, B Michel - Electronic journal of statistics, 2015 - projecteuclid.org

This paper deals with the estimation of a probability measure on the real line from data

observed with an additive noise. We are interested in rates of convergence for the

Wasserstein metric of order $ p\geq1 $. The distribution of the errors is assumed to be …

2015 see 2014 [PDF] aimsciences.org

On gradient structures for Markov chains and the passage to Wasserstein gradient flows

K Disser, M Liero - Networks & Heterogeneous Media, 2015 - aimsciences.org

We study the approximation of Wasserstein gradient structures by their finite-dimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

2015 [PDF] arxiv.org

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

BR Kloeckner, AO Lopes, M Stadlbauer - Nonlinearity, 2015 - iopscience.iop.org

… (Some figures may appear in colour only in the online journal) 1. Introduction and statement of

the main results It has already been noticed that the 1-Wasserstein distance issued from optimal

transporta- tion theory is very convenient to prove exponential contraction properties for Markov …

2015

A Review of Wasserstein Barycenter Algorithms, with a New One

https://open.library.ubc.ca › cIRcle › items › 1.0220664

Dec 2, 2015 — Learning, knowledge, research, insight: welcome to the world of UBC Library, the second-largest academic research library in Canada.

[CITATION] A Review of Wasserstein Barycenter Algorithms, with a New One

G Peyré - 2015 - open.library.ubc.ca

Search. The University of British Columbia. UBC - A Place of Mind. The University of British

Columbia. UBC Search UBC Search. Library. Library Home; Search Collections: Search; General

(Summon); Books & Media (Catalogue); Indexes, Databases & Articles; Journals; Research Guides; …

A Review of Wasserstein Barycenter Algorithms, with a New One

Gabriel Peyré speaking at BIRS workshop, Advances in Numerical Optimal Transportation, on Thursday, February 19, 2015 on the topic: A Review ...

Banff International Research Station · Banff International Research Station · Feb 19, 2015

Gabriel Peyré speaking at BIRS workshop, Advances in Numerical Optimal Transportation, on Thursday, February 19, 2015 on the topic: A Review ...

Banff International Research Station · Banff International Research Station ·

Feb 19, 2015

2015

Linear Regression Model with Histogram-Valued Variables ...

https://www.researchgate.net › ... › Linear Regression

Histogram data models and histogram regression models based on the Symbolic analysis is a new important direction to discover knowledge in a data base.

year

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

2015

2015 [PDF] arxiv.org

Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

MH Duong - Asymptotic Analysis, 2015 - content.iospress.com

In this paper, we study the Wasserstein gradient flow structure of the porous medium

equation restricted to q-Gaussians. The JKO-formulation of the porous medium equation

gives a variational functional K h, which is the sum of the (scaled-) Wasserstein distance and …

2015 L₂ Wasserstein distance

FAT de Carvalho, A Irpino… - 2015 IEEE International …, 2015 - ieeexplore.ieee.org

In this paper, a fuzzy c-means algorithm based on an adaptive L 2-Wasserstein distance for

histogram-valued data is proposed. The adaptive distance induces a set of weights

associated with the components of histogram-valued data and thus of the variables. The …

2015 [PDF] researchgate.net

[PDF] Modified Arratia flow and Wasserstein diffusion

V Konarovskyi, M von Renesse - Communications on Pure and …, 2015 - researchgate.net

Extending previous work [20] by the first author we present a variant of the Arratia flow of a

field of coalescing Brownian motions starting from every point of the unit interval. The

important new feature of the model is that individual particles carry mass which aggregated …

<——2015——2015—— —— 560—-

Title: - Learning with a Wasserstein ... - arXiv

Numerical methods for matching for teams and Wasserstein barycenters

by C Frogner · 2015 · Cited by 399 — In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural

[CITATION] Learning with a Wasserstein Loss. ArXiv e-prints

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - arXiv preprint arXiv …, 2015

2015

G Carlier, A Oberman, E Oudet - … Modelling and Numerical …, 2015 - esaim-m2an.org

Equilibrium multi-population matching (matching for teams) is a problem from mathematical

economics which is related to multi-marginal optimal transport. A special but important case

is the Wasserstein barycenter problem, which has applications in image processing and …

2015 [HTML] sciencedirect.com

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the

presence of a potential field. The non-locality is due to the appearance of the 'fractional

Laplacian'in the corresponding PDE, in place of the classical Laplacian which distinguishes …

2015 [PDF] arxiv.org

Performance and robustness analysis of stochastic jump linear systems using wasserstein metric

K Lee, A Halder, R Bhattacharya - Automatica, 2015 - Elsevier

This paper focuses on the performance and robustness analysis of stochastic jump linear systems. In the presence of stochastic jumps, state variables evolve as random process, with associated time varying probability density functions. Consequently, system analysis is …

2015 see 2014 [PDF] wiley.com Full View

Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - IET Image Processing, 2015 - Wiley Online Library

… brightness adaptive contrast energy term and a Wasserstein dispersion energy term. In the

… we describe the Wasserstein dispersion energy term based on the Wasserstein distance [21], …

2015

Research articleOpen archive
A parametric registration model for warped distributions with Wasserstein’s distance
Journal of Multivariate AnalysisMarch 2015...

Marina Agulló-AntolínJ. A. Cuesta-AlbertosJean-Michel Loubes

Download PDF

Research articleOpen archive
Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow
Applied Mathematics LettersApril 2015...

Malcolm BowlesMartial Agueh

Download PDF

Video: Hongkai Zhao, "Multi-scale Non-Rigid Point Cloud ...

Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap.

Banff International Research Station · Banff International Research Station ·

Feb 17, 2015

Seminar: Spaces of Shapes Persistent Homology for Drug Discovery

Applied Algebraic Topology Network

Published on Jul 28, 2015

Date: 4/29/15
Speaker: Anthony Bak
Abstract: We use persistence homology to create topological signatures for
chemical compounds that reflect underlying chemical and biological
properties of the compounds. By creating a space out of the compounds
using the Wasserstein metric on barcodes we localize the species
bioactivity of a class of compounds called DHFR inhibitors. Using
support vector machine built off of barcode functions out results

achieve state of the art species separability.

Apr 29, 2015

1021：Fast Optimal Transport on GPGPUs

Published on Nov 29, 2015

2015年9月18日（金）に開催されたGTC Japan 2015での講演です。
Marco Cuturi
大学院情報学研究科
京都大学
Optimal transport distances (a.k.a Wasserstein distances or Earth Mover's distances, EMD) define a geometry to compare cloud of points living in a metric space. From a computational point of view, these distances can be computed by solving an optimal transport problem, which is typically carried out using the network simplex. I will show in this brief talk how an adequate regularization of that problem can result in substantially faster computations that can then unlock several methodological approaches grounded on the optimal transport geometry, from the computation of barycenters of probability measures to that of dictionaries, PCA, or parameter estimation, all carried out using the optimal transport geometry.

Nov 29, 2015

<——2015——2015———— 570—

Jan Maas: Optimal transport methods for discrete and quantum systems (part 1)

Mar 20, 2015 2-Wasserstein metric

Barycenter in Wasserstein space existence and consistency ...

1021：Fast Optimal Transport on GPGPUs - YouTube

Barycenter in Wasserstein space existence and consistency Thibaut Le Gouic, Jean Michel Loubes. 444 views444 views.

YouTube · GSI’15 : Geometric Science of Information ·

Nov 24, 2015

- Uploaded by NVIDIA JAPAN

Marco Cuturi 大学院情報学研究科京都大学 Optimal transport distances (a.k.a ...

Optimal transport distances (a.k.a Wasserstein distances or Earth Mover's distances, EMD) define a geometry to compare cloud of points living in a metric space. From a computational point of view, these distances can be computed by solving an optimal transport problem, which is typically carried out using the network simplex. I will show in this brief talk how an adequate regularization of that problem can result in substantially faster computations that can then unlock several methodological approaches grounded on the optimal transport geometry, from the computation of barycenters of probability measures to that of dictionaries, PCA, or parameter estimation, all carried out using the optimal transport geometry.

Nov 30, 2015

2015 see 2013 2017

On interpolation and curvature via Wasserstein geodesics

Author:Kell M.
Article, 2015
Publication:Advances in Calculus of Variations, 2015, 2015
Publisher:2015

Peer-reviewed
Introduction to â€œQuantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithmâ€ by A. Durmus,Â Ã‰. MoulinesShow more

Author:H. Haario
Article, 2015
Publication:STATISTICS AND COMPUTING -LONDON-, 25, 2015, 3
Publisher:2015

2015

2015 see 2014 Peer-reviewed
Introduction to “Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm” by A. Durmus, É. MoulinesShow more

Author:Heikki Haario
Article, 2015
Publication:Statistics and Computing, 25, 201501, 3
Publisher:2015

Fuzzy clustering of distribution-valued data using an adaptive L2 Wasserstein distance

Authors:De Carvalho F.D.A.T., Irpino A., Verde R., IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2015
Article, 2015
Publication:IEEE International Conference on Fuzzy Systems, 2015-November, 2015 11 25
Publisher:2015

Peer-reviewed
Convolutional wasserstein distances efficient optimal transportation on geometric domains

Authors:Justin Solomon (

Author), Fernando de Goes (

Author), Gabriel Peyré (

Author), Marco Cuturi (

Author), Adrian Butscher (

Author), Andy Nguyen (

Author), Tao Du (

Author), Leonidas Guibas (

Author)Show more
Summary:This paper introduces a new class of algorithms for optimization problems involving optimal transportation over geometric domains. Our main contribution is to show that optimal transportation can be made tractable over large domains used in graphics, such as images and triangle meshes, improving performance by orders of magnitude compared to previous work. To this end, we approximate optimal transportation distances using entropic regularization. The resulting objective contains a geodesic distance-based kernel that can be approximated with the heat kernel. This approach leads to simple iterative numerical schemes with linear convergence, in which each iteration only requires Gaussian convolution or the solution of a sparse, pre-factored linear system. We demonstrate the versatility and efficiency of our method on tasks including reflectance interpolation, color transfer, and geometry processingShow more
Article, 2015
Publication:ACM Transactions on Graphics (TOG), 34, 20150727, 1
Publisher:2015

2015 see 2014 2016
The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

Authors:Azmoodeh, Ehsan (Creator), Peccati, Giovanni (Creator), Poly, Guillaume (Creator)

Downloadable Archival Material, 2015
English
Publisher:2015

Peer-reviewed
A parametric registration model for warped distributions with Wasserstein’s distance

Authors:Marina Agulló-Antolín, J.A. Cuesta-Albertos, Hélène Lescornel, Jean-Michel Loubes
Summary:We consider a parametric deformation model for distributions. More precisely, we assume we observe J samples of random variables which are warped from an unknown distribution template. We tackle in this paper the problem of estimating the individual deformation parameters. For this, we construct a registering criterion based on the Wasserstein distance to quantify the alignment of the distributions. We prove consistency of the empirical estimatorsShow more
Article, 2015
Publication:Journal of Multivariate Analysis, 135, 201503, 117
Publisher:2015

<——2015——2015———— 580—

2015 see 2014
Some evolution equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations)

Authors:高津, 飛鳥 (Contributor), タカツ, アスカ (Contributor), Takatsu, Asuka (Creator)
Downloadable Archival Material, 2015-03-03T07:10:04Z
English
Publisher:京都大学数理解析研究所, 2015-03-03T07:10:04Z

Fuzzy clustering of distribution-valued data using an adaptive L<inf>2</inf> Wasserstein distance

Authors:Francisco de A.T. de Carvalho, Antonio Irpino, Rosanna Verde, 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
Summary:In this paper, a fuzzy c-means algorithm based on an adaptive L2-Wasserstein distance for histogram-valued data is proposed. The adaptive distance induces a set of weights associated with the components of histogram-valued data and thus of the variables. The minimization of the criterion in the fuzzy c-means algorithm is performed according three steps such that the representation, the allocation and the weights associated to the components of the variables are alternately computed until a the convergence of the solution to a local optimum. The effectiveness of the proposed algorithm is demonstrated through experiments with synthetic and real-world datasetsShow more
Chapter, 2015
Publication:2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 201508, 1
Publisher:2015

gpeyre/2015-SIGGRAPH-convolutional-ot: J. Solomon, F. de ...

https://github.com › gpeyre › 2015-SIGGRAPH-convol...

Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains

. ACM Transactions on Graphics (Proc. SIGGRAPH 2015), 34(4), pp.

2015. [HTML] sciencedirect.com

[HTML] Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow

M Bowles, M Agueh - Applied Mathematics Letters, 2015 - Elsevier

… of weak solutions by combining a splitting technique together with a Wasserstein gradient

flow … A

2015 zzz

[CITATION] Wind/PV classical scenario set generation algorithm based on Wasserstein distance and improved K-medoids clustering

Q Wang, W Dong, L Yang - Chinese Journal of Electrical Engineering, 2015

The exponential formula for the wasserstein metric | ESAIM: Control ...

<—2015——2015———— 585— end 2015

including

571 titles with Wasserstein and 2 titles with Vaserstein

start 2016 Wasserstein

MR3489381 Craig, Katy The exponential formula for the Wasserstein metric. ESAIM Control Optim. Calc. Var. 22 (2016), no. 1, 169–187. 49Q20

by K Craig - ‎2016 - ‎Cited by 7 - ‎Related articles

The exponential formula for the wasserstein metric. ... A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the square Wasserstein metric.

[PDF]

Learning with a Wasserstein Loss - MIT 2016

by C Frogner - ‎Cited by 114 - ‎Related articles

The Wasserstein loss can encourage smoothness of the predic- tions with .... We consider the problem of learning a map from X ⇢ RD into the space Y = RK.

Learning with a Wasserstein loss

C Frogner, C Zhang, H Mobahi, M Araya… - … in neural information …, 2015 - papers.nips.cc

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The

Wasserstein distance provides a natural notion of dissimilarity for probability measures.

Although optimizing with respect to the exact Wasserstein distance is costly, recent work has

described a regularized approximation that is efficiently computed. We describe an efficient …

Markov Type constants, flat tori and Wasserstein spaces

by V Zolotov - ‎2016 - ‎Cited by 1 - ‎Related articles

Jan 20, 2017 - arXiv:1610.04886v4 [math.MG] 20 Jan 2017. MARKOV TYPE CONSTANTS, FLAT TORI AND. WASSERSTEIN SPACES. VLADIMIR ZOLOTOV.

Markov Type constants, flat tori and Wasserstein spaces

by V Zolotov - ‎2016 - ‎Cited by 1 - ‎Related articles

Oct 16, 2016 - Subjects: Metric Geometry (math.MG). MSC classes: 51F99. Cite as: arXiv:1610.04886 [math.MG]. (or arXiv:1610.04886v4 [math.MG] for this ...

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

Y Yang, B Engquist, J Sun - 2016 SEG International Exposition and …, 2016 - onepetro.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform

inversion (FWI) and prove such preperties as convexity in different aspects. Considering the

observed data and predicted data as two density functions, the quadratic Wasserstein metric …

The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baíllo, J Cárcamo, KV Getman - arXiv preprint arXiv:1603.06806, 2016 - arxiv.org

Abstract: Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the ...

Cite Cited by 2 Related articles All 2 versions

Second order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - 2016 - hal.archives-ouvertes.fr

The time discretization of gradient flows in metric spaces uses variants of the celebrated

implicit Euler-type scheme of Jordan, Kinderlehrer and Otto. We propose in this Note a

different approach which allows to construct two second order in time numerical schemes. ...

On Parallel Transport in Wasserstein Space arXiv

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

Abstract: In this short note, we would like to give a construction of parallel transport for

tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete

proof for the linear part of the tangent space, and show that a construction for the full ...

] Fast Dictionary Learning with a Smoothed Wasserstein Loss

A Rolet, M Cuturi, G Peyré - … of the 19th International Conference on …, 2016 - jmlr.org

Abstract We consider in this paper the dictionary learning problem when the observations

are normalized histograms of features. This problem can be tackled using non-negative

matrix factorization approaches, using typically Euclidean or Kullback-Leibler fitting errors. ...

Peer-reviewed
Uniform Contractivity in Wasserstein Metric for the Original 1D Kac’s Model

Author:Maxime Hauray
Summary:We study here a very popular 1D jump model introduced by Kac: it consists of N velocities encountering random binary collisions at which they randomly exchange energy. We show the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge-Kantorovich-Wasserstein: precisely the MKW metric of order 2 on the energy. The result is optimal in the sense that for each N, the contractivity constant is equal to the L 2 spectral gap of the generator associated to Kac’s dynamic. As a corollary, we get an uniform but non optimal contractivity in the MKW metric of order 4. We use a simple coupling that works better that the parallel one. The estimates are simple and new (to the best of our knowledge)Show more
Article, 2016
Publication:Journal of Statistical Physics : 1, 162, 201603, 1566
Publisher:2016

nterpretation of Finite Volume discretization schemes for the Fokker Planck equation as gradient flows for the discrete Wasserstein distance

F Al Reda, B Maury - 2016 - hal.archives-ouvertes.fr

This paper establishes a link between some space discretization strategies of the Finite

Volume type for the Fokker-Planck equation in general meshes (Voronoï tesselations) and

gradient flows on the underlying networks of cells, in the framework of discrete ...

Shape analysis with hyperbolic wasserstein distance

J Shi, W Zhang, Y Wang - Proceedings of the IEEE Conference on …, 2016 - cv-foundation.org

Abstract Shape space is an active research field in computer vision study. The shape

distance defined in a shape space may provide a simple and refined index to represent a

unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein ...

2016 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) Book Series: IEEE Conference on Computer Vision and Pattern Recognition Pages: 5051-5061 Published: 2016

A multivariate CLT in Wasserstein distance with near optimal convergence rate arXiv

A Zhai - arXiv preprint arXiv:1602.05565, 2016 - arxiv.org

Abstract: Let $ X_1,\ ldots, X_n $ be iid random vectors in $\ mathbb {R}^ d $ with $\| X_1\|\

le\ beta $. Then, we show that $\ frac {1}{\ sqrt {n}}(X_1+\ ldots+ X_n) $ converges to a

Gaussian in Wasserstein-2 distance at a rate of $ O\ left (\ frac {\ sqrt {d}\ beta\ log n}{\ sqrt { ...

A multivariate CLT in Wasserstein distance with near optimal ...

www.researchgate.net › publication › 301846996_A_mul...

Download Citation | A multivariate CLT in Wasserstein distance with near optimal convergence rate | Let $X_1, \ldots , X_n$ be i.i.d. random vectors

Wasserstein contraction properties for hypoelliptic diffusions arXiv

F Baudoin - arXiv preprint arXiv:1602.04177, 2016 - arxiv.org

Abstract: Gradient bounds had proved to be a very efficient tool for the control of the rate of

convergence to equilibrium for parabolic evolution equations. Among the gradient bounds

methods, the celebrated Bakry-\'Emery criterion is a powerful way prove to convergence to ...

s a powerful way prove to convergence to …

Cited by 13 Related articles All 4 versions
<——2016————2016—— - ———————— -60—

Guarantees in Wasserstein Distance for the Langevin Monte Carlo Algorithm arXiv

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

Abstract: We study the problem of sampling from a distribution $\ target $ using the Langevin

Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of

Wasserstein distance of order $2 $. Our result holds as long as the continuous diffusion ...

PDF] researchgate.net

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the …

Cited by 2 Rel

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces arXiv

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Abstract: Since the early nineties, it has been observed that the Schroedinger bridge

problem can be formulated as a stochastic control problem with atypical boundary

constraints. This in turn has a fluid dynamic counterpart where the flow of probability ...

Stein's method on the second Wiener chaos: 2-Wasserstein distance arXiv

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

Abstract: In the first part of the paper we use a new Fourier technique to obtain a Stein

characterizations for random variables in the second Wiener chaos. We provide the

connection between this result and similar conclusions that can be derived using Malliavin ...

CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

Gromov-Wasserstein Averaging of Kernel and Distance Matrices HAL

G Peyré, M Cuturi, J Solomon - ICML 2016, 2016 - hal.archives-ouvertes.fr

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the interrelationships between points sampled

from individual domains, are not required to have the same size or to be in row-by-row ...

Wasserstein training of restricted Boltzmann machines arXiv

G Montavon, KR Müller, M Cuturi - Advances in Neural Information …, 2016 - papers.nips.cc

Abstract Boltzmann machines are able to learn highly complex, multimodal, structured and

multiscale real-world data distributions. Parameters of the model are usually learned by

minimizing the Kullback-Leibler (KL) divergence from training samples to the learned model.

Wasserstein contraction properties for hypoelliptic diffusions

F Baudoin - arXiv preprint arXiv:1602.04177, 2016 - arxiv.org

Gradient bounds had proved to be a very efficient tool for the control of the rate of

convergence to equilibrium for parabolic evolution equations. Among the gradient bounds

methods, the celebrated Bakry-Émery criterion is a powerful way prove to convergence to …

Investigators at University of Washington Describe Findings in General Mathematics

(Wasserstein distance and the rectifiability of doubling measures: part I)

Journal of Technology & Science, 06/2016

Newsletter: Full Text Online

Researchers from Aix-Marseille University Report Recent Findings in Statistical Physics

(Uniform Contractivity in Wasserstein Metric for the Original 1D Kac's Model)

Journal of Technology & Science, 03/2016

Newsletter: Full Text Online

张洁琳，焦艳艳，罗钟铉 - 计算机辅助设计与图形学学报, 2016 - cnki.com.cn

为提高图形匹配的匹配率和精确率, 提出一种基于Gromov-Wasserstein (GW) 距离的3D

图形匹配方法. 首先将2 个图形嵌入到度量测度空间中, 通过最远采样法进行采样; 然后采用GW

距离表示2 个图形之间的差异性, 构造出目标函数和约束条件, 得到一个难于求解的二次分配 …

Investigators at University of Washington Describe Findings in General Mathematics (Wasserstein distance and the rectifiability of doubling measures: part I)

[Chinese 3D pattern matching method based on Gromov-Wasserstein distance]
<——2016————2016———70—

University of California Reports Findings in Mathematical Methods

(Discrete Wasserstein barycenters: optimal transport for discrete data)"

Journal of Technology & Science, 12/2016

Newsletter: Full Text Online

Journal of Technology & Science. (June 19, 2016) From Global Issues in Context.

Wasserstein distance and the rectifiability of doubling ...

link.springer.com › article

by J Azzam - ‎2016 - ‎Cited by 14 - ‎Related articles

Apr 12, 2015 - Wasserstein distance and the rectifiability of doubling measures: part I. Jonas Azzam ,; Guy David &; Tatiana Toro. Mathematische Annalen ...

MR3584627 Choi, Byoung Jin; Ji, Un Cig; Exponential convergence rates for weighted sums in noncommutative probability space. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), no. 4, 1650027, 13 pp. Zbl 06645470

Exponential convergence rates for weighted sums in noncommutative ...

by BJ Choi - ‎2016 - ‎Cited by 2 - ‎Related articles

Nov 21, 2016 - We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability ...

MR3573296 Durmus, Alain; Fort, Gersende; Moulines, Éric; Subgeometric rates of convergence in Wasserstein distance for Markov chains. Ann. Inst. Henri Poincaré Probab. Stat. 52 (2016), no. 4, 1799–1822.

Subgeometric rates of convergence in Wasserstein distance for ... - arXiv

by A Durmus - ‎2014 - ‎Cited by 11 - ‎Related articles

Jul 14, 2015 - Subgeometric rates of convergence in Wasserstein ... Keywords and phrases: Markov chains, Wasserstein distance, Subgeometric ergodicity, ...

MR3566931 Anderes, Ethan; Borgwardt, Steffen; Miller, Jacob; Discrete Wasserstein barycenters: optimal transport for discrete data. Math. Methods Oper. Res. 84 (2016), no. 2, 389–409.

Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data

by E Anderes - ‎2015 - ‎Cited by 22 - ‎Related articles

Jul 26, 2015 - In this paper, we develop theoretical results for Wasserstein barycenters in this discrete setting. Our results rely heavily on polyhedral theory ...

Missing: t ‎| ‎Must include: ‎t

<——2016————2016——— -75—

MR3565819 Benamou, Jean-David; Carlier, Guillaume; Laborde, Maxime An augmented Lagrangian approach to Wasserstein gradient flows and applications. Gradient flows: from theory to application, 1–17, ESAIM Proc. Surveys, 54, EDP Sci., Les Ulis, 2016. 35K57 (35K15 35K59 35Q84)

An augmented Lagrangian approach to Wasserstein gradient flows ...

by JD Benamou - ‎2016 - ‎Cited by 18 - ‎Related articles

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we propose a convex formulation for each step of the JKO scheme for Wasserstein gradient flows which can be attacked by an augmented Lagrangian method which we call the ALG2-JKO scheme.

MR3558359 Loibl, Daniel; Matthes, Daniel; Zinsl, Jonathan; Existence of Weak Solutions to a Class of Fourth Order Partial Differential Equations with Wasserstein Gradient Structure. Potential Anal. 45 (2016), no. 4, 755–776.

Existence of Weak Solutions to a Class of Fourth Order Partial ..

by D Loibl - ‎2016 - ‎Cited by 7 - ‎Related articles

May 19, 2016 - We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex ...

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

New Potential Analysis Study Findings Have Been Reported by Researchers at Technical University

(Existence of Weak Solutions to a Class of Fourth Order Partial Differential Equations with Wasserstein...

Journal of Technology & Science, 12/2016

Newsletter: Full Text Online

Existence of Weak Solutions to a Class of Fourth Order Partial ...

May 19, 2016 - Existence of Weak Solutions to a Class of Fourth Order Partial Differential Equations with Wasserstein Gradient Structure. Daniel Loibl ,; Daniel ...

by D Loibl - ‎2016 - ‎Cited by 7 - ‎Related articles

MR3551945 Jourdain, Benjamin; Reygner, Julien; A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data. J. Hyperbolic Differ. Equ. 13 (2016), no. 3, 441–602.

A multitype sticky particle construction of Wasserstein stable ...

by B Jourdain - ‎2016 - ‎Cited by 3 - ‎Related articles

Sep 29, 2016 - A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large ...

MR3545279 Rippl, Thomas; Munk, Axel; Sturm, Anja; Limit laws of the empirical Wasserstein distance: Gaussian distributions. J. Multivariate Anal. 151 (2016), 90–109.

Limit laws of the empirical Wasserstein distance: Gaussian distributions

by T Rippl - ‎2015 - ‎Cited by 22 - ‎Related articles

Jul 15, 2015 - Limit laws of the empirical Wasserstein distance: Gaussian distributions. We derive central limit theorems for the Wasserstein distance between the empirical distributions of Gaussian samples. The cases are distinguished whether the underlying laws are the same or different.

MR3544329 Piccoli, Benedetto; Rossi, Francesco On properties of the generalized Wasserstein distance. Arch. Ration. Mech. Anal. 222 (2016), no. 3, 1339–1365. 49Q20 (60B10

On Properties of the Generalized Wasserstein Distance - Springer Link

by B Piccoli - ‎2016 - ‎Cited by 33 - ‎Related articles

Jul 8, 2016 - In this paper we prove two important properties of the generalized Wasserstein distances: (1) a generalized Benamou–Brenier formula.

On properties of the generalized Wasserstein distance

same mass. To overcome such a limitation, we recently …

<——2016————2016—— - ———80 —

MR3531395 Azmoodeh, Ehsan; Peccati, Giovanni; Poly, Guillaume The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds. ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016), no. 2, 659–686. 60G22 (60F05 60F15 60G15 60H07)

The law of iterated logarithm for subordinated Gaussian ... - Alea

by E Azmoodeh - ‎2016 - ‎Cited by 2 - ‎Related articles

The law of iterated logarithm for subordinated. Gaussian sequences: uniform Wasserstein bounds. Ehsan Azmoodeh, Giovanni Peccati and Guillaume Poly.

MR3539346 Kell, Martin

q-heat flow and the gradient flow of the Renyi entropy in the

p-Wasserstein space. J. Funct. Anal. 271 (2016), no. 8, 2045–2089. 58J35 (35K92 35R01 53C23)

q-Heat flow and the gradient flow of the Renyi entropy ... - ResearchGate

Oct 10, 2018 - (2013), we show that flow of the $q$-Cheeger energy, called $q$-heat flow, solves the gradient flow problem of the Renyi entropy functional in ...

[CITATION] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space, Preprint (2014)

M Kell - Available at arXiv

Absolutely continuous curves in extended ... - ESAIM: COCV

MR3527938 Lisini, Stefano Absolutely continuous curves in extended Wasserstein-Orlicz spaces. ESAIM Control Optim. Calc. Var. 22 (2016), no. 3, 670–687. 49J27 (49Q20)

by S Lisini - ‎2016 - ‎Cited by 6 - ‎Related articles

Apr 27, 2016 - ABSOLUTELY CONTINUOUS CURVES IN EXTENDED. WASSERSTEIN−ORLICZ SPACES. Stefano Lisini. 1. Abstract. In this paper we extend ...

MR3515734 Polyanskiy, Yury; Wu, Yihong Wasserstein continuity of entropy and outer bounds for interference channels. IEEE Trans. Inform. Theory 62 (2016), no. 7, 3992–4002. 94A17

Wasserstein Continuity of Entropy and Outer Bounds for ... - IEEE Xplore

by Y Polyanskiy - ‎2016 - ‎Cited by 49 - ‎Related articles

Wasserstein Continuity of Entropy and Outer. Bounds for Interference Channels. Yury Polyanskiy, Senior Member, IEEE, and Yihong Wu, Member, IEEE.

MR3463787 Hauray, Maxime Uniform contractivity in Wasserstein metric for the original 1D Kac's model. J. Stat. Phys. 162 (2016), no. 6, 1566–1570. 82C40 (60J75 76P05)

Uniform Contractivity in Wasserstein Metric for the Original 1D Kac's ...

by M Hauray - ‎2016 - ‎Cited by 4 - ‎Related articles

Feb 10, 2016 - J Stat Phys (2016) 162:1566–1570. DOI 10.1007/s10955-016-1476-1. Uniform Contractivity in Wasserstein Metric for the Original 1D Kac's ...

MR3474827 Wang, Jian Lp-Wasserstein distance for stochastic differential equations driven by Lévy processes. Bernoulli 22 (2016), no. 3, 1598–1616. (Reviewer: Ying Hui Dong) 60H10 (60J75)

Lp-Wasserstein distance for stochastic differential equations driven by ...

by J Wang - ‎2016 - ‎Cited by 15 - ‎Related articles

Mar 17, 2016 - stochastic differential equation driven by Lévy noise; symmetric stable ... where (Zt)t≥0 is a d-dimensional Lévy process, and b:Rd → Rd is a ...

Wasserstein distance for stochastic differential equations driven by ...

by J Wang - ‎2016 - ‎Cited by 15 - ‎Related articles

Mar 16, 2016 - ... for stochastic differential equations driven by Lévy processes ... for a class of stochastic differential equations (SDEs) driven by Lévy noises.

Lp-Wasserstein distance for stochastic differential equations driven by Lévy processes

MR3466197 Cuturi, Marco; Peyré, Gabriel A smoothed dual approach for variational Wasserstein problems. SIAM J. Imaging Sci. 9 (2016), no. 1, 320–343. 94A08 (49Q20 65C50 68U10 90C08 90C25)

A Smoothed Dual Approach for Variational Wasserstein Problems

by M Cuturi - ‎2016 - ‎Cited by 48 - ‎Related articles

A smoothed dual approach for variational Wasserstein problems

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

… (Wasserstein distances) that are themselves hard to compute. We show that the dual

formulation of Wasserstein variational problems … In this paper, we introduced a dual framework

for the resolution of certain variational problems involving Wasserstein distances. The key …

MR3451384 Azzam, Jonas; David, Guy; Toro, Tatiana Wasserstein distance and the rectifiability of doubling measures: part I. Math. Ann. 364 (2016), no. 1-2, 151–224. (Reviewer: Matthew Badger) 28A75 (28A12)

Wasserstein distance and the rectifiability of doubling measures: part I ...

by J Azzam - ‎2016 - ‎Cited by 12 - ‎Related articles

Let [equation] be a doubling measure in [equation]. We investigate quantitative relations between the rectifiability of [equation] and its distance to flat measures.

CJM: Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

by J Bigot - ‎2016 - ‎Cited by 7 - ‎Related articles

Jun 3, 2016 - Penalized Barycenters in the Wasserstein Space. In this paper, a regularization of Wasserstein barycenters for random measures supported on R is introduced via convex penalization. The existence and uniqueness of such barycenters is first proved for a large class of penalization functions.

Dec 6, 2016 - In this paper, we prove that, on a compact, n-dimensional Alexandrov space with curvature , the Wasserstein barycenter of Borel probability ...

<——2016————2016—— - ———————— -90—

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

by B Berckmoes - ‎2016 - ‎Cited by 1 - ‎Related articles

Sep 29, 2016 - More precisely, we introduce a canonical approach structure, called the ... between the relative Hausdorff measure of non-compactness for the ...

arXiv

[HTML] Суперпозиция метода балансировки и универсального градиентного метода для поиска энтропийно-регуляризованного барицентра Вассерштейна и равновесий в многостадийных моделях транспортных потоко

АВ Гасников, ПЕ Двуреченский… - Труды Московского …, 2016 - cyberleninka.ru

Представлен обзор современных численных методов поиска барицентра

Вассерштейна конечного семейства вероятностных мер с одинаковым конечным

носителем. Такие задачи в последнее время стали очень популярны в связи с …

[Russian Superposition of the balancing method and the universal gradient method for searching the entropy-regularized Wasserstein barycenter and equilibria in multistage models of traffic flows

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

Sliced Wasserstein kernels for probability distributions

S Kolouri, Y Zou, GK Rohde - Proceedings of the IEEE Conference …, 2016 - cv-foundation.org

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as powerful discrepancy measures for probability distributions. The recent developments on alternative formulations …

[PDF] Comparison between W2 distance and H− norm, and Localisation of Wasserstein distance

R Peyre - 2016 - normalesup.org

It is well known that the quadratic Wasserstein distance W2 (·,·) is formally equivalent, for infinitesimally small perturbations, to some weighted H− 1 homogeneous Sobolev norm. In this article I show that this equivalence can be integrated to get non-asymptotic comparison …

2016

Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information,

which appear in variational problems to find optimal channel (OCP) from the rate distortion

and the value of information theories. We show that OTP is equivalent to OCP with one

additional constraint fixing the output measure, and therefore OCP with constraints on the KL …

Calculus of variations and Hamilton-Jacobi equations in the Wasserstein space

Dr. Truyen Nguyen

Optimal mass transportation theory was originally developed as a way of solving optimization problems in the areas of operations research, probability and statistics. However, as recent applications of this theory have shown, certain analytical and geometric problems on the Euclidean space can effectively be treated in the corresponding Wasserstein space of probability measures. This project aims to study a class of dynamical systems on the Wasserstein space of probability measures corresponding to some fundamental systems of partial differential equations in fluid and quantum mechanics. A nice feature of the Wasserstein space approach is its ability to handle singular data and singular solutions. In addition, there is also a possibility of handling discrete and continuous models with the same formalism. The core of this program lies in the development of an appropriate theory for calculus of variations and Hamilton-Jacobi equations in the Wasserstein space.

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

Numerical Schemes for Calculating the Discrete Wasserstein Distance

PDF Bonn 2016

by B Cabrera - ‎2016 - ‎Related articles

Feb 26, 2016 - The problem we are focusing on in this thesis is the Wasserstein distance on discrete (finite) sets. We will see later that the original Wasserstein ...

2016 100

Using Gromov-Wasserstein distance to explore sets of networks - CORE

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PDF Tartu Ph.D.

by R Hendrikson · ‎Cited by 7 · ‎Related articles

Memoli (2011) artiklis ”Gromov–Wasserstein. Distances and the Metric Approach to Object Matching”. Antud kaugus määrab arvuliselt objektide, mis on esitatud ...

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

Using Gromov-Wasserstein distance to explore sets of networks

... thesis is to study, implement, and apply one Gromov-Wasserstein type of distance introduced by F.Memoli (2011) in his paper "Gromov-Wasserstein Distances .. 2016

<--——2016————2016—— - ——----100—

Cуперпозиция метода балансировки и универсальногоградиентного метода для поискаэнтропийно-регуляризованного барицентра Вассерштейна и равновесий в многостадийных моделяхтранспортных потоков

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расстоянию Вассерштейна. Такое (регуляризованное) расстояние можно заметно эф- фективнее посчитать, чем исходное расстояние Вассерштейна.

ТРУДЫ МФТИ. 2016. Том 8, No 3Информатика, вычисл. техника и управление5УДК 519.688А. В. Гасников1,2, П. Е. Двуреченский2,4, В. Г. Спокойный1,2,3,4, П. И. Стецюк5,А. Л. Суворикова1,2,61Московский физико-технический институт (государственный университет)2Институт проблем передачи информации РАН3Национальный исследовательский университет Высшая школа экономики4Weierstrass Institute for Applied Analysis and Stochastics, Berlin5Институт кибернетики им. В. М. Глушкова НАН Украины6The International Research Training Group 1792, Berlin

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance.

The quantification of sensitivity is obtained by measuring the Wasserstein distance between two LWR solutions corresponding to different inputs.Jul 30, 2016

arXiv

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

by Briani, Maya; Cristiani, Emiliano; Iacomini, Elisa 07/2016

Commun. Math. Sci., 16 (2018), 123-144 In this paper we investigate the sensitivity of the LWR model on network to its parameters and to the network itself....

Newspaper Article: Full Text Online

Comparison between W2distance and ̇H−1norm,and Localisation of Wasserstein distance

PDF arXiv

by R Peyre - ‎2016 - ‎Cited by 17 - ‎Related articles

 Page 2 W2 distance and ˙H−1 norm Rémi Peyre W2 is a (possibly infinite) distance, called the quadratic Wasserstein distance [Villani, 2003, § 7.1]. Note that this distance is finite only between measures having the same total mass. ... Note that this norm is finite only for measures having zero total mass.

2016 thesis

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein

by Laborde, Maxime

Depuis l’article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu’une large classe d’équations paraboliques peuvent être vues comme des...

Dissertation/Thesis:

Full Text Online

Laborde, Maxime. Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein : Interacting particles systems, Wasserstein gradient flow approach.

Degree: Docteur es, Sciences, 2016, Paris Sciences et Lettres

URL: http://www.theses.fr/2016PSLED014

Depuis l’article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu’une large classe d’équations paraboliques peuvent être vues comme des flots… (more)

Subjects/Keywords: Distance de Wasserstein; Flots de gradient; Schéma JKO; Splitting; Dérive non locale; Diffusions non linéaires; Diffusions croisées; Systèmes de réaction-Diffusion; Équations d'Hele-Shaw; Transport optimal; Transport multi-Marges; Formule de Benamou-Brenier; Lagrangien augmenté; Mouvement de foules; Espèces en interaction; Wasserstein distance; Gradient flows; JKO scheme; Splitting; Nonlocal drift; Nonlinear diffusions; Cross-Diffusion; Reaction-Diffusion systems; Hele-Shaw equation; Optimal transport; Multi-Marginal transport; Benamou-Brenier formula; Augmented lagrangian; Crowd motions; Interacting species; 519.2

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Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein

M Laborde - 2016 - theses.fr

Résumé Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu

qu'une large classe d'équations paraboliques peuvent être vues comme des flots de

gradient dans l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein: Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - oatd.org

Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature

Mar 18, 2016 - Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature. for some constants c,\ll>0 for a class of diffusion semigroups with negative curvature where the constant c is essentially larger than 1.

by FY Wang - ‎2016 - ‎Cited by 17 - ‎Related articles

Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels

71 citations* for all

61 citations*

2016 IEEE Transactions on Information Theory

Yury Polyanskiy ¹, Yihong Wu ²

¹ Massachusetts Institute of Technology ,

² University of Illinois at Urbana–Champaign

nference for Empirical Wasserstein Distances on Finite Spaces

by M Sommerfeld - ‎2016 - ‎Cited by 73 - ‎Related articles

Oct 11, 2016 - To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of empirical Wasserstein distances as the optimal value of a linear program with random objective function. ...

LECTURES ONMEANFIELDGAMES:II. CALCULUS OVER WASSERSTEIN SPACE, CONTROL OFMCKEAN-VLASOVDYNAMICS,AND THEMASTEREQUATIONRené CarmonaDepartment of Operations Research & Financial Eng., Princeton U, Oct 2016

Evolution of the Wasserstein distance between the marginals of two Markov processes

Aurélien Alfonsi, Jacopo Corbetta, Benjamin Jourdain

In this paper, we are interested in the time derivative of the Wasserstein distance between the marginals of two Markov processes. As recalled in the introduction, the Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the integrals with respect to each of the two marginals of the corresponding generator applied to the corresponding Kantorovich potential. For pure jump processes with bounded intensity of jumps, we prove that the evolution of the Wasserstein distance is actually given by this candidate. In dimension one, we show that this remains true for Piecewise Deterministic Markov Processes. We apply the formula to estimate the exponential decrease rate of the Wasserstein distance between the marginals of two birth and death processes with the same generator in terms of the Wasserstein curvature.

Subjects:	Probability (math.PR); Optimization and Control (math.OC)
MSC classes:	60J75, 49K99
Cite as:	arXiv:1606.02994 [math.PR]
	(or arXiv:1606.02994v2 [math.PR] for this version)

Submission history

From: Jacopo Corbetta [view email]

[v1] Thu, 9 Jun 2016 15:21:03 UTC (26 KB)

[v2] Thu, 8 Dec 2016 12:38:29 UTC (33 KB)

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Sample out-of-sample inference based on Wasserstein distance

J Blanchet, Y Kang - arXiv preprint arXiv:1605.01340, 2016 - arxiv.org

We present a novel inference approach which we call Sample Out-of-Sample (or SOS)

inference. Our motivation is to propose a method which is well suited for data-driven stress

testing, in which emphasis is placed on measuring the impact of (plausible) out-of-sample …

[PDF] Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates

M Iacobelli - pdfs.semanticscholar.org

… Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates Mikaela Iacobelli

University of Cambridge Cambridge, May 10, 2016 Mikaela Iacobelli Quasineutral limit for

Vlasov-Poisson … Mikaela Iacobelli Quasineutral limit for Vlasov-Poisson Page 10. Debye length …

Shape analysis with hyperbolic Wasserstein distance

J Shi, W Zhang, Y Wang - Proceedings of the IEEE …, 2016 - openaccess.thecvf.com

Shape space is an active research field in computer vision study. The shape distance

defined in a shape space may provide a simple and refined index to represent a unique

shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It …

Wasserstein Loss for Image Synthesis and Restoration

Guillaume Tartavel, Gabriel Peyré, and Yann Gousseau

SIAM Journal on Imaging Sciences Vol. 9, No. 4, pp. 1726–17552016

Wasserstein loss for image synthesis and restoration

G Tartavel, G Peyré, Y Gousseau - SIAM Journal on Imaging Sciences, 2016 - SIAM

This paper presents a novel variational approach to imposing statistical constraints on the

output of both image generation (typically to perform texture synthesis) and image

restoration (for instance, to achieve denoising and inpainting) methods. The empirical …

On properties of the generalized Wasserstein distance

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2016 - Springer

The Wasserstein distances W p (p\geqq≧ 1), defined in terms of a solution to the Monge–

Kantorovich problem, are known to be a useful tool to investigate transport equations. In

particular, the Benamou–Brenier formula characterizes the square of the Wasserstein …

Inference for empirical Wasserstein distances on finite spaces

M Sommerfeld, A Munk - arXiv preprint arXiv:1610.03287, 2016 - arxiv.org

The Wasserstein distance is an attractive tool for data analysis but statistical inference is

hindered by the lack of distributional limits. To overcome this obstacle, for probability

measures supported on finitely many points, we derive the asymptotic distribution of …

[

[PDF] Wasserstein training of restricted Boltzmann machines

G Montavon, KR Müller… - Proceedings of the 30th …, 2016 - pdfs.semanticscholar.org

Boltzmann machines are able to learn highly complex, multimodal, structured and multiscale

real-world data distributions. Parameters of the model are usually learned by minimizing the

Kullback-Leibler (KL) divergence from training samples to the learned model. We propose in …

A smoothed dual approach for variational Wasserstein problems

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

Cited by 107 Related articles

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

Sliced Wasserstein kernels for probability distributions

S Kolouri, Y Zou, GK Rohde - Proceedings of the IEEE Conference …, 2016 - cv-foundation.org

Optimal transport distances, otherwise known as Wasserstein distances, have recently

drawn ample attention in computer vision and machine learning as powerful discrepancy

measures for probability distributions. The recent developments on alternative formulations …

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[PDF] Gromov-wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on Machine …, 2016 - jmlr.org

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the interrelationships between points sampled

from individual domains, are not required to have the same size or to be in row-by-row …

[PDF] Fast dictionary learning with a smoothed Wasserstein loss

A Rolet, M Cuturi, G Peyré - Artificial Intelligence and Statistics, 2016 - jmlr.org

We consider in this paper the dictionary learning problem when the observations are

normalized histograms of features. This problem can be tackled using non-negative matrix

factorization approaches, using typically Euclidean or Kullback-Leibler fitting errors …

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

2016

Wasserstein continuity of entropy and outer bounds for interference channels

Y Polyanskiy, Y Wu - IEEE Transactions on Information Theory, 2016 - ieeexplore.ieee.org

It is shown that under suitable regularity conditions, differential entropy is O (√ n)-Lipschitz

as a function of probability distributions on Ilin with respect to the quadratic Wasserstein

distance. Under similar conditions,(discrete) Shannon entropy is shown to be O (n)-Lipschitz …

[PDF] esaim-proc.org

An augmented Lagrangian approach to Wasserstein gradient flows and applications

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

[PDF] Wasserstein barycentric coordinates: histogram regression using optimal transport.

N Bonneel, G Peyré, M Cuturi - ACM Trans. Graph., 2016 - perso.liris.cnrs.fr

This article defines a new way to perform intuitive and geometrically faithful regressions on

histogram-valued data. It leverages the theory of optimal transport, and in particular the

definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric …

Discrete Wasserstein barycenters: Optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for

several marginals, and as such have a wide range of applications ranging from economics

to statistics and computer science. When the marginal probability measures are absolutely …

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

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Wasserstein distance and the rectifiability of doubling measures: part I

J Azzam, G David, T Toro - Mathematische Annalen, 2016 - Springer

Let μ μ be a doubling measure in R^ n R n. We investigate quantitative relations between

the rectifiability of μ μ and its distance to flat measures. More precisely, for xx in the support Σ

Σ of μ μ and r> 0 r> 0, we introduce a number α (x, r) ∈ (0, 1 α (x, r)∈(0, 1 that measures, in …

year 2016 pdf

[PDF] Learning in Wasserstein Space

J Ye - personal.psu.edu

Learning from empirical probability measures is an emerging problem that has potential benefiting multiple domains. My research focuses on developing scalable and effective learning algorithms that handle large-scale data in form of measures. In particular, the …

2016

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - pdfs.semanticscholar.org

Given a collection of absolutely continuous measures on Rd, we consider the complementary problems of: determining their Fréchet mean with respect to the L2-Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

2016

On Parallel Transport in Wasserstein Space

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

In this short note, we would like to give a construction of parallel transport for tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the linear part of the tangent space, and show that a construction for the full tangent cones …

2016

128.84.21.199 › abs

Jul 5, 2016 — ... k-barycenters in Wasserstein Space and Wide Consensus Clustering ... A robust clustering method for probabilities in Wasserstein space is ...

[CITATION] Robust k-barycenters in wasserstein space and wide consensus clustering

E del Barrio, J Cuesta-Albertos, C Matrán, A Mayo-Íscar - arXiv preprint arXiv, 2016

Penalized Barycenters in the Wasserstein Space - NASA/ADS

2016

ui.adsabs.harvard.edu/abs/2016arXiv160601025B/...

Penalized Barycenters in the Wasserstein Space. In this paper, a regularization of Wasserstein barycenters for random measures supported on $\mathbb {R}^ {d}$ is introduced via convex penalization. The existence and uniqueness of such barycenters is first proved for a large class of penalization functions. The Bregman divergence associated to the penalization term is then considered to obtain a stability result on penalized barycenters.

Author: Jérémie Bigot, Elsa Cazelles, Nicolas Papadakis
Cited by: 5

[CITATION] Penalized barycenters in the Wasserstein space. Submitted

J Bigot, E Cazelles, N Papadakis

Sliced Wasserstein kernels for probability distributions

[PDF] Euler sprays and Wasserstein geometry of the space of shapes

JG Liu, RL Pego, D Slepcev - arXiv preprint arXiv:1604.03387, 2016 - ki-net.umd.edu

We study a distance between shapes defined by minimizing the integral of kinetic energy along transport paths constrained to measures with characteristic-function densities. The formal geodesic equations for this shape distance are Euler equations for incompressible …

S Kolouri, Y Zou, GK Rohde - Proceedings of the IEEE Conference …, 2016 - cv-foundation.org

Optimal transport distances, otherwise known as Wasserstein distances, have recently

drawn ample attention in computer vision and machine learning as powerful discrepancy

measures for probability distributions. The recent developments on alternative formulations …

Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

In the first part of the paper we use a new Fourier technique to obtain a Stein

characterizations for random variables in the second Wiener chaos. We provide the

connection between this result and similar conclusions that can be derived using Malliavin …

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

On properties of the generalized Wasserstein distance

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2016 - Springer

The Wasserstein distances W p (p\geqq≧ 1), defined in terms of a solution to the Monge–

Kantorovich problem, are known to be a useful tool to investigate transport equations. In

particular, the Benamou–Brenier formula characterizes the square of the Wasserstein …

<--—2016————2016———— - 140—

The exponential formula for the Wasserstein metric

K Craig - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the

square Wasserstein metric. In this paper, we develop a class of transport metrics that have

better convexity properties and use these metrics to prove an Euler− Lagrange equation …

-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

[PDF] sfds.asso.fr

[PDF] Regularized Wasserstein barycenter

E Cazelles, J Bigot, N Papadakis - papersjds16.sfds.asso.fr

The concept of barycenter in the Wasserstein space allows the defintion of a notion of

Fréchet mean of a set of probability measures. However, depending on the considered data,

such barycenters may be irregular. In this paper, we thus introduce a convex regularization …

张洁琳，焦艳艳，罗钟铉 - 计算机辅助设计与图形学学报, 2016 - cqvip.com

为提高图形匹配的匹配率和精确率, 提出一种基于Gromov-Wasserstein (GW) 距离的3D

图形匹配方法. 首先将2 个图形嵌入到度量测度空间中, 通过最远采样法进行采样; 然后采用GW

距离表示2 个图形之间的差异性, 构造出目标函数和约束条件, 得到一个难于求解的二次分配 …

DF] Matricial Wasserstein and Unsupervised Tracking

[Chinese 3D graphics matching method based on Gromov-Wasserstein distance] see 2017

L Ning, R Sandhu, TT Georgiou, A Tannenbaum - romeilsandhu.com

The context of this work is spectral analysis of multivariable times-series as this may arise in

processing signals originating in antenna and sensor arrays. The salient feature of these

time signals is that they contain information about moving scatterers/targets which may not …

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

Y Yang, B Engquist, J Sun - SEG Technical Program Expanded …, 2016 - library.seg.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform

inversion (FWI) and prove such preperties as convexity in different aspects. Considering the

observed data and predicted data as two density functions, the quadratic Wasserstein metric …

Geometric construction of Wasserstein Barycenters

N Bonneel, J Digne - perso.liris.cnrs.fr

Optimal Transport theory consists in finding a map T pushing forward an input measure µ to

a target measure ν, which minimizes a “transport cost”. This cost often consists in the sum of

the squared distances travelled by all particles during their motion. Formally, the Monge …

[PDF] buffalo.edu

Gaze-Wasserstein: a quantitative screening approach to autism spectrum disorders

KW Cho, F Lin, C Song, X Xu… - 2016 IEEE Wireless …, 2016 - ieeexplore.ieee.org

Early detection of children with autism spectrum disorder (ASD) has been of great interest to

researchers due to an increase in the rate of autism incidence around the world. However, a

diagnosis of ASD is still challenging to receive in a timely manner for the large-scale …

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the …

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Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time spot follows a …

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_

{n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying

stochastic process. We consider the situation of practical importance where the random …

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

In this paper we extend a previous result of the author [S. Lisini, Calc. Var. Partial Differ. Eq.

28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein

spaces to a more general class of spaces: the spaces of probability measures endowed with …

2016 [HTML] sciencedirect.com

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem of finding the barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

[PDF] umd.edu

[PDF] Euler sprays and Wasserstein geometry of the space of shapes

JG Liu, RL Pego, D Slepcev - arXiv preprint arXiv:1604.03387, 2016 - ki-net.umd.edu

We study a distance between shapes defined by minimizing the integral of kinetic energy

along transport paths constrained to measures with characteristic-function densities. The

formal geodesic equations for this shape distance are Euler equations for incompressible …

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process

associated with the algorithm converges exponentially fast to the target distribution along

with some technical assumptions. While such an exponential convergence holds for

example in the log-concave measure case, it also holds for the more general case of …

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between

stationary measures for iterated function scheme on the unit interval. In particular, we

consider two stationary measures with different configurations of the weights associated to …

<——2016————2016———— - 170—

2016

Shape analysis with hyperbolic wasserstein distance

J Shi, W Zhang, Y Wang - Proceedings of the IEEE …, 2016 - openaccess.thecvf.com

Shape space is an active research field in computer vision study. The shape distance

defined in a shape space may provide a simple and refined index to represent a unique

shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It …

[CITATION] Regularization of barycenters in the Wasserstein space

J Bigot, C Elsa, N Papadakis - 2016 - hal.archives-ouvertes.fr

… hal-01333397, version 1. Regularization of barycenters in the Wasserstein space. Jérémie Bigot

1 Cazelles Elsa Nicolas Papadakis 1 Détails. 1 IMB - Institut de Mathématiques de Bordeaux.

Jérémie Bigot 1 AuthorId : 1352913 Auteur. Cazelles Elsa AuthorId : 1352914 Auteur …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - epfl.ch

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances

A Irpino, F De Carvalho, R Verde - arXiv preprint arXiv:1605.00513, 2016 - arxiv.org

Distributional (or distribution-valued) data are a new type of data arising from several

sources and are considered as realizations of distributional variables. A new set of fuzzy c-

means algorithms for data described by distributional variables is proposed. The algorithms …

2016

[PDF] CONFORMAL WASSERSTEIN DISTANCE: AN OVERVIEW AND ANALYSIS

A HAGERTY, Y SOLIMAN - 2016 - pdfs.semanticscholar.org

Three-dimensional shape analysis has been developing extremely rapidly over the course

of the past decade, and much of the research in this field has been catalyzed by the many

advances in 3D scanning and printing. Two of the central problems in shape analysis are …

[PDF] uni-due.de

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - pdfs.semanticscholar.org

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein

2016

M Laborde - 2016 - theses.fr

Résumé Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu

qu'une large classe d'équations paraboliques peuvent être vues comme des flots de

gradient dans l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à …

Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu'une

large classe d'équations paraboliques peuvent être vues comme des flots de gradient dans

l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à certaines …

<——2016————2016———— - 180—

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

symmetry of the given measure. An empirical bound on this asymmetric correction term is …

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

[PDF] Cortical Surface Classification with Hyperbolic Wasserstein Distance

J Shi, Y Wang - gsl.lab.asu.edu

The Wasserstein space consists of all probability measures that are defined on a

Riemannian manifold. The Wasserstein distance defines a Riemannian metric for the

Wasserstein space and it intrinsically measures the similarities between shapes …

On Parallel Transport in Wasserstein Space

X Sisi Shen - arXiv, 2016 - ui.adsabs.harvard.edu

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

On Parallel Transport in Wasserstein Space

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

[PDF] ijpam.eu

ON EXPONENTIAL CONVERGENCE OF GENERIC QUANTUM MARKOV SEMIGROUPS IN A WASSERSTEIN-TYPE DISTANCE

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups

using an generalization of the Lipschitz seminorm and a noncommutative analogue of

Wasserstein distance. We show turns out to be closely related with classical convergence …

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

Wasserstein approximations of the L\'evy area random walk via polynomial perturbations of Gaussian distributions

G Flint - arXiv preprint arXiv:1605.08996, 2016 - arxiv.org

We construct a coupling between the random walk composed of Lévy area increments from

a $ d $-dimensional Brownian motion and a random walk composed of quadratic

polynomials of Gaussian random variables. This coupling construction is used to produce a …

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station,

TX 77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density …

2016 [PDF] jmlr.org

[PDF] Gromov-wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on Machine …, 2016 - jmlr.org

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the interrelationships between points sampled

from individual domains, are not required to have the same size or to be in row-by-row …

[CITATION] Gromov-Wasserstein averaging of kernel and distance matrices International Conference on Machine Learning (ICML)

G Peyré, M Cuturi, J Solomon - 2016

<——2016————2016———— - 190—

Robust k-barycenters in Wasserstein Space and Wide ...

www.researchgate.net › publication › 304858224_Robust...

Request PDF | Robust k-barycenters in Wasserstein Space and Wide Consensus Clustering | A robust clustering method for probabilities in Wasserstein space ...

2016

Robust k-barycenters in Wasserstein Space and Wide ...

www.researchgate.net › ... › Physiology › Cluster Analysis

Robust k-barycenters in Wasserstein Space and Wide Consensus Clustering. July 2016. Authors: Eustasio del Barrio at Universidad de Valladolid · Eustasio del ...

[CITATION] Robust k-barycenters in wasserstein space and wide consensus clustering

E del Barrio, J Cuesta-Albertos, C Matrán, A Mayo-Íscar - arXiv preprint arXiv, 2016

istributionally Robust Stochastic Optimization with ...

Distributionally Robust Stochastic Optimization with ...

Apr 8, 2016 — arXiv:1604.02199 (math) ... Robust Stochastic Optimization with Wasserstein Distance ... Subjects: Optimization and Control (math.OC).

by R Gao · ‎2016 · ‎Cited by 241 · ‎Related articles

Apr 8, 2016 — Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is an underlying probability distribution that is known exactly, one hedges against a chosen set of distributions.

by R Gao · ‎2016 · ‎Cited by 242 · ‎Related articles

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance. arXiv. org

R Gao, AJ Kleywegt - 2016 - April

Interacting particles systems, Wasserstein gradient flow approach

2016

by Laborde, MaximEcole doctorale SDOSE (Paris), 2016

Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a large class of parabolic equations can be seen as gradient flows in...

Dissertation/ThesisCitation Online

2016

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

See 2915

2016

[PDF] Wasserstein barycentric coordinates: histogram regression using optimal transport.

N Bonneel, G Peyré, M Cuturi - ACM Trans. Graph., 2016 - perso.liris.cnrs.fr

This article defines a new way to perform intuitive and geometrically faithful regressions on histogram-valued data. It leverages the theory of optimal transport, and in particular the definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric …

On Parallel Transport in Wasserstein Space

X Sisi Shen - arXiv e-prints, 2016 - ui.adsabs.harvard.edu

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

On Parallel Transport in Wasserstein Space

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

Mathematics > Statistics Theory. arXiv:1606.01025 (math). [Submitted on 3 Jun 2016 (v1), last revised 18 Mar 2019 ( ...

by J Bigot · ‎2016 · ‎Cited by 15 · ‎Related articles

[CITATION] Penalized barycenters in the Wasserstein space. arXiv e-prints, art

J Bigot, E Cazelles, N Papadakis - arXiv preprint arXiv:1606.01025, 2016

PR ] 9 A ug 2 01 8 Conjugate Duality on Wasserstein Spaces with ...

https://www.semanticscholar.org › paper › PR-]-9-A-ug-2...

The paper develops easily implemented approximations to stationary policies based on finitely transient policies and shows that the concave hull of an ...

[CITATION] Conjugate Duality on Wasserstein Spaces with Applications in Partially Observable Markov Decision Processes

Y Shen, V Laschos, W Stannat, K Obermayer - arXiv preprint arXiv:1603.02882, 2016

[CITATION] Conjugate Duality on Wasserstein Spaces with Applications in Partially Observable Markov Decision Processes

Y Shen, V Laschos, W Stannat, K Obermayer - arXiv preprint arXiv:1603.02882, 2016

[CITATION] Conjugate Duality on Wasserstein Spaces with Applications in Partially Observable Markov Decision Processes

Y Shen, V Laschos, W Stannat, K Obermayer - arXiv preprint arXiv:1603.02882, 2016

[CITATION] Conjugate Duality on Wasserstein Spaces with Applications in Partially Observable Markov Decision Processes

Y Shen, V Laschos, W Stannat, K Obermayer - arXiv preprint arXiv:1603.02882, 2016

[CITATION] Conjugate Duality on Wasserstein Spaces with Applications in Partially Observable Markov Decision Processes

Y Shen, V Laschos, W Stannat, K Obermayer - arXiv preprint arXiv:1603.02882, 2016

<——2016————2016———— - 200—-

[PDF] uva.es

Baricentros e Holiday Greetings from Cruise Brothers n el espacio de Wasserstein: aplicación a modelos estadísticos de deformación

P Gordaliza Pastor - 2016 - uvadoc.uva.es

En el análisis de la homogeneidad de una colección de distribuciones y de relaciones

estructurales entre las observaciones, son muy útiles los baricentros y la variación en

distancia de Wasserstein. Estudiamos la estimación de los cuantiles del proceso empírico …

Using Gromov-Wasserstein distance to explore sets of networks

www.semanticscholar.org › paper › Using-Gromov-Wass...

Corpus ID: 33619373. Using Gromov-Wasserstein distance to explore sets of networks. @inproceedings{Hendrikson2016UsingGD, title={Using ...

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

基于 Wasserstein 距离和 SBGFRLS 方法的活动轮廓模型图像分割算法

王瑜，闫沫 - 西安航空学院学报, 2016 - cqvip.com

提出一种结合Wasserstein 距离和SBGFRLS 方法的非参数化活动轮廓图像分割算法.

该算法采用二值函数作为水平集函数并利用高斯核函数对其正则化, 有效避免水平集演化中的

重新初始化过程, 提高分割速度. 算法本身具有选择局部和全局分割的属性. 利用Wasserstein …

grandes déviations: applications à des modèles issus de la combinatoire et à l'analyse de sensibilité. Bornes minimax et distance de Wasserstein en statistique semi …

[Chinese Active contour model image segmentation algorithm based on Wasserstein distance and SBGFRLS method]

2016

T Klein - 2016 - hal.archives-ouvertes.fr

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific

research documents, whether they are pub- lished or not. The documents may come from teaching

and research institutions in France or abroad, or from public or private research centers …

[French large deviations: applications to models from combinatorics and to sensitivity analysis. Minimax bounds and Wasserstein distance in semi statistics…]

… grandes déviations: applications à des modèles issus de la combinatoire et à l'analyse de sensibilité. Bornes minimax et distance de Wasserstein en statistique semi …

T Klein - 2016 - hal.archives-ouvertes.fr

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific

research documents, whether they are pub- lished or not. The documents may come from teaching

and research institutions in France or abroad, or from public or private research centers …

Wasserstein contraction properties for hypoelliptic diffusions

F Baudoin - arXiv preprint arXiv:1602.04177, 2016 - arxiv.org

Gradient bounds had proved to be a very efficient tool for the control of the rate of

convergence to equilibrium for parabolic evolution equations. Among the gradient bounds

methods, the celebrated Bakry-Émery criterion is a powerful way prove to convergence to …

2016

Wasserstein stability of the entropy power inequality for log-concave densities

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

We establish quantitative stability results for the entropy power inequality (EPI). Specifically,

we show that if uniformly log-concave densities nearly saturate the EPI, then they must be

close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the …

[PDF] tandfonline.com

Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

A Farchi, M Bocquet, Y Roustan… - Tellus B: Chemical …, 2016 - Taylor & Francis

The verification of simulations against data and the comparison of model simulation of

pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based

on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called …

[PDF] web-proxy.io

Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - 2016 - web-proxy.io

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired. The aim of this Master thesis is to study, implement, and …

A weighted approximation approach to the study of the empirical Wasserstein distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

<——2016————2016———— - 210—

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

PDF] semanticscholar.org

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

PDF] ijpam.eu

ON EXPONENTIAL CONVERGENCE OF GENERIC QUANTUM MARKOV SEMIGROUPS IN A WASSERSTEIN-TYPE DISTANCE

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups

using an generalization of the Lipschitz seminorm and a noncommutative analogue of

Wasserstein distance. We show turns out to be closely related with classical convergence …

Evolution of the Wasserstein distance between the marginals of two Markov processes

A Alfonsi, J Corbetta, B Jourdain - arXiv preprint arXiv:1606.02994, 2016 - arxiv.org

In this paper, we are interested in the time derivative of the Wasserstein distance between

the marginals of two Markov processes. As recalled in the introduction, the Kantorovich

duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the …

Evolution of the Wasserstein distance between the marginals of two Markov processes

A Alfonsi, J Corbetta, B Jourdain - arXiv, 2016 - ui.adsabs.harvard.edu

In this paper, we are interested in the time derivative of the Wasserstein distance between

the marginals of two Markov processes. As recalled in the introduction, the Kantorovich

duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the …

y Declaración de la Asociación de Estadística Americana Sobre ...

https://www.researchgate.net › 30577...

Declaración de la Asociación de Estadística Americana Sobre la Significancia Estadística y Los Valores-P. June 2016; The American Statistician 70(2):Material ...

[CITATION] Declaración de la Asociación de Estadística Americana sobre la significancia estadística y los valores P (editado por Ronald L. Wasserstein)

…, M Goldenberg, F Aristimuño, F Oddi, LA Garibaldi - The American Statistician, 2016

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

The law of iterated logarithm for subordinated Gaussian ...

orbilu.uni.lu › handle

Title : The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds. Language : English. Author, co-author : Azmoodeh, ...

by E Azmoodeh · ‎2016 · ‎Cited by 6 · ‎Related articles

W-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

<——2016———— - 220—
2016

The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances

J Zinsl - arXiv preprint arXiv:1603.01375, 2016 - arxiv.org

This article is concerned with the existence of nonnegative weak solutions to a particular

fourth-order partial differential equation: it is a formal gradient flow with respect to a

generalized Wasserstein transportation distance with nonlinear mobility. The corresponding …

[CITATION] The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances, 2016

J Zinsl - Preprint

L^p-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - pdfs.semanticscholar.org

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

An augmented Lagrangian approach to Wasserstein gradient flows and applications

2016

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

2016

-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

2016

The gradient flow of a generalized Fisher information ...

[PDF] Fast dictionary learning with a smoothed Wasserstein loss

Mar 4, 2016 — ... formal gradient flow with respect to a generalized Wasserstein transportation distance with nonlinear mobility. The corresponding free energy ...

by J Zinsl · ‎2016 ·

2016 [PDF] jmlr.org

A Rolet, M Cuturi, G Peyré - Artificial Intelligence and Statistics, 2016 - jmlr.org

We consider in this paper the dictionary learning problem when the observations are

normalized histograms of features. This problem can be tackled using non-negative matrix

factorization approaches, using typically Euclidean or Kullback-Leibler fitting errors …

2016

Wasserstein loss for image synthesis and restoration

G Tartavel, G Peyré, Y Gousseau - SIAM Journal on Imaging Sciences, 2016 - SIAM

This paper presents a novel variational approach to imposing statistical constraints on the

output of both image generation (typically to perform texture synthesis) and image

restoration (for instance, to achieve denoising and inpainting) methods. The empirical …

2016

Wasserstein training of restricted Boltzmann machines

G Montavon, KR Müller, M Cuturi - Advances in Neural Information …, 2016 - papers.nips.cc

Boltzmann machines are able to learn highly complex, multimodal, structured and multiscale

real-world data distributions. Parameters of the model are usually learned by minimizing the

Kullback-Leibler (KL) divergence from training samples to the learned model. We propose in …

<——2016——————2016———— - 230

2016

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_

{n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying

stochastic process. We consider the situation of practical importance where the random …

2016

Discrete Wasserstein barycenters: Optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for

several marginals, and as such have a wide range of applications ranging from economics

to statistics and computer science. When the marginal probability measures are absolutely …

2016

[PDF] sfds.asso.fr

[PDF] Regularized Wasserstein barycenter

E Cazelles, J Bigot, N Papadakis - papersjds16.sfds.asso.fr

The concept of barycenter in the Wasserstein space allows the defintion of a notion of

Fréchet mean of a set of probability measures. However, depending on the considered data,

such barycenters may be irregular. In this paper, we thus introduce a convex regularization …

[CITATION] Superposition of the balancing and universal gradient methods for finding an entropy-smoothed Wasserstein barycenter and equilibria in multistage traffic …

AV Gasnikov, PE Dvurechensky, VG Spokoinyi… - Tr. Mosk. Fiz.-Tekh. Inst, 2016

year 2016

[CITATION] … of the balancing and universal gradient methods for finding an entropy-smoothed Wasserstein barycenter and equilibria in multistage traffic flow models

AV Gasnikov, PE Dvurechensky, VG Spokoinyi… - Tr. Mosk. Fiz.-Tekh. Inst., 2016

[CITATION] Superposition of the balancing and universal gradient methods for finding an entropy-smoothed Wasserstein barycenter and equilibria in multistage traffic …

AV Gasnikov, PE Dvurechensky, VG Spokoinyi… - Tr. Mosk. Fiz.-Tekh. Inst., 2016

Geometric construction of Wasserstein Barycenters

—2018

year 2016

N Bonneel, J Digne - perso.liris.cnrs.fr

Optimal Transport theory consists in finding a map T pushing forward an input measure µ to

a target measure ν, which minimizes a “transport cost”. This cost often consists in the sum of

the squared distances travelled by all particles during their motion. Formally, the Monge …

year 2016

[CITATION] Regularization of barycenters in the Wasserstein space

J Bigot, C Elsa, N Papadakis - 2016 - hal.archives-ouvertes.fr

… hal-01333397, version 1. Regularization of barycenters in the Wasserstein space. Jérémie Bigot 1 Cazelles Elsa Nicolas Papadakis 1 Détails. 1 IMB - Institut de Mathématiques de Bordeaux. Jérémie Bigot 1 AuthorId : 1352913 Auteur. Cazelles Elsa AuthorId : 1352914 Auteur …

See 2017

Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

In the first part of the paper we use a new Fourier technique to obtain a Stein

characterizations for random variables in the second Wiener chaos. We provide the

connection between this result and similar conclusions that can be derived using Malliavin …

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

Using Gromov-Wasserstein distance to explore sets of networks

[PDF] web-proxy.io

R Hendrikson - 2016 - web-proxy.io

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired. The aim of this Master thesis is to study, implement, and …

2016

Spectral Gromov-Wasserstein distances for shape matching

F Mémoli - 2009 IEEE 12th International Conference on …, 2009 - ieeexplore.ieee.org

We introduce a spectral notion of distance between shapes and study its theoretical

properties. We show that our distance satisfies the properties of a metric on the class of

isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if …

2016

基于 Gromov-Wasserstein 距离的 3D 图形匹配方法

张洁琳，焦艳艳，罗钟铉 - 计算机辅助设计与图形学学报, 2016 - cqvip.com

为提高图形匹配的匹配率和精确率, 提出一种基于Gromov-Wasserstein (GW) 距离的3D

图形匹配方法. 首先将2 个图形嵌入到度量测度空间中, 通过最远采样法进行采样; 然后采用GW

距离表示2 个图形之间的差异性, 构造出目标函数和约束条件, 得到一个难于求解的二次分配 …

From Monge-Kantorovich to Gromov-Wasserstein - Optimal ...

[Chinese 3D graphics matching method based on Gromov-Wasserstein distance]

speakerdeck.com › gpeyre › from-monge-kantorovich-...

Jun 21, 2016 — From Monge-Kantorovich to Gromov-Wasserstein - Optimal Transport and Barycenters Between Several Metric Spaces. Talk @ICML 2016 ...

<——2016——————2016———— - 240—

Inference for empirical Wasserstein distances on finite spaces

M Sommerfeld, A Munk - arXiv preprint arXiv:1610.03287, 2016 - arxiv.org

Page 1. Inference for empirical Wasserstein distances on finite spaces Max Sommerfeld∗

Axel Munk∗† Abstract The Wasserstein distance is an attractive tool for data analysis but

statistical inference is hindered by the lack of distributional lim- its …

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

2016 [HTML] springer.com

[HTML] A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

… the Wasserstein metric between two GMMs. The new Aggregated Wasserstein distance is a

semi-metric … 1 that states this semi-metric as an upper bound on the true Wasserstein metric. …

2016

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

… Eq. 28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein

spaces to a more general class of spaces: the spaces of probability measures endowed with

the Wasserstein−Orlicz distance constructed on extended Polish spaces (in general non …

Distributionally robust stochastic optimization with Wasserstein distance

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016 - arxiv.org

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under

uncertainty in which, instead of assuming that there is an underlying probability distribution

that is known exactly, one hedges against a chosen set of distributions. In this paper, we …

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance

AJ Kleywegt, R Gao - arXiv preprint arXiv:1604.02199, 2016

[CITATION] Distributionally robust stochastic optimization with wasserstein distance. arXiv e-prints, page

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance. arXiv. org

R Gao, AJ Kleywegt - 2016 - April

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

[PDF] jmlr.org

[PDF] Fast dictionary learning with a smoothed Wasserstein loss

A Rolet, M Cuturi, G Peyré - Artificial Intelligence and Statistics, 2016 - jmlr.org

… Top: examples of data histograms. Bottom: dictionary learned with Wasserstein (left) and

Kullback-Leibler (right) NMF … 2.2 Entropic Regularization Solving problems with Wasserstein

distance fitting er- rors can require solving several costly optimal trans- port problems …

[PDF] 213.230.96.51

A weighted approximation approach to the study of the empirical Wasserstein distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

[PDF]

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station,

TX 77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density …

An augmented Lagrangian approach to Wasserstein gradient flows and applications

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

… we get (3.7) d dt D(ρt ¯ρ) = ∫ RN ∇ [ log ρt + 1 kT H(x) ] · vρtdx = 〈∇ log ρt + 1

kT ∇H(x),v〉L2 ρt . Thus, the Wasserstein gradient of D(ρt ¯ρ) is ∇W2 D(ρt ¯ρ) = ∇

log ρt + 1 kT ∇H(x). The corresponding gradient flow is (3.8 …

<——2016——————2016———— - 250

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - tel.archives-ouvertes.fr

Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a

large class of parabolic equations can be seen as gradient flows in the Wasserstein space.

This thesis is devoted to extensions of this theory to equations and systems which do not …

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

See 2017

Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances

A Irpino, F De Carvalho, R Verde - arXiv preprint arXiv:1605.00513, 2016 - arxiv.org

Distributional (or distribution-valued) data are a new type of data arising from several

sources and are considered as realizations of distributional variables. A new set of fuzzy c-

means algorithms for data described by distributional variables is proposed. The algorithms …

On properties of the generalized Wasserstein distance

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2016 - Springer

The Wasserstein distances W p (p\geqq≧ 1), defined in terms of a solution to the Monge–

Kantorovich problem, are known to be a useful tool to investigate transport equations. In

particular, the Benamou–Brenier formula characterizes the square of the Wasserstein …

Distributionally robust stochastic optimization with Wasserstein distance

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016 - arxiv.org

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under

uncertainty in which, instead of assuming that there is an underlying probability distribution

that is known exactly, one hedges against a chosen set of distributions. In this paper, we …

[CITATION] Distributionally robust stochastic optimization with wasserstein distance. arXiv e-prints, page

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance

AJ Kleywegt, R Gao - arXiv preprint arXiv:1604.02199, 2016

<——2016——————2016———— - 260—

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

Sample out-of-sample inference based on Wasserstein distance

J Blanchet, Y Kang - arXiv preprint arXiv:1605.01340, 2016 - arxiv.org

We present a novel inference approach which we call Sample Out-of-Sample (or SOS)

inference. Our motivation is to propose a method which is well suited for data-driven stress

testing, in which emphasis is placed on measuring the impact of (plausible) out-of-sample …

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential convergence of diffusion semigroups with respect

to the standard‐Wasserstein distance for all. In particular, we show that for the Itô stochastic …

Shape analysis with hyperbolic Wasserstein distance

J Shi, W Zhang, Y Wang - Proceedings of the IEEE …, 2016 - openaccess.thecvf.com

Shape space is an active research field in computer vision study. The shape distance

defined in a shape space may provide a simple and refined index to represent a unique

shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It …

Wasserstein distance and the rectifiability of doubling measures: part I

J Azzam, G David, T Toro - Mathematische Annalen, 2016 - Springer

Let μ μ be a doubling measure in R^ n R n. We investigate quantitative relations between

the rectifiability of μ μ and its distance to flat measures. More precisely, for xx in the support Σ

Σ of μ μ and r> 0 r> 0, we introduce a number α (x, r) ∈ (0, 1 α (x, r)∈(0, 1 that measures, in …

[PDF] tandfonline.com

Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

A Farchi, M Bocquet, Y Roustan… - Tellus B: Chemical …, 2016 - Taylor & Francis

The verification of simulations against data and the comparison of model simulation of

pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based

on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called …

[PDF] web-proxy.io

Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - 2016 - web-proxy.io

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired. The aim of this Master thesis is to study, implement, and …

A weighted approximation approach to the study of the empirical Wasserstein distance

[PDF]

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

<——2016——————2016———— - 270—

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between

stationary measures for iterated function scheme on the unit interval. In particular, we

consider two stationary measures with different configurations of the weights associated to …

[PDF] CONFORMAL WASSERSTEIN DISTANCE: AN OVERVIEW AND ANALYSIS

A HAGERTY, Y SOLIMAN - 2016 - pdfs.semanticscholar.org

Three-dimensional shape analysis has been developing extremely rapidly over the course

of the past decade, and much of the research in this field has been catalyzed by the many

advances in 3D scanning and printing. Two of the central problems in shape analysis are …

[PDF] uni-due.de

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

PDF] Cortical Surface Classification with Hyperbolic Wasserstein Distance

J Shi, Y Wang - gsl.lab.asu.edu

The Wasserstein space consists of all probability measures that are defined on a

Riemannian manifold. The Wasserstein distance defines a Riemannian metric for the

Wasserstein space and it intrinsically measures the similarities between shapes …

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

[CITATION] Stein's method and Poisson process approximation for a class of Wasserstein metrics. Bernoulli 15 550–568

D Schuhmacher - … (MathSciNet): MR2543874 Digital Object Identifier: doi, 2009

Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

In the first part of the paper we use a new Fourier technique to obtain a Stein

characterizations for random variables in the second Wiener chaos. We provide the

connection between this result and similar conclusions that can be derived using Malliavin …

<——2016——————2016———— - 280—

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

The exponential formula for the Wasserstein metric

K Craig - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the

square Wasserstein metric. In this paper, we develop a class of transport metrics that have

better convexity properties and use these metrics to prove an Euler− Lagrange equation …

A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time spot follows a …

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

Y Yang, B Engquist, J Sun - SEG Technical Program Expanded …, 2016 - library.seg.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform

inversion (FWI) and prove such preperties as convexity in different aspects. Considering the

observed data and predicted data as two density functions, the quadratic Wasserstein metric …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Application of optimal transport and the ... - SEG Library

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

2016

https://library.seg.org › doi › abs › geo2016-0663

by Y Yang · 2018 · Cited by 167 — ABSTRACTConventional full-waveform inversion (FWI) using the least-squares norm as a misfit function is known to suffer from cycle-skipping issues that ...

(PDF) Application of Optimal Transport and the Quadratic ...

https://www.researchgate.net › ... › Optimal Transport

Dec 17, 2016 — We propose a new way of using the W2 metric trace-by-trace in FWI and compare it to global W2 via the solution of the Monge-Ampere equation.

[CITATION] Application of optimal transport and the quadratic wasserstein metric to full-waveform inversion: arXiv preprint arXiv: 1612.05075

Y Yang, B Engquist, J Sun, BD Froese - 2016

[PDF] Euler sprays and Wasserstein geometry of the space of shapes

JG Liu, RL Pego, D Slepcev - arXiv preprint arXiv:1604.03387, 2016 - ki-net.umd.edu

We study a distance between shapes defined by minimizing the integral of kinetic energy

along transport paths constrained to measures with characteristic-function densities. The

formal geodesic equations for this shape distance are Euler equations for incompressible …

<——2016——————2016———— - 290 —

2016

-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

2016

Wasserstein stability of the entropy power inequality for log-concave densities

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

We establish quantitative stability results for the entropy power inequality (EPI). Specifically,

we show that if uniformly log-concave densities nearly saturate the EPI, then they must be

close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the …

2016

Wasserstein continuity of entropy and outer bounds for interference channels

Y Polyanskiy, Y Wu - IEEE Transactions on Information Theory, 2016 - ieeexplore.ieee.org

It is shown that under suitable regularity conditions, differential entropy is O (√ n)-Lipschitz

as a function of probability distributions on Ilin with respect to the quadratic Wasserstein

distance. Under similar conditions,(discrete) Shannon entropy is shown to be O (n)-Lipschitz …

An augmented Lagrangian approach to Wasserstein gradient flows and applications

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

2016

[HTML] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - Journal of Functional Analysis, 2016 - Elsevier

Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014)[5], we show that the

L 2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient

flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of …

[CITATION] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space, Preprint (2014)

M Kell - Available at arXiv

Stein's method on the second Wiener chaos: 2-Wasserstein distance

2016

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

In the first part of the paper we use a new Fourier technique to obtain a Stein

[PDF] arxiv.orgcharacterizations for random variables in the second Wiener chaos. We provide the

connection between this result and similar conclusions that can be derived using Malliavin …

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

istogram Regression Using Optimal Transport - YouTube

Title: Wasserstein Barycentric Coordinates: Histogram Regression Using ... and in particular the definition of Wasserstein barycenters, ...

YouTube · Nicolas Bonneel ·

Apr 13, 2016

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_

{n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying

stochastic process. We consider the situation of practical importance where the random …

<——2016—————2016——- 300—

Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances

A Irpino, F De Carvalho, R Verde - arXiv preprint arXiv:1605.00513, 2016 - arxiv.org

Distributional (or distribution-valued) data are a new type of data arising from several

sources and are considered as realizations of distributional variables. A new set of fuzzy c-

means algorithms for data described by distributional variables is proposed. The algorithms …

Sample out-of-sample inference based on Wasserstein distance

J Blanchet, Y Kang - arXiv preprint arXiv:1605.01340, 2016 - arxiv.org

We present a novel inference approach which we call Sample Out-of-Sample (or SOS)

inference. Our motivation is to propose a method which is well suited for data-driven stress

testing, in which emphasis is placed on measuring the impact of (plausible) out-of-sample …

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

2016

Application of optimal transport and the ... - SEG Library

https://library.seg.org › doi › abs › geo2016-0663

(PDF) Application of Optimal Transport and the Quadratic ...

https://www.researchgate.net › ... › Optimal Transport

Dec 17, 2016 — We propose a new way of using the W2 metric trace-by-trace in FWI and compare it to global W2 via the solution of the Monge-Ampere equation.

[CITATION] Application of optimal transport and the quadratic wasserstein metric to full-waveform inversion: arXiv preprint arXiv: 1612.05075

Y Yang, B Engquist, J Sun, BD Froese - 2016

2016

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the …

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

Geometric construction of Wasserstein Barycenters

N Bonneel, J Digne - perso.liris.cnrs.fr

Optimal Transport theory consists in finding a map T pushing forward an input measure µ to

a target measure ν, which minimizes a “transport cost”. This cost often consists in the sum of

the squared distances travelled by all particles during their motion. Formally, the Monge …

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

<——2016—————2016——- 310—

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential convergence of diffusion semigroups with respect

to the standard‐Wasserstein distance for all. In particular, we show that for the Itô stochastic …

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

An augmented Lagrangian approach to Wasserstein gradient flows and applications

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

[HTML] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - Journal of Functional Analysis, 2016 - Elsevier

Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014)[5], we show that the

L 2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient

flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of …

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

2016

-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances

J Zinsl - arXiv preprint arXiv:1603.01375, 2016 - arxiv.org

This article is concerned with the existence of nonnegative weak solutions to a particular

fourth-order partial differential equation: it is a formal gradient flow with respect to a

generalized Wasserstein transportation distance with nonlinear mobility. The corresponding …

Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - tel.archives-ouvertes.fr

Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a

large class of parabolic equations can be seen as gradient flows in the Wasserstein space.

This thesis is devoted to extensions of this theory to equations and systems which do not …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein: Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - oatd.org

Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu'une

large classe d'équations paraboliques peuvent être vues comme des flots de gradient dans

l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à certaines …

2016 see 2017

On some non linear evolution systems which are perturbations ...

by M Laborde · 2015 · Cited by 18 — Abstract: This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal ...

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

Lp-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

<——2016—————2016——- 320—

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

Wasserstein training of restricted Boltzmann machines

G Montavon, KR Müller, M Cuturi - Proceedings of the 30th International …, 2016 - dl.acm.org

Boltzmann machines are able to learn highly complex, multimodal, structured and multiscale

real-world data distributions. Parameters of the model are usually learned by minimizing the

Kullback-Leibler (KL) divergence from training samples to the learned model. We propose in …

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions

defined on the same metric space. In order to compare distributions on different metric

spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

[HTML] … метода балансировки и универсального градиентного метода для поиска энтропийно-регуляризованного барицентра Вассерштейна и равновесий в …

АВ Гасников, ПЕ Двуреченский… - Труды Московского …, 2016 - cyberleninka.ru

Представлен обзор современных численных методов поиска барицентра Вассерштейна конечного семейства вероятностных мер с одинаковым конечным носителем. Такие задачи в последнее время стали очень популярны в

связи с …

speakerdeck.com › gpeyre › from-monge-kantorovich-...

[Russian Superposition of balancing method and universal gradient method for searching entropy-regulizated Wasserstein barycenter and equilibria fin many-stage models of transportation flows]

Jun 21, 2016 — From Monge-Kantorovich to Gromov-Wasserstein - Optimal Transport and Barycenters Between Several Metric Spaces. Talk @ICML 2016 ...

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions

defined on the same metric space. In order to compare distributions on different metric

spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

2016

Declaración de la Asociación de Estadística Americana Sobre ...

[HTML] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - Journal of Functional Analysis, 2016 - Elsevier

Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014)[5], we show that the

L 2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient

flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of …

www.researchgate.net › publication

Download Citation | Declaración de la Asociación de Estadística Americana Sobre la Significancia Estadística y Los Valores-P | Introducción El aumento del ...

[CITATION] Declaración de la Asociación de Estadística Americana sobre la significancia estadística y los valores P (editado por Ronald L. Wasserstein)

F Laco Mazzone, M Grampa, M Goldenberg… - The American Statistician, 2016

2016 Vaserstein

The Vaserstein symbol on real smooth affine threefolds arXiv

J Fasel - arXiv preprint arXiv:1606.01266, 2016 - arxiv.org

Abstract: We give a necessary and sufficient topological condition for the Vaserstein symbol

to be injective on smooth affine real threefolds. More precisely, we show that the Vaserstein

symbol is a bijection for such a threefold X if and only if the set of compact connected ...

[HTML] … метода балансировки и универсального градиентного метода для поиска энтропийно-регуляризованного барицентра Вассерштейна и равновесий в …

2016 Vaserstein

АВ Гасников, ПЕ Двуреченский… - Труды Московского …, 2016 - cyberleninka.ru

Представлен обзор современных численных методов поиска барицентра Вассерштейна конечного семейства вероятностных мер с одинаковым конечным носителем. Такие задачи в последнее время стали очень популярны в связи с …

2016 Vaserstein

] arxiv.org

The Vaserstein symbol on real smooth affine threefolds

J Fasel - arXiv preprint arXiv:1606.01266, 2016 - arxiv.org

We give a necessary and sufficient topological condition for the Vaserstein symbol to be

injective on smooth affine real threefolds. More precisely, we show that the Vaserstein

symbol is a bijection for such a threefold X if and only if the set of compact connected …

<——2016—————2016——- 330—

Wasserstein loss for image synthesis and restoration

G Tartavel, G Peyré, Y Gousseau - SIAM Journal on Imaging Sciences, 2016 - SIAM

This paper presents a novel variational approach to imposing statistical constraints on the output of both image generation (typically to perform texture synthesis) and image restoration (for instance, to achieve denoising and inpainting) methods. The empirical …

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the exponential distribution with the same mean approximates the probability distribution of X, based on the information provided by a sample from X. Specifically, we consider the …

Wasserstein continuity of entropy and outer bounds for interference channels

Y Polyanskiy, Y Wu - IEEE Transactions on Information Theory, 2016 - ieeexplore.ieee.org

It is shown that under suitable regularity conditions, differential entropy is O (√ n)-Lipschitz as a function of probability distributions on Ilin with respect to the quadratic Wasserstein distance. Under similar conditions,(discrete) Shannon entropy is shown to be O (n)-Lipschitz …

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

2016

Fast dictionary learning with a smoothed Wasserstein loss

A Rolet, M Cuturi, G Peyré - Artificial Intelligence and …, 2016 - proceedings.mlr.press

We consider in this paper the dictionary learning problem when the observations are normalized histograms of features. This problem can be tackled using non-negative matrix factorization approaches, using typically Euclidean or Kullback-Leibler fitting errors …

2016

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

2016

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to Fluid Equations

K Kang, HK Kim - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider a coupled system of Keller--Segel-type equations and the incompressible

Navier--Stokes equations in spatial dimension two and three. We first establish the existence

of a weak solution of a Fokker--Plank equation in the Wasserstein space under the …

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-space Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex near infinity, we establish the exponential convergence of diffusion semigroups with respect to the standard‐Wasserstein distance for all. In particular, we show that for the Itô stochastic …

<——2016—————2016——- 340—

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_ {n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying stochastic process. We consider the situation of practical importance where the random …

[PDF] ijpam.eu

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence …

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

Wasserstein approximations of the L\'evy area random walk via polynomial perturbations of Gaussian distributions

G Flint - arXiv preprint arXiv:1605.08996, 2016 - arxiv.org

We construct a coupling between the random walk composed of Lévy area increments from a $ d $-dimensional Brownian motion and a random walk composed of quadratic polynomials of Gaussian random variables. This coupling construction is used to produce a …

Wasserstein stability of the entropy power inequality for log-concave densities

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the …

2016

Shape analysis with hyperbolic wasserstein distance

J Shi, W Zhang, Y Wang - Proceedings of the IEEE …, 2016 - openaccess.thecvf.com

Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It …

2016

Inference for empirical Wasserstein distances on finite spaces

M Sommerfeld, A Munk - arXiv preprint arXiv:1610.03287, 2016 - arxiv.org

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters and to the network itself. The quantification of sensitivity is obtained by measuring the Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a …

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

<——2016—————2016——- 350—

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between stationary measures for iterated function scheme on the unit interval. In particular, we consider two stationary measures with different configurations of the weights associated to …

Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived using Malliavin …

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

[PDF] ijpam.eu

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence …

On Parallel Transport in Wasserstein Space

X Sisi Shen - arXiv e-prints, 2016 - ui.adsabs.harvard.edu

In this short note, we would like to give a construction of parallel transport for tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the linear part of the tangent space, and show that a construction for the full tangent cones …

On Parallel Transport in Wasserstein Space

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

2016

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

A smoothed dual approach for variational Wasserstein problems

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

Cited by 115 Related articles

2016 modified

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions defined on the same metric space. In order to compare distributions on different metric spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

Using Gromov-Wasserstein distance to explore sets of networks

2016 359

2016 master thesis Tartu

dspace.ut.ee/bitstream/handle/10062/50406/...

Using Gromov-Wasserstein distance to explore sets of networks In many elds such as social sciences or biology, relations between data or variables are presented as networks. To compare these networks, a mean-ingful notion of distance between networks is highly desired. The aim of this Master thesis is to study, implement, and apply one Gromov-Wasser-

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

Discrete Wasserstein barycenters: optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics and computer science. When the marginal probability measures are absolutely …

<——2016—————2016——- 360—

2016

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions defined on the same metric space. In order to compare distributions on different metric spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

2016

[CITATION] … some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon Series …

M Laborde - Appl. Math, 2016

See 2 2015,017

2016

arxiv.org › physics

by Y Yang · 2016 · Cited by 123 — Application of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion. ... In our previous work, we proposed the quadratic Wasserstein metric (W_2) as a new misfit function for FWI. The W_2 metric has been proved to have many ideal properties with regards to convexity and insensitivity to noise.

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full‐waveform inversion. arXiv preprint arXiv: 1612.05075

Y Yang, B Engquist, J Sun, BD Froese - 2016

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full‐waveform inversion. arXiv preprint arXiv: 1612.05075

Y Yang, B Engquist, J Sun, BD Froese - 2016

2016

The Vaserstein symbol on real smooth affine threefolds

J Fasel - arXiv preprint arXiv:1606.01266, 2016 - arxiv.org

We give a necessary and sufficient topological condition for the Vaserstein symbol to be injective on smooth affine real threefolds. More precisely, we show that the Vaserstein symbol is a bijection for such a threefold X if and only if the set of compact connected …

CITATION] The Vaserstein symbol on real smooth affine threefolds, to appear

Gromov-Wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on …, 2016 - proceedings.mlr.press

This paper presents a new technique for computing the barycenter of a set of distance or kernel matrices. These matrices, which define the inter-relationships between points sampled from individual domains, are not required to have the same size or to be in row-by …

2016

[French Habilitation to Direct Research: Central limit theorem, inequalities of concentration and principles of large deviations: applications to models resulting from combinatorics and to sensitivity analysis. Minimax bounds and Wasserstein distance in semi-parametric statistics] HAL

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this asymmetric correction term is …

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this asymmetric correction term is …

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

2016

Y Yang, B Engquist, J Sun - SEG Technical Program Expanded …, 2016 - library.seg.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform inversion (FWI) and prove such preperties as convexity in different aspects. Considering the observed data and predicted data as two density functions, the quadratic Wasserstein metric …

Wasserstein Training of Boltzmann Machines

swoh.web.engr.illinois.edu › handout › fall2016_slide13

by G Montavon · 2016 · Cited by 82 — Definition: Restricted Boltzmann machines (RBM). Restricted Boltzmann machine is a special type of Boltzmann machine with d binary observed ...

<——2016—————2016——- 370—

2016

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure of the equation with …

2016 [PDF] researchgate.net

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time invariant (LTI) control system steers a given Gaussian probability density function (PDF) close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - epfl.ch

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein

2016

M Laborde - 2016 - theses.fr

Résumé Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu

qu'une large classe d'équations paraboliques peuvent être vues comme des flots de

gradient dans l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à …

2016 zzz 31 see 2018

CITATION] Barycenter: Wasserstein Barycenter

M Klatt - 2016

2016

[PDF] Euler sprays and Wasserstein geometry of the space of shapes

JG Liu, RL Pego, D Slepcev - arXiv preprint arXiv:1604.03387, 2016 - ki-net.umd.edu

We study a distance between shapes defined by minimizing the integral of kinetic energy

along transport paths constrained to measures with characteristic-function densities. The

formal geodesic equations for this shape distance are Euler equations for incompressible …

Discrete Wasserstein barycenters: optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for

several marginals, and as such have a wide range of applications ranging from economics

to statistics and computer science. When the marginal probability measures are absolutely …

2016

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

2016

Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances

A Irpino, F De Carvalho, R Verde - arXiv preprint arXiv:1605.00513, 2016 - arxiv.org

Distributional (or distribution-valued) data are a new type of data arising from several

sources and are considered as realizations of distributional variables. A new set of fuzzy c-

means algorithms for data described by distributional variables is proposed. The algorithms …

A smoothed dual approach for variational Wasserstein problems

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

Cited by 116 Related articles

<——2016—————2016——- 380—

An augmented Lagrangian approach to Wasserstein gradient flows and applications

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

[PDF] esaim-proc.org

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

[PDF] buffalo.edu

Gaze-Wasserstein: a quantitative screening approach to autism spectrum disorders

KW Cho, F Lin, C Song, X Xu… - 2016 IEEE Wireless …, 2016 - ieeexplore.ieee.org

Early detection of children with autism spectrum disorder (ASD) has been of great interest to

researchers due to an increase in the rate of autism incidence around the world. However, a

diagnosis of ASD is still challenging to receive in a timely manner for the large-scale …

Robust k-barycenters in Wasserstein Space and Wide ...

www.researchgate.net › publication › 304858224_Robust...

Request PDF | Robust k-barycenters in Wasserstein Space and Wide Consensus Clustering | A robust clustering method for probabilities in Wasserstein space ...

[CITATION] Robust k-barycenters in wasserstein space and wide consensus clustering

E del Barrio, J Cuesta-Albertos, C Matrán, A Mayo-Íscar - arXiv preprint arXiv, 2016

2016

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

In this paper we extend a previous result of the author [S. Lisini, Calc. Var. Partial Differ. Eq.

28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein

spaces to a more general class of spaces: the spaces of probability measures endowed with …

2016

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

2016

hal.archives-ouvertes.fr › hal-01333...

by J Bigot · ‎2016 · ‎Cited by 6 · ‎Related articles

Jun 17, 2016 — Citation. Jérémie Bigot, Cazelles Elsa, Nicolas Papadakis. Regularization of barycenters in the Wasserstein space. 2016. ⟨hal-01333397⟩ ...

[CITATION] Regularization of barycenters in the Wasserstein space

J Bigot, C Elsa, N Papadakis - 2016 - hal.archives-ouvertes.fr

… 01333397, version 1. Pré-publication, Document de travail. Regularization of barycenters in the

Wasserstein space. Jérémie Bigot 1 Cazelles Elsa Nicolas Papadakis 1 Détails. 1 IMB - Institut

de Mathématiques de Bordeaux. Jérémie Bigot 1 AuthorId : 1352913 Mail : Auteur. Cazelles …

2016

Penalization of barycenters in the Wasserstein space - ‎Bigot - Cited by 15

… complexity of approximating Wasserstein barycenters - ‎Kroshnin - Cited by 43

Web results

by J Bigot · ‎2016 · ‎Cited by 15 · ‎Related articles

In this paper, a regularization of Wasserstein barycenters for random measures supported on \mathbb{R}^{d} is introduced via convex penalizati

[CITATION] Penalized barycenters in the Wasserstein space. arXiv e-prints, art

J Bigot, E Cazelles, N Papadakis - arXiv preprint arXiv:1606.01025, 2016

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Conditional Wasserstein Generative Adversarial Networks

cameronfabbri.github.io › papers › conditionalWGAN

PDF

Conditional Wasserstein Generative Adversarial Networks. Cameron ... Generative Adversarial Networks (GANs) have been able to model complex data distributions such ... auxiliary classifier gans,” arXiv preprint arXiv:1610.09585, 2016.

[CITATION] Conditional Wasserstein generative adversarial networks

C Fabbri - Preprint to be searched in a search engine, 2016

Using Gromov-Wasserstein distance to explore sets of networks

<——2016—————2016——- 390—

1library.net › Other

Thepresent work focuses on Gromov-Wasserstein (GW) distance which allows to ... UNIVERSITY OF TARTU ... the possibilities of GW distance to discover patterns in multiple networks' data sets. ... [Online; accessed 17-January-2016].

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

Sliced Wasserstein kernels for probability distributions

2016

S Kolouri, Y Zou, GK Rohde - Proceedings of the IEEE Conference …, 2016 - cv-foundation.org

Optimal transport distances, otherwise known as Wasserstein distances, have recently

drawn ample attention in computer vision and machine learning as powerful discrepancy

measures for probability distributions. The recent developments on alternative formulations …

2016

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

2016

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

2016

M Laborde - 2016 - theses.fr

Résumé Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu

qu'une large classe d'équations paraboliques peuvent être vues comme des flots de

gradient dans l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à …

2016

[PDF] Baricentros en el espacio de Wasserstein: aplicación a modelos estadísticos de deformación

P Gordaliza Pastor - 2016 - core.ac.uk

En el análisis de la homogeneidad de una colección de distribuciones y de relaciones

estructurales entre las observaciones, son muy útiles los baricentros y la variación en

distancia de Wasserstein. Estudiamos la estimación de los cuantiles del proceso empírico …

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the …

[CITATION] Wasserstein and Zolotarev distances

N Belili, H Heinich - COMPTES RENDUS DE L …, 2000 - … MEDICALES ELSEVIER 23 RUE …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein: Interacting particles systems, Wasserstein gradient flow approach

C Frogner, C Zhang, H Mobahi, M Araya-Polo… - arXiv preprint arXiv …, 2015 - arxiv.org

Learning to predict multi-label outputs is challenging, but in many problems there is a

natural metric on the outputs that can be used to improve predictions. In this paper we

develop a loss function for multi-label learning, based on the Wasserstein distance. The …

2016

M Laborde - 2016 - oatd.org

Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu'une

large classe d'équations paraboliques peuvent être vues comme des flots de gradient dans

l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à certaines …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein

M Laborde - 2016 - theses.fr

Résumé Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu

qu'une large classe d'équations paraboliques peuvent être vues comme des flots de

gradient dans l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à …

Distributionally robust stochastic optimization with Wasserstein distance

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016 - arxiv.org

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under

uncertainty in which, instead of assuming that there is an underlying probability distribution

that is known exactly, one hedges against a chosen set of distributions. In this paper, we …

[CITATION] Distributionally Robust Stochastic Optimization with Wasserstein Distance

G Rui, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016

[CITATION] Distributionally robust stochastic optimization with wasserstein distance. arXiv e-prints, page

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance. arXiv. org

R Gao, AJ Kleywegt - 2016 - April

<——2016—————2016——- 400—

2016

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

See 2015, 2017

The exponential formula for the Wasserstein metric

K Craig - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the

square Wasserstein metric. In this paper, we develop a class of transport metrics that have

better convexity properties and use these metrics to prove an Euler− Lagrange equation …

W-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

2016 [PDF] tandfonline.com

Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

A Farchi, M Bocquet, Y Roustan… - Tellus B: Chemical …, 2016 - Taylor & Francis

The verification of simulations against data and the comparison of model simulation of

pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based

on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called …

2016

Application of Optimal Transport and the Quadratic ...

arxiv.org › physics

by Y Yang · ‎2016 · ‎Cited by 124 · ‎Related articles

Physics > Geophysics. arXiv:1612.05075 (physics). [Submitted on 15 Dec 2016 (v1), last revised 10 May 2017 (this version, v2)] ...

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full‐waveform inversion. arXiv preprint arXiv: 1612.05075

Y Yang, B Engquist, J Sun, BD Froese - 2016

An augmented Lagrangian approach to Wasserstein gradient flows and applications

2016

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

2016 [PDF] archives-ouvertes.fr

… et principes de grandes déviations: applications à des modèles issus de la combinatoire et à l'analyse de sensibilité. Bornes minimax et distance de Wasserstein en …

T Klein - 2016 - hal.archives-ouvertes.fr

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific

research documents, whether they are pub- lished or not. The documents may come from teaching

and research institutions in France or abroad, or from public or private research centers …

Shape Analysis With Hyperbolic Wasserstein Distance - CVF ...

2016

https://openaccess.thecvf.com › papers › Shi_Sha...

https://openaccess.thecvf.com › papers › Shi_Sha...PDF

by J Shi · 2016 · Cited by 11 — stein distance to encode the integral shape invariants com- puted at multiple scales and to measure the dissimilarities between two shapes.

[PDF] Cortical Surface Classification with Hyperbolic Wasserstein Distance

J Shi, Y Wang - gsl.lab.asu.edu

The Wasserstein space consists of all probability measures that are defined on a

Riemannian manifold. The Wasserstein distance defines a Riemannian metric for the

Wasserstein space and it intrinsically measures the similarities between shapes …

The Vaserstein symbol on real smooth affine threefolds

J Fasel - arXiv preprint arXiv:1606.01266, 2016 - arxiv.org

We give a necessary and sufficient topological condition for the Vaserstein symbol to be

injective on smooth affine real threefolds. More precisely, we show that the Vaserstein

symbol is a bijection for such a threefold X if and only if the set of compact connected …

The Vaserstein symbol on real smooth affine threefolds

J Fasel - arXiv preprint arXiv:1606.01266, 2016 - arxiv.org

We give a necessary and sufficient topological condition for the Vaserstein symbol to be

injective on smooth affine real threefolds. More precisely, we show that the Vaserstein

symbol is a bijection for such a threefold X if and only if the set of compact connected …

[CITATION] The Vaserstein symbol on real smooth affine threefolds, to appear in the

J Fasel - Proceedings of the International Colloquium on K …

Existence of Solutions to Wasserstein Gradient Flows and Their Long Time Asymptotic Behaviors

<——2016—————2016——- 410—

2016 7 master Hong Kong

Ng, Wing Kit. Thesis M.Phil. Chinese University of Hong Kong 2016. Includes bibliographical references (leaves ). Abstracts also in Chinese. Title from PDF...

Dissertation/ThesisCitation Online

2016 PDF

Lectures on Mean Field Games: II. Calculus over Wasserstein ...

www.math.columbia.edu › probability › seminar › Min...

CALCULUS OVER WASSERSTEIN SPACE, CONTROL OF ... Wasserstein space P2(Rd ) is a metric space for W2 ... DERIVING THE MASTER EQUATION.

[PDF] Wasserstein barycentric coordinates: histogram regression using optimal transport.

N Bonneel, G Peyré, M Cuturi - ACM Trans. Graph., 2016 - perso.liris.cnrs.fr

This article defines a new way to perform intuitive and geometrically faithful regressions on

histogram-valued data. It leverages the theory of optimal transport, and in particular the

definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric …

[PDF] tandfonline.com

Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

A Farchi, M Bocquet, Y Roustan… - Tellus B: Chemical …, 2016 - Taylor & Francis

The verification of simulations against data and the comparison of model simulation of

pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based

on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances

A Irpino, F De Carvalho, R Verde - arXiv preprint arXiv:1605.00513, 2016 - arxiv.org

Distributional (or distribution-valued) data are a new type of data arising from several

sources and are considered as realizations of distributional variables. A new set of fuzzy c-

means algorithms for data described by distributional variables is proposed. The algorithms …

Using Gromov-Wasserstein distance to explore sets of networks

core.ac.uk › download › pdf

PDF

by R Hendrikson · Cited by 7 — UNIVERSITY OF TARTU. FACULTY OF ... Raul Vicente Zafra. Tartu 2016 ... metric measure spaces and compare them on basis of Gromov-Wasserstein distance. ... GW distance to discover patterns in multiple networks' data sets. The thesis is ...

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

Inference for empirical Wasserstein distances on finite spaces

M Sommerfeld, A Munk - arXiv preprint arXiv:1610.03287, 2016 - arxiv.org

The Wasserstein distance is an attractive tool for data analysis but statistical inference is

hindered by the lack of distributional limits. To overcome this obstacle, for probability

measures supported on finitely many points, we derive the asymptotic distribution of …

2016 [HTML] sciencedirect.com

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

2016

A weighted approximation approach to the study of the empirical Wasserstein distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

<——2016—————2016——- 420—

2016

[PDF] romeilsandhu.com

[PDF] Matricial Wasserstein and Unsupervised Tracking

L Ning, R Sandhu, TT Georgiou, A Tannenbaum - romeilsandhu.com

The context of this work is spectral analysis of multivariable times-series as this may arise in

processing signals originating in antenna and sensor arrays. The salient feature of these

time signals is that they contain information about moving scatterers/targets which may not …

[PDF] Wasserstein barycentric coordinates: histogram regression using optimal transport.

N Bonneel, G Peyré, M Cuturi - ACM Trans. Graph., 2016 - perso.liris.cnrs.fr

This article defines a new way to perform intuitive and geometrically faithful regressions on

histogram-valued data. It leverages the theory of optimal transport, and in particular the

definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric …

Discrete Wasserstein barycenters: optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for

several marginals, and as such have a wide range of applications ranging from economics

to statistics and computer science. When the marginal probability measures are absolutely …

2016

On Parallel Transport in Wasserstein Space

X Sisi Shen - arXiv e-prints, 2016 - ui.adsabs.harvard.edu

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

On Parallel Transport in Wasserstein Space

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions

defined on the same metric space. In order to compare distributions on different metric

spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

Sample out-of-sample inference based on Wasserstein distance

2016

J Blanchet, Y Kang - arXiv preprint arXiv:1605.01340, 2016 - arxiv.org

We present a novel inference approach which we call Sample Out-of-Sample (or SOS)

inference. Our motivation is to propose a method which is well suited for data-driven stress

testing, in which emphasis is placed on measuring the impact of (plausible) out-of-sample …

A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time spot follows a …

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

symmetry of the given measure. An empirical bound on this asymmetric correction term is …

Wasserstein stability of the entropy power inequality for log-concave densities

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

We establish quantitative stability results for the entropy power inequality (EPI). Specifically,

we show that if uniformly log-concave densities nearly saturate the EPI, then they must be

close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the …

2016

[PDF] uni-due.de

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

<——2016—————2016——- 430—

2016

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

2016

Discrete Wasserstein barycenters: optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for

several marginals, and as such have a wide range of applications ranging from economics

to statistics and computer science. When the marginal probability measures are absolutely …

(PDF) Linear models for histogram data based on Wasserstein distance: scalar and functional models

www.researchgate.net › publication › 303445026_Linear...

May 23, 2016 — PDF | The presentation was made at the Workshop on Functional data analysis held in Caserta in 2012. The presentation shows some ...

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

2016

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

2016

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_

{n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying

stochastic process. We consider the situation of practical importance where the random …

<——2016—————2016——- 440—

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - tel.archives-ouvertes.fr

Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a

large class of parabolic equations can be seen as gradient flows in the Wasserstein space.

This thesis is devoted to extensions of this theory to equations and systems which do not …

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein: Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - oatd.org

Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu'une

large classe d'équations paraboliques peuvent être vues comme des flots de gradient dans

l'espace de Wasserstein. Le but de cette thèse est d'étendre cette théorie à certaines …

2016

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost - IEEE Conference ...

ieeexplore.ieee.org › abstract › document

by A Halder · 2016 · Cited by 32 — We show that the LQG control problem can be recovered as a special case of our density regulator problem, and illustrate our formulation on a numerical example.

Date Added to IEEE Xplore: 01 August 2016	Date of Conference: 6-8 July 2016
DOI: 10.1109/ACC.2016.7526817

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station,

TX 77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density …

2016 see 2020

onditional Wasserstein Generative Adversarial Networks

https://cameronfabbri.github.io › conditionalWGAN

https://cameronfabbri.github.io › conditionalWGANPDF

Wang, et al., “Photo-realistic single image super-resolution using a generative adversarial network,” arXiv preprint arXiv:1609.04802, 2016. [17] M. Berger, J.

11 pages

[CITATION] Conditional Wasserstein generative adversarial networks

C Fabbri - Preprint to be searched in a search engine, 2016

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

On reproduction of

[CITATION] Regularization of barycenters in the Wasserstein space

J Bigot, C Elsa, N Papadakis - 2016 - hal.archives-ouvertes.fr

… 01333397, version 1. Pré-publication, Document de travail. Regularization of barycenters in the

Wasserstein space. Jérémie Bigot 1 Cazelles Elsa Nicolas Papadakis 1 Détails. 1 IMB - Institut

de Mathématiques de Bordeaux. Jérémie Bigot 1 AuthorId : 1352913 Mail : Auteur. Cazelles …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

<——2016—————2016——- 450—

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

2016 [PDF] ijpam.eu

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups

using an generalization of the Lipschitz seminorm and a noncommutative analogue of

Wasserstein distance. We show turns out to be closely related with classical convergence …

2016

Sliced Wasserstein kernels for probability distributions

S Kolouri, Y Zou, GK Rohde - Proceedings of the IEEE Conference …, 2016 - cv-foundation.org

Optimal transport distances, otherwise known as Wasserstein distances, have recently

drawn ample attention in computer vision and machine learning as powerful discrepancy

measures for probability distributions. The recent developments on alternative formulations …

2016

2016 [PDF] researchgate.net

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

2016

Finite horizon linear quadratic Gaussian density regulator with ...

http://ieeexplore.ieee.org › document

by A Halder · 2016 · Cited by 34 — Finite horizon linear quadratic Gaussian density regulator with Wasserstein ... the two density functions, and penalize the lack of closeness as terminal cost. ... We show that the LQG control problem can be recovered as a special case of our ...

Date Added to IEEE Xplore: 01 August 2016	Date of Conference: 6-8 July 2016
DOI: 10.1109/ACC.2016.7526817

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station,

TX 77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density …

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential convergence of diffusion semigroups with respect

2016

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

2016

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station, TX

77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density Regulator …

<——2016—————2016——- 460—

2016 see 2015

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

2016

Evolution of the Wasserstein distance between the marginals ...

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

by A Alfonsi · 2016 · Cited by 8 — Abstract: In this paper, we are interested in the time derivative of the Wasserstein distance between the marginals of

two Markov processes.. arXiv

2016 [HTML] sciencedirect.com

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

2016

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station, TX

77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density Regulator …

2016

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

In this paper we extend a previous result of the author [S. Lisini, Calc. Var. Partial Differ. Eq.

28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein

spaces to a more general class of spaces: the spaces of probability measures endowed with …

Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - 2016 American Control Conference …, 2016 - ieeexplore.ieee.org

We formulate and solve an optimal control problem in which a finite dimensional linear time

invariant (LTI) control system steers a given Gaussian probability density function (PDF)

close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost …

2016

Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost

A Halder - abhishekhalder.org

Page 1. Finite Horizon LQG Density Regulator with Wasserstein Terminal Cost Abhishek Halder

Department of Electrical and Computer Engineering Texas A&M University College Station,

TX 77843 Joint work with Eric DB Wendel (Draper Laboratory) Page 2. Finite Horizon Density …

Gromov-Wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on …, 2016 - proceedings.mlr.press

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the inter-relationships between points

sampled from individual domains, are not required to have the same size or to be in row-by …

<——2016—————2016——- 470—

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

Wasserstein continuity of entropy and outer bounds for interference channels

Y Polyanskiy, Y Wu - IEEE Transactions on Information Theory, 2016 - ieeexplore.ieee.org

It is shown that under suitable regularity conditions, differential entropy is O (√ n)-Lipschitz

as a function of probability distributions on Ilin with respect to the quadratic Wasserstein

distance. Under similar conditions,(discrete) Shannon entropy is shown to be O (n)-Lipschitz …

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

2016

Wasserstein distance and the rectifiability of doubling measures: part I

J Azzam, G David, T Toro - Mathematische Annalen, 2016 - Springer

Let μ μ be a doubling measure in R^ n R n. We investigate quantitative relations between

the rectifiability of μ μ and its distance to flat measures. More precisely, for xx in the support Σ

Σ of μ μ and r> 0 r> 0, we introduce a number α (x, r) ∈ (0, 1 α (x, r)∈(0, 1 that measures, in …

Wasserstein stability of the entropy power inequality for log-concave densities

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

We establish quantitative stability results for the entropy power inequality (EPI). Specifically,

we show that if uniformly log-concave densities nearly saturate the EPI, then they must be

close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the …

2016

[PDF] Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - University of Tartu, Master Thesis, 2016 - core.ac.uk

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired. The aim of this Master thesis is to study, implement, and …

A weighted approximation approach to the study of the empirical Wasserstein distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

A Farchi, M Bocquet, Y Roustan… - Tellus B: Chemical …, 2016 - Taylor & Francis

The verification of simulations against data and the comparison of model simulation of

pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based

on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

<——2016—————2016——- 480—

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_

{n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying

stochastic process. We consider the situation of practical importance where the random …

[HTML] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - Journal of Functional Analysis, 2016 - Elsevier

Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014)[5], we show that the

L 2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient

flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of …

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the …

-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

We introduce Perelman's $ W $-entropy and prove the $ W $-entropy formula along

geodesic flow on the Wasserstein space $ P^\infty_2 (M,\mu) $ over compact Riemannian

manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we …

The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances

[PDF] Euler sprays and Wasserstein geometry of the space of shapes

JG Liu, RL Pego, D Slepcev - arXiv preprint arXiv:1604.03387, 2016 - ki-net.umd.edu

We study a distance between shapes defined by minimizing the integral of kinetic energy

along transport paths constrained to measures with characteristic-function densities. The

formal geodesic equations for this shape distance are Euler equations for incompressible …

J Zinsl - arXiv preprint arXiv:1603.01375, 2016 - arxiv.org

This article is concerned with the existence of nonnegative weak solutions to a particular

fourth-order partial differential equation: it is a formal gradient flow with respect to a

generalized Wasserstein transportation distance with nonlinear mobility. The corresponding …

[PDF] ijpam.eu

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups

using an generalization of the Lipschitz seminorm and a noncommutative analogue of

Wasserstein distance. We show turns out to be closely related with classical convergence …

Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances

A Irpino, F De Carvalho, R Verde - arXiv preprint arXiv:1605.00513, 2016 - arxiv.org

Distributional (or distribution-valued) data are a new type of data arising from several

sources and are considered as realizations of distributional variables. A new set of fuzzy c-

means algorithms for data described by distributional variables is proposed. The algorithms …

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

symmetry of the given measure. An empirical bound on this asymmetric correction term is …

<——2016—————2016——- 490—

Wasserstein approximations of the L\'evy area random walk via polynomial perturbations of Gaussian distributions

G Flint - arXiv preprint arXiv:1605.08996, 2016 - arxiv.org

We construct a coupling between the random walk composed of Lévy area increments from

a $ d $-dimensional Brownian motion and a random walk composed of quadratic

polynomials of Gaussian random variables. This coupling construction is used to produce a …

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

Y Yang, B Engquist, J Sun - SEG Technical Program Expanded …, 2016 - library.seg.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform

inversion (FWI) and prove such preperties as convexity in different aspects. Considering the

observed data and predicted data as two density functions, the quadratic Wasserstein metric …

DF) Regularization of barycenters in the Wasserstein space

https://www.researchgate.net › ... › Regularization

PDF | The concept of barycenter in the Wasserstein space allows to define a notion of ... A stability result of regularized barycenters in terms of Bregman distance associated to the ... Probability Theory and Related Fields, pages 1–17, 2016.

[CITATION] Regularization of barycenters in the Wasserstein space

J Bigot, C Elsa, N Papadakis - 2016 - hal.archives-ouvertes.fr

… 01333397, version 1. Pré-publication, Document de travail. Regularization of barycenters in the

Wasserstein space. Jérémie Bigot 1 Cazelles Elsa Nicolas Papadakis 1 Détails. 1 IMB - Institut

de Mathématiques de Bordeaux. Jérémie Bigot 1 AuthorId : 1352913 Mail : Auteur. Cazelles …

2015 see 2016

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

Using Gromov-Wasserstein distance to explore sets of networks

see 2015

https://core.ac.uk › download › pdf

PDF

by R Hendrikson · Cited by 9 — Reigo Hendrikson. Using Gromov-Wasserstein distance to explore sets of networks. Master thesis (30 EAP). Supervisor: PhD Raul Vicente Zafra. Tartu 2016 ...

48 pages

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

2016

[CITATION] Superposition of the balancing and universal gradient methods for finding an entropy-smoothed Wasserstein barycenter and equilibria in multistage traffic …

AV Gasnikov, PE Dvurechensky, VG Spokoinyi… - Tr. Mosk. Fiz.-Tekh. Inst., 2016

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

[PDF] esaim-proc.org

An augmented Lagrangian approach to Wasserstein gradient flows and applications

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

Wasserstein loss for image synthesis and restoration

G Tartavel, G Peyré, Y Gousseau - SIAM Journal on Imaging Sciences, 2016 - SIAM

This paper presents a novel variational approach to imposing statistical constraints on the

output of both image generation (typically to perform texture synthesis) and image

restoration (for instance, to achieve denoising and inpainting) methods. The empirical …

A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time spot follows a …

<——2016—————2016——- 500—

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - epfl.ch

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

[PDF] romeilsandhu.com

[PDF] Matricial Wasserstein and Unsupervised Tracking

L Ning, R Sandhu, TT Georgiou, A Tannenbaum - romeilsandhu.com

The context of this work is spectral analysis of multivariable times-series as this may arise in

processing signals originating in antenna and sensor arrays. The salient feature of these

time signals is that they contain information about moving scatterers/targets which may not …

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions

defined on the same metric space. In order to compare distributions on different metric

spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

[1607.01179v1] Robust k-barycenters in Wasserstein Space ...

2016

https://128.84.21.199 › abs

Jul 5, 2016 — ... k-barycenters in Wasserstein Space and Wide Consensus Clustering ... A robust clustering method for probabilities in Wasserstein space is ...

[CITATION] Robust k-barycenters in wasserstein space and wide consensus clustering

E del Barrio, J Cuesta-Albertos, C Matrán, A Mayo-Íscar - arXiv preprint arXiv, 2016

[PDF] CONFORMAL WASSERSTEIN DISTANCE : AN ...

[CITATION] CONFORMAL WASSERSTEIN DISTANCE: AN OVERVIEW AND ANALYSIS

A HAGERTY, Y SOLIMAN - 2016

https://www.semanticscholar.org › paper › CONFORMAL...

Three-dimensional shape analysis has been developing extremely rapidly over ... CONFORMAL WASSERSTEIN DISTANCE : AN OVERVIEW AND ANALYSIS.

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

The exponential formula for the Wasserstein metric

K Craig - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the

square Wasserstein metric. In this paper, we develop a class of transport metrics that have

better convexity properties and use these metrics to prove an Euler− Lagrange equation …

<——2016—————2016——- 510—

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh, G Poly, Y Swan - arXiv preprint arXiv:1601.03301, 2016 - arxiv.org

In the first part of the paper we use a new Fourier technique to obtain a Stein

characterizations for random variables in the second Wiener chaos. We provide the

connection between this result and similar conclusions that can be derived using Malliavin …

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

[CITATION] Penalized barycenters in the Wasserstein space. arXiv e-prints, art

J Bigot, E Cazelles, N Papadakis - arXiv preprint arXiv:1606.01025, 2016

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between

stationary measures for iterated function scheme on the unit interval. In particular, we

consider two stationary measures with different configurations of the weights associated to …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

2016

[PDF] uni-due.de

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

Inference for empirical Wasserstein distances on finite spaces

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

2016

M Sommerfeld, A Munk - arXiv preprint arXiv:1610.03287, 2016 - arxiv.org

The Wasserstein distance is an attractive tool for data analysis but statistical inference is

hindered by the lack of distributional limits. To overcome this obstacle, for probability

measures supported on finitely many points, we derive the asymptotic distribution of …

2016

A smoothed dual approach for variational Wasserstein problems

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

Cited by 122 Related articles

<——2016—————2016——- 520—

[PDF] cv-foundation.org

Sliced Wasserstein kernels for probability distributions

S Kolouri, Y Zou, GK Rohde - Proceedings of the IEEE Conference …, 2016 - cv-foundation.org

Optimal transport distances, otherwise known as Wasserstein distances, have recently

drawn ample attention in computer vision and machine learning as powerful discrepancy

measures for probability distributions. The recent developments on alternative formulations …

Discrete Wasserstein barycenters: optimal transport for discrete data

E Anderes, S Borgwardt, J Miller - Mathematical Methods of Operations …, 2016 - Springer

Wasserstein barycenters correspond to optimal solutions of transportation problems for

several marginals, and as such have a wide range of applications ranging from economics

to statistics and computer science. When the marginal probability measures are absolutely …

L^p-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential convergence of diffusion semigroups with respect

to the standard‐Wasserstein distance for all. In particular, we show that for the Itô stochastic …

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

2016

Wasserstein contraction properties for hypoelliptic diffusions

F Baudoin - arXiv preprint arXiv:1602.04177, 2016 - arxiv.org

Gradient bounds had proved to be a very efficient tool for the control of the rate of

convergence to equilibrium for parabolic evolution equations. Among the gradient bounds

methods, the celebrated Bakry-Émery criterion i

Wasserstein Discriminant Analysis

A smoothed dual approach for variational Wasserstein problems

by R Flamary · 2016 · Cited by 55 — [Submitted on 29 Aug 2016 (v1), last revised 23 May 2018 (this version, v2)] ... Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA ...

Cite as: arXiv:1608.08063

2016

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such

problems are computationally challenging because they involve minimizing over quantities …

Cited by 122 Related articles

Fast dictionary learning with a smoothed Wasserstein loss

A Rolet, M Cuturi, G Peyré - Artificial Intelligence and …, 2016 - proceedings.mlr.press

We consider in this paper the dictionary learning problem when the observations are

normalized histograms of features. This problem can be tackled using non-negative matrix

factorization approaches, using typically Euclidean or Kullback-Leibler fitting errors …

A weighted approximation approach to the study of the empirical Wasserstein distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

<——2016—————2016——- 530—

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue t

he geometric study of ${\scr {W} _2}(X) …

[PDF] buffalo.edu

Gaze-Wasserstein: a quantitative screening approach to autism spectrum disorders

KW Cho, F Lin, C Song, X Xu… - 2016 IEEE Wireless …, 2016 - ieeexplore.ieee.org

Early detection of children with autism spectrum disorder (ASD) has been of great interest to

researchers due to an increase in the rate of autism incidence around the world. However, a

diagnosis of ASD is still challenging to receive in a timely manner for the large-scale …

A distance for HMMS based on aggregated Wasserstein metric and state registration

Y Chen, J Ye, J Li - European Conference on Computer Vision, 2016 - Springer

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time spot follows a …

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

2016

The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances

J Zinsl - arXiv preprint arXiv:1603.01375, 2016 - arxiv.org

This article is concerned with the existence of nonnegative weak solutions to a particular

fourth-order partial differential equation: it is a formal gradient flow with respect to a

generalized Wasserstein transportation distance with nonlinear mobility. The corresponding …

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

J Agredo - International Journal of Pure and Applied Mathematics, 2016 - ijpam.eu

We investigate about exponential convergence for generic quantum Markov semigroups

using an generalization of the Lipschitz seminorm and a noncommutative analogue of

Wasserstein distance. We show turns out to be closely related with classical convergence …

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

Y Yang, B Engquist, J Sun - SEG Technical Program Expanded …, 2016 - library.seg.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform

inversion (FWI) and prove such preperties as convexity in different aspects. Considering the

observed data and predicted data as two density functions, the quadratic Wasserstein metric …

<——2016—————2016——- 540—

PDF] unipv.it

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

[PDF] Baricentros en el espacio de Wasserstein: aplicación a modelos estadísticos de deformación

P Gordaliza Pastor - 2016 - core.ac.uk

En el análisis de la homogeneidad de una colección de distribuciones y de relaciones

estructurales entre las observaciones, son muy útiles los baricentros y la variación en

distancia de Wasserstein. Estudiamos la estimación de los cuantiles del proceso empírico …

From Monge to Gromov-Wasserstein: Optimal transport and barycenters between several metric spaces

G Peyré - crm.umontreal.ca

Optimal transport is the de-facto standard to compare and average probability distributions

defined on the same metric space. In order to compare distributions on different metric

spaces, the Gromov-Wasserstein (GW) distance introduced by Mémoli [1](see also [2]) …

(PDF) Regularization of barycenters in the Wasserstein space

https://www.researchgate.net › ... › Regularization

PDF | The concept of barycenter in the Wasserstein space allows to define a notion of ... A stability result of regularized barycenters in terms of Bregman distance associated to the ... Probability Theory and Related Fields, pages 1–17, 2016.

[CITATION] Regularization of barycenters in the Wasserstein space

J Bigot, C Elsa, N Papadakis - 2016 - hal.archives-ouvertes.fr

… 01333397, version 1. Pré-publication, Document de travail. Regularization of barycenters in the

Wasserstein space. Jérémie Bigot 1 Cazelles Elsa Nicolas Papadakis 1 Détails. 1 IMB - Institut

de Mathématiques de Bordeaux. Jérémie Bigot 1 AuthorId : 1352913 Mail : Auteur. Cazelles …

[1607.01179v1] Robust k-barycenters in Wasserstein Space ...

https://128.84.21.199 › abs

[Submitted on 5 Jul 2016 (this version), latest version 23 Nov 2016 (v2)]. Title:Robust k-barycenters in Wasserstein Space and Wide Consensus Clustering.

[CITATION] Robust k-barycenters in wasserstein space and wide consensus clustering

E del Barrio, J Cuesta-Albertos, C Matrán, A Mayo-Íscar - arXiv preprint arXiv, 2016

[PDF] Information Geometry and its Applications IV Liblice, Czech Republic

V Kratochvíl, AV ÚTIA - 2016 - igaia.utia.cz

… 3 Felix Otto Riemannian Interpretation of the Wasserstein Geometry 4 … Morning session Hiroshi

Nagaoka Revisit to the Autoparallelity and the Canonical Divergence for Dually Flat Spaces 15 -

viii … Information Geometry and its Applications IV June 12-17, 2016 Poster sessions …

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

Application of Optimal Transport and the Quadratic ...

2016

https://arxiv.org › physics

by Yang · 2016 · Cited by 128 — [Submitted on 15 Dec 2016 (v1), last revised 10 May 2017 (this version, v2)] ... of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion ... In our previous work, we proposed the quadratic Wasserstein metric (W_2) ...

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full‐waveform inversion. arXiv preprint arXiv: 1612.05075

Y Yang, B Engquist, J Sun, BD Froese - 2016

[PDF] Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - University of Tartu, Master Thesis, 2016 - core.ac.uk

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired. The aim of this Master thesis is to study, implement, and

apply one Gromov-Wasserstein type of distance introduced by F. Mémoli (2011) in his

paper” Gromov–Wasserstein Distances and the Metric Approach to Object Matching” to

study sets of complex networks. Taking into account theoretical underpinnings introduced in …

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

by J Bigot · 2016 · Cited by 15 — Mathematics > Statistics Theory. arXiv:1606.01025 (math). [Submitted on 3 Jun 2016 (v1), last revised 18 Mar 2019 ( ...

Missing: prints, ‎art

[CITATION] Penalized barycenters in the Wasserstein space. arXiv e-prints, art

J Bigot, E Cazelles, N Papadakis - arXiv preprint arXiv:1606.01025, 2016

https://samurai.nims.go.jp › articles

2016 see 2021 book

Dissimilarity measure of local structure in inorganic crystals using Wasserstein distance to search for novel phosphors.

<——2016—————2016——- 550—

Robust Wasserstein profile inference and applications to machine learning

J Blanchet, Y Kang, K Murthy - arXiv preprint arXiv:1610.05627, 2016 - arxiv.org

We show that several machine learning estimators, including square-root LASSO (Least

Absolute Shrinkage and Selection) and regularized logistic regression can be represented

as solutions to distributionally robust optimization (DRO) problems. The associated …

An augmented Lagrangian approach to Wasserstein gradient flows and applications

[HTML] A fixed-point approach to barycenters in Wasserstein space

PC Álvarez-Esteban, E Del Barrio… - Journal of Mathematical …, 2016 - Elsevier

Let P 2, ac be the set of Borel probabilities on R d with finite second moment and absolutely

continuous with respect to Lebesgue measure. We consider the problem of finding the

barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k∈ P 2, ac with respect to …

[PDF] esaim-proc.org

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient

flows which can be attacked by an augmented Lagrangian method which we call the ALG2 …

The Wasserstein metric and robustness in risk management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

In the aftermath of the financial crisis, it was realized that the mathematical models used for

the valuation of financial instruments and the quantification of risk inherent in portfolios

consisting of these financial instruments exhibit a substantial model risk. Consequently …

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

2016

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential convergence of diffusion semigroups with respect

to the standard‐Wasserstein distance for all. In particular, we show that for the Itô stochastic …

Exponential contraction in Wasserstein distances for diffusion semigroups with negative curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted

Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a

convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a …

A weighted approximation approach to the study of the empirical Wasserstein distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

In Sect. 2 we shall describe the weighted approximation tools that we shall be using. Next, in

Sect. 3 we shall apply them to obtain rates at which $Ed_{1}\left (F_{n},F\right )$ converges to

zero. Then in Sect. 4 we shall discuss the original motivation to develop the exponential inequality …

[PDF] Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - University of Tartu, Master Thesis, 2016 - core.ac.uk

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired.

The aim of this Master thesis is to study, implement, and …

[PDF] tandfonline.com

Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

A Farchi, M Bocquet, Y Roustan… - Tellus B: Chemical …, 2016 - Taylor & Francis

The verification of simulations against data and the comparison of model simulation of

pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based

on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called …

<——2016—————2016——- 560—

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

In this paper we extend a previous result of the author [S. Lisini, Calc. Var. Partial Differ. Eq.

28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein

spaces to a more general class of spaces: the spaces of probability measures endowed with …

[PDF] buffalo.edu

Gaze-Wasserstein: a quantitative screening approach to autism spectrum disorders

KW Cho, F Lin, C Song, X Xu… - 2016 IEEE Wireless …, 2016 - ieeexplore.ieee.org

Early detection of children with autism spectrum disorder (ASD) has been of great interest to

researchers due to an increase in the rate of autism incidence around the world. However, a

diagnosis of ASD is still challenging to receive in a timely manner for the large-scale …

2016

[HTML] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - Journal of Functional Analysis, 2016 - Elsevier

Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014)[5], we show that the

L 2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient

flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of …

[PDF] The estimation of Wasserstein and Zolotarev distances to the class of exponential variables

A Baıllo, J Cárcamo, K Getman - arXiv preprint arXiv:1603.06806, 2016 - researchgate.net

Given a positive random variable X, we are interested in measuring how well the

exponential distribution with the same mean approximates the probability distribution of X,

based on the information provided by a sample from X. Specifically, we consider the …

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between

stationary measures for iterated function scheme on the unit interval. In particular, we

consider two stationary measures with different configurations of the weights associated to …

2016

Wasserstein stability of the entropy power inequality for log-concave densities

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

We establish quantitative stability results for the entropy power inequality (EPI). Specifically,

we show that if uniformly log-concave densities nearly saturate the EPI, then they must be

close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the …

<——2016—————2016——- 570—

2016

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

[PDF] CONFORMAL WASSERSTEIN DISTANCE : AN ...

https://www.semanticscholar.org › paper › CONFORMAL...

CONFORMAL WASSERSTEIN DISTANCE : AN OVERVIEW AND ANALYSIS · Adrian Hagerty, Y. Soliman · Published 2016.

[CITATION] CONFORMAL WASSERSTEIN DISTANCE: AN OVERVIEW AND ANALYSIS

A HAGERTY, Y SOLIMAN - 2016

Declaración de la Asociación de Estadística Americana Sobre ...

https://www.researchgate.net › 30577...

Declaración de la Asociación de Estadística Americana Sobre la Significancia Estadística y Los Valores-P.

June 2016; The American Statistician 70(2)

[CITATION] Declaración de la Asociación de Estadística Americana sobre la significancia estadística y los valores P (editado por Ronald L. Wasserstein)

F Laco Mazzone, M Grampa, M Goldenberg… - The American Statistician, 2016

Gromov-Wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on …, 2016 - proceedings.mlr.press

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the inter-relationships between points

sampled from individual domains, are not required to have the same size or to be in row-by …

Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

This paper is focused on the statistical analysis of probability measures $\nu_ {1},\ldots,\nu_

{n} $ on $\mathbb {R} $ that can be viewed as independent realizations of an underlying

stochastic process. We consider the situation of practical importance where the random …

2016

Subgeometric rates of convergence in Wasserstein distance for Markov chains

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - epfl.ch

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

2016

… grandes déviations: applications à des modèles issus de la combinatoire et à l'analyse de sensibilité. Bornes minimax et distance de Wasserstein en statistique semi …

T Klein - 2016 - hal.archives-ouvertes.fr

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific

research documents, whether they are pub- lished or not. The documents may come from teaching

and research institutions in France or abroad, or from public or private research centers …

year 2016

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

[PDF] Cortical Surface Classification with Hyperbolic Wasserstein Distance

J Shi, Y Wang - gsl.lab.asu.edu

The Wasserstein space consists of all probability measures that are defined on a

Riemannian manifold. The Wasserstein distance defines a Riemannian metric for the

Wasserstein space and it intrinsically measures the similarities between shapes …

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

<——2016—————2016——- 580—

2016

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

In this paper we extend a previous result of the author [S. Lisini, Calc. Var. Partial Differ. Eq.

28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein

spaces to a more general class of spaces: the spaces of probability measures endowed with …

2016

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

2016

[HTML] q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

M Kell - Journal of Functional Analysis, 2016 - Elsevier

Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014)[5], we show that the

L 2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient

flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of …

2016 see 2015, 2017

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

[PDF] romeilsandhu.com

2016

year 2016

[PDF] Matricial Wasserstein and Unsupervised Tracking

L Ning, R Sandhu, TT Georgiou, A Tannenbaum - romeilsandhu.com

The context of this work is spectral analysis of multivariable times-series as this may arise in

processing signals originating in antenna and sensor arrays. The salient feature of these

time signals is that they contain information about moving scatterers/targets which may not …

Convexity of the quadratic Wasserstein metric as a misfit function for full-waveform inversion

2016

Y Yang, B Engquist, J Sun - SEG Technical Program Expanded …, 2016 - library.seg.org

We analyze the properties of Wasserstein metric, a new mis-fit function for full waveform

inversion (FWI) and prove such preperties as convexity in different aspects. Considering the

observed data and predicted data as two density functions, the quadratic Wasserstein metric …

Gromov-Wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on …, 2016 - proceedings.mlr.press

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the inter-relationships between points

sampled from individual domains, are not required to have the same size or to be in row-by …

2016

[CITATION] Superposition of the balancing and universal gradient methods for finding an entropy-smoothed Wasserstein barycenter and equilibria in multistage traffic …

AV Gasnikov, PE Dvurechensky, VG Spokoinyi… - Tr. Mosk. Fiz.-Tekh. Inst., 2016

2-16

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between

stationary measures for iterated function scheme on the unit interval. In particular, we

consider two stationary measures with different configurations of the weights associated to …

Create alert

2009

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2009 - numdam.org

We study existence and approximation of non-negative solutions of partial differential

equations of the type∂ tu− div (A (∇(f (u))+ u∇ V))= 0 in (0,+∞)× Rn,(0.1) where A is a

symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity …

<——2016—————2016——- 590—

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

2016

Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence

RV Belavkin - Information Geometry and its Applications IV, 2016 - Springer

We discuss a relation between the Kantorovich–Wasserstein (KW) metric and the Kullback–

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

Wasserstein contraction properties for hypoelliptic diffusions

F Baudoin - arXiv preprint arXiv:1602.04177, 2016 - arxiv.org

Gradient bounds had proved to be a very efficient tool for the control of the rate of

convergence to equilibrium for parabolic evolution equations. Among the gradient bounds

methods, the celebrated Bakry-\'Emery criterion is a powerful way prove to convergence to …

[PDF] uni-due.de

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

We propose a fully discrete variational scheme for nonlinear evolution equations with

gradient flow structure on the space of finite Radon measures on an interval with respect to a

generalized version of the Wasserstein distance with nonlinear mobility. Our scheme relies …

Guarantees in wasserstein distance for the langevin monte carlo algorithm

2016

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

2016

Habilitation à Diriger des Recherches: Théorème central limite, inégalités de concentration et principes de grandes déviations: applications à des modèles issus de la …

T Klein - 2016 - hal.archives-ouvertes.fr

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific

research documents, whether they are pub- lished or not. The documents may come from teaching

and research institutions in France or abroad, or from public or private research centers …

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces

Y Chen, T Georgiou, M Pavon - arXiv preprint arXiv:1601.04891, 2016 - arxiv.org

Since the early nineties, it has been observed that the Schroedinger bridge problem can be

formulated as a stochastic control problem with atypical boundary constraints. This in turn

has a fluid dynamic counterpart where the flow of probability densities represents an …

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

Wasserstein contraction properties for hypoelliptic diffusions

2016 [PDF] psu.edu

[PDF] Dynamic clustering of histograms using Wasserstein metric

A Irpino, R Verde, Y Lechevallier - COMPSTAT, 2006 - Citeseer

In the present paper we present a new distance, based on the Wasserstein metric, in order

to cluster a set of data described by distributions with finite continue support. The proposed

distance allows to define a measure of inertia of data with respect a barycenter that satisfies …

2016 [PDF] arxiv.org

F Baudoin - arXiv preprint arXiv:1602.04177, 2016 - arxiv.org

Gradient bounds had proved to be a very efficient tool for the control of the rate of

convergence to equilibrium for parabolic evolution equations. Among the gradient bounds

methods, the celebrated Bakry-\'Emery criterion is a powerful way prove to convergence to …

<——2016—————2016——- 600—

2016

On properties of the generalized Wasserstein distance

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2016 - Springer

The Wasserstein distances W p (p\geqq≧ 1), defined in terms of a solution to the Monge–

Kantorovich problem, are known to be a useful tool to investigate transport equations. In

particular, the Benamou–Brenier formula characterizes the square of the Wasserstein …

2016 [PDF] cnrs.fr

[PDF] Wasserstein barycentric coordinates: histogram regression using optimal transport.

N Bonneel, G Peyré, M Cuturi - ACM Trans. Graph., 2016 - perso.liris.cnrs.fr

This article defines a new way to perform intuitive and geometrically faithful regressions on

histogram-valued data. It leverages the theory of optimal transport, and in particular the

definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric …

2016

(PDF) Linear models for histogram data based on Wasserstein ...

https://www.researchgate.net › publication › 303445026_...

May 23, 2016 — Linear models for histogram data. based on Wasserstein distance: scalar and functional models. Antonio Irpino - Rosanna Verde.

[PDF] Linear models for histogram data based on Wasserstein distance: scalar and functional models

AIR Verde - researchgate.net

A Modal variable is a multi-valued variable with a frequency, probability, or weight πi

associated to each of its specific values U (i). Ie, the modal variable Y is a mapping Y (i)={U

(i), πi} for i∈ Ω where πi is a nonnegative measure or a distribution on the domain Y of …

2016 [PDF] archives-ouvertes.fr

Wasserstein loss for image synthesis and restoration

G Tartavel, G Peyré, Y Gousseau - SIAM Journal on Imaging Sciences, 2016 - SIAM

This paper presents a novel variational approach to imposing statistical constraints on the

output of both image generation (typically to perform texture synthesis) and image

restoration (for instance, to achieve denoising and inpainting) methods. The empirical …

2016 [PDF] arxiv.org

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

symmetry of the given measure. An empirical bound on this asymmetric correction term is …

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

2016

2016 [PDF] arxiv.org

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

2016

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

year 2016 [PDF] unipv.it

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

1 August q2016

L ^p-Wasserstein distance, coupling by reflection, exponential Symmetric stable process contractivity, stochastic differential equation driven by Lévy ^noise,

Robust Wasserstein Profile Inference and Applications to Machine Learning

SAVE TO MY LIBRARY

2016 ARXIV: STATISTICS THEORY

Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels

2016 IEEE TRANSACTIONS ON INFORMATION THEORY

76 citations*

Yury Polyanskiy ¹,Yihong Wu ²

¹ Massachusetts Institute of Technology ,² University of Illinois at Urbana–Champaign

Differential entropy

Lipschitz continuity

View More (8+)

<——2016—————2016——- 610—

{ Euclidean, Metric, and Wasserstein } Gradient Flows: an overview

2016 ARXIV: ANALYSIS OF PDES

Fast Dictionary Learning with a Smoothed Wasserstein Loss

121 citations*

2016 INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS

Antoine Rolet ¹,Marco Cuturi ¹,Gabriel Peyré ²

¹ Kyoto University ,² CEREMADE

Guarantees in wasserstein distance for the langevin monte carlo algorithm

T Bonis - arXiv preprint arXiv:1602.02616, 2016 - arxiv.org

We study the problem of sampling from a distribution $\target $ using the Langevin Monte

Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein

distance of order $2 $. Our result holds as long as the continuous diffusion process …

2016 [PDF] buffalo.edu

Gaze-Wasserstein: A quantitative screening approach to autism spectrum disorders

KW Cho, F Lin, C Song, X Xu… - 2016 IEEE Wireless …, 2016 - ieeexplore.ieee.org

Early detection of children with autism spectrum disorder (ASD) has been of great interest to

researchers due to an increase in the rate of autism incidence around the world. However, a

diagnosis of ASD is still challenging to receive in a timely manner for the large-scale …

2016

{ Euclidean, Metric, and Wasserstein } Gradient Flows: an overview

2016 ARXIV: ANALYSIS OF PDES

From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage

93 citations* for all

89 citations*

2011 COMMUNICATIONS IN MATHEMATICAL PHYSICS

Stefan Adams ¹,Nicolas P. Dirr ²,Mark A. Peletier ³,Johannes Zimmer ⁴

¹ University of Warwick ,² Cardiff University ,³ Eindhoven University of Technology ,⁴ University of Bath

Diffusion equation

Brownian motion

View More (8+)

We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional J h characterizes the behaviour of the particle system at t = h in terms of the initial d... View Full Abstract

2016

Exponential convergence in Lp‐Wasserstein distance for diffusion processes without uniformly dissipative drift

19 citations*

2016 MATHEMATISCHE NACHRICHTEN

Dejun Luo ¹,Jian Wang ²

¹ Chinese Academy of Sciences ,² Fujian Normal University

Coupling (probability)

Constant (mathematics)

View More (8+)

By adopting the coupling by reflection and choosing an auxiliary function which is convex near infinity, we establish the exponential convergence of diffusion semigroups with respect to the standard -Wasserstein distance for all . In particular, we show that for the Ito stochastic differential equat... View Full Abstract

2016

Inference for Empirical Wasserstein Distances on Finite Spaces

11 citations*

2016 ARXIV: METHODOLOGY

Wasserstein Divergence for GANs

60 citations* for all

59 citations*

2018 EUROPEAN CONFERENCE ON COMPUTER VISION

Jiqing Wu ,Zhiwu Huang ,Janine Thoma ,Dinesh Acharya ,Luc Van Gool

ETH Zurich

Fast dictionary learning with a smoothed Wasserstein loss

View More (6+)

In many domains of computer vision, generative adversarial networks (GANs) have achieved great success, among which the family of Wasserstein GANs (WGANs) is considered to be state-of-the-art due to the theoretical contributions and competitive qualitative performance. However, it is very challengin... View Full Abstract

2016 [PDF] mlr.press

A Rolet, M Cuturi, G Peyré - Artificial Intelligence and …, 2016 - proceedings.mlr.press

We consider in this paper the dictionary learning problem when the observations are

normalized histograms of features. This problem can be tackled using non-negative matrix

factorization approaches, using typically Euclidean or Kullback-Leibler fitting errors …

2016 [PDF] arxiv.org

{Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - arXiv preprint arXiv:1609.03890, 2016 - arxiv.org

This is an expository paper on the theory of gradient flows, and in particular of those PDEs

which can be interpreted as gradient flows for the Wasserstein metric on the space of

probability measures (a distance induced by optimal transport). The starting point is the …

2016 [PDF] core.ac.uk

[PDF] Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - University of Tartu, Master Thesis, 2016 - core.ac.uk

In many fields such as social sciences or biology, relations between data or variables are

presented as networks. To compare these networks, a meaningful notion of distance

between networks is highly desired. The aim of this Master thesis is to study, implement, and …

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

2016 see 2017 [PDF] arxiv.org

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

<——2016—————2016——- 620—

2016 [PDF] arxiv.org

On Parallel Transport in Wasserstein Space

XS Shen - arXiv preprint arXiv:1604.03504, 2016 - arxiv.org

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

On Parallel Transport in Wasserstein Space

X Sisi Shen - arXiv e-prints, 2016 - ui.adsabs.harvard.edu

In this short note, we would like to give a construction of parallel transport for tangent cones

lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the

linear part of the tangent space, and show that a construction for the full tangent cones …

2016 [PDF] semanticscholar.org

[PDF] A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

MV Lekgari - Bulletin of Mathematical Sciences and …, 2016 - pdfs.semanticscholar.org

We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and

show that the finiteness of the expectation E (i, j)[∑ τΔ− 1 k= 0 r (k)], where τΔ is the hitting

time on the coupling set Δ and r is a subgeometric rate function, is equivalent to a sequence …

2016

[CITATION] On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological Optimization and Optimal Transport. Radon …

M Laborde - Appl. Math, 2016

2016

[CITATION] CONFORMAL WASSERSTEIN DISTANCE: AN OVERVIEW AND ANALYSIS

A HAGERTY, Y SOLIMAN - 2016

2016

[CITATION] Using Gromov-Wasserstein distance to, explore sets of networks., University of Tartu

R Hendrikson - 2016 - Master Thesis,,, 2016., 2

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

Cited by 22 All 8 versions

[CITATION] CONFORMAL WASSERSTEIN DISTANCE: AN OVERVIEW AND ANALYSIS

A HAGERTY, Y SOLIMAN - 2016

2016

2016 [PDF] projecteuclid.org

A Durmus, G Fort, É Moulines - Annales de l'Institut Henri Poincaré …, 2016 - projecteuclid.org

In this paper, we provide sufficient conditions for the existence of the invariant distribution

and for subgeometric rates of convergence in Wasserstein distance for general state-space

Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 …

2016

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

10 citations*

2016 ARXIV: OPTIMIZATION AND CONTROL

View Less

Grani A. Hanasusanto ¹,Daniel Kuhn ²

¹ University of Texas at Austin ,² École Polytechnique Fédérale de Lausanne

Linear programming

Robust optimization

View More (8+)

Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust and distributionally robust linear programs... View Full Abstract

Hausdorff and Wasserstein metrics on graphs and other structured data

5 citations* for all

1 citatio Linear programming

ns*

2020 INFORMATION AND INFERENCE: A JOURNAL OF THE IMA

View More (8+)

Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to the matching of graphs and other structured data. This struc... View Full Abstract

2016 see 2017

Wasserstein distance and the rectifiability of doubling measures: part I

17 citations*

2016 MATHEMATISCHE ANNALEN

Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

43 citations* for all

43 citations*

2018 INFORMATION GEOMETRY

Shun-ichi Amari ¹,Ryo Karakida ²,Masafumi Oizumi ¹

¹ RIKEN Brain Science Institute ,² National Institute of Advanced Industrial Science and Technology

Simplex

Kullback–Leibler divergence

View More (8+)

Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is based on the Wasserstein distance of optimal transportation... View Full Abstract

2016 [PDF] arxiv.org

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

B Jourdain, J Reygner - Journal of Hyperbolic Differential Equations, 2016 - World Scientific

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension,

with cumulative distribution functions or, more generally, nonconstant monotonic bounded

functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic …

year 2016

Geometric construction of Wasserstein Barycenters

N Bonneel, J Digne - perso.liris.cnrs.fr

Optimal Transport theory consists in finding a map T pushing forward an input measure µ to

a target measure ν, which minimizes a “transport cost”. This cost often consists in the sum of

the squared distances travelled by all particles during their motion. Formally, the Monge …

<——2016—————2016——- 630—

2016 [PDF] arxiv.org

A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

BR Kloeckner - International Mathematics Research Notices, 2016 - ieeexplore.ieee.org

Given a metric space $ X $, one defines its Wasserstein space ${\scr {W} _2}(X) $ as a set of

sufficiently decaying probability measures on $ X $ endowed with a metric defined from

optimal transportation. In this article, we continue the geometric study of ${\scr {W} _2}(X) …

2016 [PDF] buffalo.edu

Gaze-Wasserstein: A quantitative screening approach to autism spectrum disorders

KW Cho, F Lin, C Song, X Xu… - 2016 IEEE Wireless …, 2016 - ieeexplore.ieee.org

2016 IEEE Wireless Health (WH)

Wasserstein approximations of the L\'evy area random walk via polynomial perturbations of Gaussian distributions

G Flint - arXiv preprint arXiv:1605.08996, 2016 - arxiv.org

We construct a coupling between the random walk composed of L\'evy area increments from

a $ d $-dimensional Brownian motion and a random walk composed of quadratic

polynomials of Gaussian random variables. This coupling construction is used to produce a …

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

2016 [PDF] arxiv.org

I Cipriano - arXiv preprint arXiv:1611.00092, 2016 - arxiv.org

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between

stationary measures for iterated function scheme on the unit interval. In particular, we

consider two stationary measures with different configurations of the weights associated to …

2016

Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein: Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - oatd.org

Depuis l'article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu'une

large classe d'équations paraboliques peuvent être vues comme des flots de gradient dans …

2016

2016 [PDF] archives-ouvertes.fr

Interacting particles systems, Wasserstein gradient flow approach

M Laborde - 2016 - tel.archives-ouvertes.fr

Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a

large class of parabolic equations can be seen as gradient flows in the Wasserstein space …

2016

Wasserstein loss for image synthesis and restoration

G Tartavel, G Peyré, Y Gousseau - SIAM Journal on Imaging Sciences, 2016 - SIAM

This paper presents a novel variational approach to imposing statistical constraints on the

output of both image generation (typically to perform texture synthesis) and image …

2016 see 2015

A smoothed dual approach for variational Wasserstein problems

M Cuturi, G Peyré - SIAM Journal on Imaging Sciences, 2016 - SIAM

Variational problems that involve Wasserstein distances have been recently proposed to

summarize and learn from probability measures. Despite being conceptually simple, such …

Cited by 145 Related articles

2016 [PDF] esaim-proc.org

An augmented Lagrangian approach to Wasserstein gradient flows and applications

JD Benamou, G Carlier, M Laborde - ESAIM: Proceedings and …, 2016 - esaim-proc.org

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we

propose a convex formulation for each step of the JKO scheme for Wasserstein gradient …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

M Briani, E Cristiani, E Iacomini - arXiv preprint arXiv:1608.00126, 2016 - arxiv.org

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the …

<——2016—————2016——- 640—

Distributionally robust stochastic optimization with Wasserstein distance

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016 - arxiv.org

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under

uncertainty in which, instead of assuming that there is an underlying probability distribution

that is known exactly, one hedges against a chosen set of distributions. In this paper, we …

Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

symmetry of the given measure. An empirical bound on this asymmetric correction term is …

Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

2016 [PDF] arxiv.org

D Loibl, D Matthes, J Zinsl - Potential Analysis, 2016 - Springer

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth

order partial differential equations on a convex bounded domain in arbitrary spatial

dimensions. Our proof relies on the formal gradient flow structure of the equation with …

2016 [PDF] uni-due.de

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

2016

A Simulated Annealing Based Inexact Oracle for Wasserstein ...

https://arxiv.org › pdfPDF

by J Ye · 2016 · Cited by 4 — We will call such problems Wasserstein loss minimization. (WLM). Examples of WLMs include ... rithm corrigenda for this article is available here. ACM.

2016

Distributionally robust stochastic optimization with Wasserstein distance

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016 - arxiv.org

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is an underlying probability distribution that is known exactly, one hedges against a chosen set of distributions. In this paper, we …

[CITATION] Distributionally robust stochastic optimization with wasserstein distance. arXiv e-prints, page

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance. arXiv. org

[CITATION] Distributionally Robust Stochastic Optimization with Wasserstein Distance

G Rui, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016

-Wasserstein distance for stochastic differential equations driven by Lévy processes

[CITATION] Distributionally robust stochastic optimization with Wasserstein distance

AJ Kleywegt, R Gao - arXiv preprint arXiv:1604.02199, 2016

2016 [PDF] projecteuclid.org

J Wang - Bernoulli, 2016 - projecteuclid.org

Coupling by reflection mixed with synchronous coupling is constructed for a class of stochastic differential equations (SDEs) driven by Lévy noises. As an application, we establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ge0} $ with …

[1610.05627] Robust Wasserstein Profile Inference and ... - arXiv

by J Blanchet · 2016 · Cited by 198 — Abstract: We show that several machine learning estimators, including square-root LASSO (Least Absolute Shrinkage and Selection) and ...

Journal reference: Journal of Applied Probabili...

Cite as: arXiv:1610.05627

[CITATION] Robust wasserstein profile inference and applications to machine learning. arXiv e-prints, page

J Blanchet, Y Kang, K Murthy - arXiv preprint arXiv:1610.05627, 2016

https://www.researchgate.net › publication › 225752681_...

2016 see 2009Euler–Poisson Systems as Action-Minimizing Paths in the ...

Feb 7, 2016 — PDF | This paper uses a variational approach to establish existence of solutions (σ t , v t ) for the 1-d Euler–Poisson system by minimizing ...

[CITATION] Euler-Poisson systems as action-minimizing paths in the Wasserstein space. to appear in Arch

W Gangbo, T Nguyen, A Tudorascu - Rational Mech. Anal

Exponential convergence in‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

By adopting the coupling by reflection and choosing an auxiliary function which is convex

near infinity, we establish the exponential convergence of diffusion semigroups with respect

to the standard‐Wasserstein distance for all. In particular, we show that for the Itô stochastic …

<——2016—————2016——- 650—

Blog, Podcast, or Website Full Text

Wasserstein's "Sisters Rosensweig" coasts on comedy at Theater J (Posted 2016-01-19 21:58:07): The 1990s play is revived with a surfeit of style.
Pressley, Nelson.The Washington Post (Online), Washington, D.C.: WP Company LLC d/b/a The Washington Post. 2016.

Details Full text

2016 thesis

Using Gromov-Wasserstein distance to explore sets of networks

https://core.ac.uk › download › pdfPDF

by R Hendrikson · Cited by 10 — The present work focuses on Gromov-Wasserstein (GW) distance which allows to compare objects presented as metric measure spaces. Current work is built on the ...

48 pages

[CITATION] Using Gromov–Wasserstein distance to explore sets of networks (Doctoral dissertation)

R Hendrikson - 2016

Wasserstein stability of the entropy power inequality for log-concave densities

2016 [PDF] arxiv.org

TA Courtade, M Fathi, A Pananjady - arXiv preprint arXiv:1610.07969, 2016 - arxiv.org

… for the entropy … Wasserstein distance. Further, if one of the densities is log-concave

and the other is Gaussian, then the deficit in the EPI can be controlled in terms of the L1-Wasserstein …

2016 Computer Program,
Subgeometric rates of convergence in Wasserstein distance for Markov chainsAuthors:Durmus, Alain (Creator), Fort, Gersende (Creator), Moulines, Éric (Creator)
Summary:In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-space Markov chains which are (possibly) not irreducible. Compared to (Ann. Appl. Probab. 24 (2) (2014) 526–552), our approach is based on a purely probabilistic coupling construction which allows to retrieve rates of convergence matching those previously reported for convergence in total variation in (Bernoulli 13 (3) (2007) 831–848). ¶ Our results are applied to establish the subgeometric ergodicity in Wasserstein distance of non-linear autoregressive models and of the pre-conditioned Crank–Nicolson Markov chain Monte Carlo algorithm in Hilbert spaceShow more
Computer Program, 2016-11
English
Publisher:Institut Henri Poincaré, 2016-11

Семинары: А. В. Гасников, Лекция 5 (часть 1). Алгебра над ...

www.mathnet.ru › present13489

The Wasserstein Metric a.k.a Earth Mover's Distance: A Quick and Convenient Introduction

Примеры приложения (поиск равновесия в многостадийной модели транспортных потоков, поиск барицентра Вассерштейна).

Math-Net.Ru · Optimization and Statistics ·

Mar 26, 2016

2016

The Wasserstein Metric a.k.a Earth Mover's Distance - YouTube

A Distance for HMMs Based on Aggregated Wasserstein and State Registration

Here are two papers that describe this in more detail:Y. Lavin, R. Kumar Batra, and L. Hesselink. Feature Comparisons of Vector Fields Using ...

YouTube · Bob Laramee ·

Jul 29, 2016

Oct 13, 2016

A Non-Commutative Analog of the Metric for which the... Gradient Flow for the Entropy - Eric Carlen Published on Aug 17, 2016

Eric Carlen
Rutgers, The State University of New Jersey
November 13, 2012
The Fermionic Fokker-Planck equation is a quantum-mechanical analog of the classical Fokker-Planck equation with which it has much in common, such as the same optimal hypercontractivity properties. In this paper we construct a Riemannian metric on the space of density matrices that we show to be a natural analog of the classical 22-Wasserstein metric, and we show that, in analogy with the classical case, the Fermionic Fokker-Planck equation is gradient flow in this metric for the relative entropy with respect to the ground state. We derive a number of consequences of this, such as a sharp Talagrand inequality for this metric, and we prove a number of results pertaining to this metric. Several open problems are raised. This is joint work with Jann Maas.

Similarity Function - YouTube

Feb 23, 2015 - Uploaded by Udacity

The Wasserstein Metric a.k.a Earth Mover's Distance: A Quick and ... Regularized Wasserstein Distances ...

Peer-reviewed
$L^{p}$-Wasserstein distance for stochastic differential equations driven by L??vy processes

Author:Jian Wang
Summary:Coupling by reflection mixed with synchronous coupling is constructed for a class of stochastic differential equations (SDEs) driven by L??vy noises. As an application, we establish the exponential contractivity of the associated semigroups $(P_{t})_{t\ge0}$ with respect to the standard $L^{p}$-Wasserstein distance for all $p\in[1,\infty)$. In particular, consider the following SDE:??\[\mathrm{d}X_{t}=\mathrm{d}Z_{t}+b(X_{t})\,\mathrm{d}t,\] where $(Z_{t})_{t\ge0}$ is a symmetric $\alpha$-stable process on $\mathbb{R}^{d}$ with $\alpha\in(1,2)$. We show that if the drift term $b$ satisfies that for any $x,y\in\mathbb{R}^{d}$,??\[\langle b(x)-b(y),x-y\rangle\le\cases{K_{1}|x-y|^{2},\quad\phantom{-} |x-y|\le L_{0};\cr-K_{2}|x-y|^{\theta},\quad |x-y|>L_{0}}\] holds with some positive constants $K_{1}$, $K_{2}$, $L_{0}>0$ and $\theta\ge2$, then there is a constant $\lambda:=\lambda(\theta,K_{1},K_{2},L_{0})>0$ such that for all $p\in[1,\infty)$, $t>0$ and $x,y\in\mathbb{R}^{d}$,??\[W_{p}(\delta_{x}P_{t},\delta_{y}P_{t})\le C(p,\theta,K_{1},K_{2},L_{0})\mathrm{e}^{-\lambda t/p}[\frac{|x-y|^{1/p}\vee|x-y|}{1+|x-y|{\mathbf{1}}_{(1,\infty)\times(2,\infty)}(t,\theta)}].\]Show more
Downloadable Article
Publication:Bernoulli, 22, 2016-08, 1598

$ L^{p} $-Wasserstein distance for stochastic differential equations driven by Lévy processes

J Wang - Bernoulli, 2016 - projecteuclid.org

Abstract Coupling by reflection mixed with synchronous coupling is constructed for a class of

stochastic differential equations (SDEs) driven by Lévy noises. As an application, we

establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ ge0} $ ...

<——2016—————2016——- 660—

Peer-reviewed
Exponential convergence in Lp-Wasserstein distance for diffusion processes without uniformly dissipative drift

Authors:Dejun Luo, Jian Wang
Summary:By adopting the coupling by reflection and choosing an auxiliary function which is convex near infinity, we establish the exponential convergence of diffusion semigroups (Pt)t≥0 with respect to the standard Lp-Wasserstein distance for all p∈[1,∞). In particular, we show that for the Itô stochastic differential equationdXt=dBt+b(Xt)dt,if the drift term b is such that for any x,y∈Rd,⟨b(x)−b(y),x−y⟩≤K1|x−y|2,|x−y|≤L;−K2|x−y|2,|x−y|>Lholds with some positive constants K₁, K₂ and L>0, then there is a constant λ:=λ(K1,K2,L)>0 such that for all p∈[1,∞), t>0 and x,y∈Rd,Wp(δxPt,δyPt)≤Ce−λt/p|x−y|1/p,if|x−y|≤1;|x−y|,if|x−y|>1where C:=C(K1,K2,L,p) is a positive constant. This improves the main result in where the exponential convergence is only proved for the L¹-Wasserstein distanceShow more
Article, 2016
Publication:Mathematische Nachrichten, 289, October 2016, 1909
Publisher:2016

Peer-reviewed
q-Heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

Author:Martin Kell
Summary:Based on the idea of a recent paper by Ambrosio-Gigli-Savaré (2014) , we show that the L 2 -gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of the q-heat flow is presented including a condition for its mass preservation. Under a convexity assumption on the upper gradient, which holds for all q ≥ 2 , one gets uniqueness of the gradient flow and the two flows can be identified. Smooth solutions of the q-heat flow are solutions to the parabolic q-Laplace equation, i.e. ∂ t f t = Δ q f tShow more
Article, 2016
Publication:Journal of Functional Analysis, 271, 20161015, 2045
Publisher:2016

2016 see 2014 Peer-reviewed
Wasserstein distance and the rectifiability of doubling measures: part I

Authors:Jonas Azzam, Guy David, Tatiana Toro
Summary:Let μ be a doubling measure in R n . We investigate quantitative relations between the rectifiability of μ and its distance to flat measures. More precisely, for x in the support Σ of μ and r > 0 , we introduce a number α ( x , r ) ∈ ( 0 , 1 ] that measures, in terms of a variant of the L 1 -Wasserstein distance, the minimal distance between the restriction of μ to B ( x , r ) and a multiple of the Lebesgue measure on an affine subspace that meets B ( x , r / 2 ) . We show that the set of points of Σ where ∫ 0 1 α ( x , r ) d r r < ∞ can be decomposed into rectifiable pieces of various dimensions. We obtain additional control on the pieces and the size of μ when we assume that some Carleson measure estimates hold. Soit μ une mesure doublante dans R n . On étudie des relations quantifiées entre la rectifiabilité de μ et la distance entre μ et les mesures plates. Plus précisément, on utilise une variante de la L 1 -distance de Wasserstein pour définir, pour x dans le support Σ de μ et r > 0 , un nombre α ( x , r ) qui mesure la distance minimale entre la restriction de μ à B ( x , r ) et une mesure de Lebesgue sur un sous-espace affine passant par B ( x , r / 2 ) . On décompose l’ensemble des points x ∈ Σ tels que ∫ 0 1 α ( x , r ) d r r < ∞ en parties rectifiables de dimensions diverses, et on obtient un meilleur contrôle de ces parties et de la taille de μ quand les α ( x , r ) vérifient certaines conditions de CarlesonShow more
Article, 2016
Publication:Mathematische Annalen, 364, 201602, 151
Publisher:2016

Peer-reviewed
Absolutely continuous curves in extended Wasserstein−Orlicz spaces

Author:Stefano Lisini
Summary:In this paper we extend a previous result of the

Author [S. Lisini, Calc. Var. Partial Differ. Eq. 28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein spaces to a more general class of spaces: the spaces of probability measures endowed with the Wasserstein−Orlicz distance constructed on extended Polish spaces (in general non separable), recently considered in [L. Ambrosio, N. Gigli and G. Savaré, Invent. Math. 195 (2014) 289–391.] An application to the geodesics of this Wasserstein−Orlicz space is also givenShow more
Article, 2016
Publication:ESAIM: Control, Optimisation and Calculus of Variations, 22, 201607, 670
Publisher:2016

2016 see 2014 Peer-reviewed
Absolutely continuous curves in extended Wasserstein-Orlicz spaces

Author:Lisini S.
Article, 2016
Publication:ESAIM - Control, Optimisation and Calculus of Variations, 266, 2016 04 28
Publisher:2016

2016

2016 see 2015
An augmented Lagrangian approach to Wasserstein gradient flows and applications

Authors:Jean-David Benamou, Guillaume Carlier, Maxime Laborde
Summary:Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we propose a convex formulation for each step of the JKO scheme for Wasserstein gradient flows which can be attacked by an augmented Lagrangian method which we call the ALG2-JKO scheme. We test the algorithm in particular on the porous medium equation. We also consider a semi implicit variant which enables us to treat nonlocal interactions as well as systems of interacting species. Regarding systems, we can also use the ALG2-JKO scheme for the simulation of crowd motion models with several speciesShow more
Article, 2016
Publication:ESAIM: Proceedings and Surveys, 54, 201606, 1
Publisher:2016

2016 see 2015 Peer-reviewed
The law of iterated logarithm for subordinated Gaussian sequences: Uniform Wasserstein bounds

Authors:Azmoodeh E., Peccati G., Poly G.
Article, 2016
Publication:Alea (Rio de Janeiro), 13, 2016, 659
Publisher:2016

Peer-reviewed
Wasserstein barycentric coordinates histogram regression using optimal transport

Authors:Nicolas Bonneel (

Author), Gabriel Peyré (

Author), Marco Cuturi (

Author)
Summary:This article defines a new way to perform intuitive and geometrically faithful regressions on histogram-valued data. It leverages the theory of optimal transport, and in particular the definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric coordinates for histograms. These coordinates take into account the underlying geometry of the ground space on which the histograms are defined, and are thus particularly meaningful for applications in graphics to shapes, color or material modification. Beside this abstract construction, we propose a fast numerical optimization scheme to solve this backward problem (finding the barycentric coordinates of a given histogram) with a low computational overhead with respect to the forward problem (computing the barycenter). This scheme relies on a backward algorithmic differentiation of the Sinkhorn algorithm which is used to optimize the entropic regularization of Wasserstein barycenters. We showcase an illustrative set of applications of these Wasserstein coordinates to various problems in computer graphics: shape approximation, BRDF acquisition and color editingShow more
Article, 2016
Publication:ACM Transactions on Graphics (TOG), 35, 20160711, 1
Publisher:2016

2016 see 2917 Peer-reviewed
On tangent cones in Wasserstein space

Author:John Lott
Article, 2016
Publication:Proceedings of the American Mathematical Society, 145, 20161208, 3127
Publisher:2016

2016 see 2014 Peer-reviewed
q-Heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

Author:Martin Kell
Article, 2016
Publication:Journal of functional analysis, 271, 2016, 2045
Publisher:2016

<——2016—————2016——- 670—

Convexity of the quadratic Wasserstein metric as a misfit function for full waveform inversion

Authors:Yang Y., Engquist B., Sun J., SEG International Exposition and 86th Annual Meeting, SEG 2016
Article, 2016
Publication:SEG Technical Program Expanded Abstracts, 35, 2016, 1385
Publisher:2016

3D shape matching based on gromov-wasserstein distance

Authors:Zhang J., Jiao Y., Luo Z.
Article, 2016
Publication:Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics, 28, 2016 11 01, 2027
Publisher:2016

2016 see 2913
Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula (Potential Theory and its Related Fields)

Author:KUWADA, Kazumasa (Creator)
Downloadable Archival Material, 2016-03-11T05:42:43Z
English
Publisher:京都大学数理解析研究所 Research Institute for Mathematical Sciences, Kyoto University, 2016-03-11T05:42:43Z

2016 see 2015 Peer-reviewed
Existence and consistency of Wasserstein barycenters

Authors:Thibaut Le Gouic, Jean-Michel Loubes, SpringerLink (Online service)
Downloadable Article, 2016
English
Publication:Probability theory and related fields.
Publisher:2016

2016 see 2017 2018

Markov Type constants, flat tori and Wasserstein spaces - arXiv

Absolutely continuous curves in extended Wasserstein− Orlicz spaces

by V Zolotov · 2016 · Cited by 1 — As an application of (a) we show that all compact flat manifolds have Markov type 2 with constant 1. In particular the circle with its intrinsic ...

Of a metric space: X, where p \ge 1. We show t...

2016

2016. [PDF] unipv.it

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - mate.unipv.it

… steepest descent type algorithm generated by a variational problem associated with the

Wasserstein … The convergence of the steepest descent algorithms reveals that the dynamic of the …

2016. [PDF] esaim-cocv.org

S Lisini - ESAIM: Control, Optimisation and Calculus of …, 2016 - esaim-cocv.org

… in the first one we consider a socalled extended Polish space (X, τ, d) … Wasserstein

distance induced by an increasing convex function ψ : [0, +∞) → [0, +∞] instead of the p-Wasserstein …

<——2016—————2016——- 677— end 2016

Includes 5 titles with Vaserstein

start 2017 Wasserstein

see my name in title from Math Reviews

Construction of Non-asymptotic Confidence Sets in 2-Wasserstein space arXiv

by J Ebert - ‎2017 - ‎Cited by 3 - ‎Related articles Spokoiny

Mar 10, 2017 - Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et al. (2014)). The main focus lies ...

MR3737719 Karakida, Ryo (J-NAISTKO); Amari, Shun-ichi (J-IPCR-BSI)

Information geometry of Wasserstein divergence. (English summary) Geometric science of information, 119–126,

Lecture Notes in Comput. Sci., 10589, Springer, Cham, 2017.

94A17

Series Chapter

Information Geometry of Wasserstein Divergence

R Karakida, S Amari - International Conference on Geometric Science of …, 2017 - Springer

There are two geometrical structures in a manifold of probability distributions. One is

invariant, based on the Fisher information, and the other is based on the Wasserstein

distance of optimal transportation. We propose a unified framework which connects the …

A Comparison between Wasserstein Distance and a Distance Induced by Fisher-Rao Metric in Complex Shapes Clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

A Stochastic gradient method to compute Wasserstein barycenters of distributions

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1]

基于 Wasserstein 距离和分裂 Bregman 方法的图像分割算法

王瑜，闫沫 - 电子设计工程, 2017 - cqvip.com

针对基于CV 模型的活动轮廓分割算法无法应用于灰度非均匀图像分割的问题.

采用Wasserstein 距离作为区域直方图相似性测度, 提出基于该测度的非参数活动轮廓分割模型.

在模型求解时引入全局凸分割和分裂Bregman 方法, 减少了计算量. 大量实验结果表明该模型不

[Chinese Image segmentation algorithm based on Wasserstein distance and split Bregman method]

[PDF] 基于 Wasserstein 距离概率分布模型的非线性降维

曹小鹿，辛云宏 - 计算机应用, 2017 - joca.cn

摘要: 降维是大数据分析和可视化领域中的核心问题, 其中基于概率分布模型的的降维算法通过

最优化高维数据模型和低维数据模型之间的代价函数来实现降维. 这种策略的核心在于构建最能

体现数据特征的概率分布模型. 基于此, 本文将Wasserstein 距离引入降维, 提出一个基于

基于 LBP 特征和熵正则化 Wasserstein 距离的人脸表情识别

[Chinese Nonlinear dimensionality reduction based on Wasserstein distance probability distribution model

郑昌金，章登义，苏科华，武小平，洪程 - 计算机与数字工程, 2017 - cqvip.com

针对K 最近邻分类中相似度量的量化问题, 结合最优传输理论中Wasserstein 距离数学特性,

提出一种基于LBP 特征和熵正则化Wasserstein 距离的K 近邻分类方法. 首先对人脸表情图像

进行预处理, 然后使用LBP 算子对图像进行特征提取获得LBP 特征直方图, 最后使用熵正则化的

[HTML] Vers un théorème de la limite centrale dans l'espace de Wasserstein?

[Chinese Facial expression recognition based on LBP features and entropy regularized Wasserstein distance]

M Agueh, G Carlier - Comptes Rendus Mathematique, 2017 - Elsevier

Résumé Les barycentres dans l'espace de Wasserstein constituent une manière naturelle

d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines

appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons

Related articles All 3 versions
[French Towards a central limit theorem in Wasserstein space? ]

——————————————2017———————2017 -10

——————

On a Wasserstein-type distance between solutions to stochastic differential equations

J Bion-Nadal, D Talay - 2017 - hal.inria.fr

In this paper we introduce a Wasserstein-type distance on the set of the probability

distributions of strong solutions to stochastic differential equations. This new distance is

defined by restricting the set of possible coupling measures. We prove that it may also be

CONTRACTIVE BARYCENTRIC MAPS

[PDF] u-bordeaux.fr

[PDF] Barycentres dans l'espace de Wasserstein

G CARLIER, I Journées - math.u-bordeaux.fr

Page 1. 1 Barycentres dans l'espace de Wasserstein Guillaume CARLIER a Journées IOPS -

Image, Optimisation, Probabilités et Statistique Réserve ornithologique du Teich, 5-8 Juillet 2017.

aCEREMADE, Université Paris Dauphine et MOKAPLAN, Inria-Paris /1 Page 2. Plan 2 Plan ➀

By: Lawson, Jimmie D.; Lim, Yongdo

JOURNAL OF OPERATOR THEORY Volume: 77 Issue: 1 Pages: 87-107 Published: WIN 2017

Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods

By: Fedeli, L.; Pandolfi, A.; Ortiz, M.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Volume: 112 Issue: 9 Pages: 1175-1193 Published: NOV 30 2017

Framework Planning of Active Distribution Network Considering Active Management

By: Gao, Peng; Chen, Hongkun; Zheng, Xu; et al.

JOURNAL OF ENGINEERING-JOE Published: NOV 16 2017

From optimal transportation to optimal teleportation

By: Wolansky, G.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE Volume: 34 Issue: 7 Pages: 1669-1685 Published: DEC 2017

Convergence order of upwind type schemes for transport equations with discontinuous coefficients

By: Delarue, Francois; Lagoutiere, Frederic; Vauchelet, Nicolas

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES Volume: 108 Issue: 6 Pages: 918-951 Published: DEC 2017

MR3717960 Lott, John An intrinsic parallel transport in Wasserstein space. Proc. Amer. Math. Soc. 145 (2017), no. 12, 5329–5340. (Reviewer: Martin Kell) 58B20 (51K10 58J99)

Journal Article

AN INTRINSIC PARALLEL TRANSPORT IN WASSERSTEIN SPACE

By: Lott, John

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume: 145 Issue: 12 Pages: 5329-5340 Published: DEC 2017

al Curves in Wasserstein Space - ResearchGate

Nov 27, 2017 - solution ﬂows of OMT, SBP and NSM may all be seen as extremal curves in. Wasserstein space of a suitable action. The actions only diﬀer by ...

The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation

Abstract: We introduce a new technique, which we call the boundary method, for solving the

semi-discrete optimal transport problem, a special, but quite general, type of optimal

transportation. We provide mathematical justification, convergence analysis, algorithmic

The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation

<——2017———————2017 ——20—

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017 - arxiv.org

On the Wasserstein distance between mutually singular measures HAL

We study the Wasserstein distance between two measures µ, ν which are mutually singular.

In particular, we are interested in minimization problems of the form W (µ, A)= inf W (µ, ν): ν∈

A where µ is a given probability and A is contained in the class µ⊥ of probabilities that are

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G

All 7 versions [PDF] arxiv.org

Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber, CP Robert - arXiv preprint arXiv …, 2017 - arxiv.org

Abstract: In purely generative models, one can simulate data given parameters but not

necessarily evaluate the likelihood. We use Wasserstein distances between empirical

distributions of observed data and empirical distributions of synthetic data drawn from such

All 4 versions [PDF] u-bordeaux.fr

2017

Low dose CT image denoising using a generative adversarial network with wasserstein distance and perceptual loss

Abstract: In this paper, we introduce a new CT image denoising method based on the

generative adversarial network (GAN) with Wasserstein distance and perceptual similarity.

The Wasserstein distance is a key concept of the optimal transform theory, and promises to

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

Sinkhorn-AutoDiff: Tractable Wasserstein Learning of Generative Models

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

… In this article, we advocate for a different approach, which is to consider generic optimal transport

(OT) metrics which can be used over general spaces X (not just the Euclidean space Rd and

not only the 1-Wasserstein distance). The OT metric between two probability …

A Genevay, G Peyré, M Cuturi - arXiv preprint arXiv:1706.00292, 2017 - arxiv.org

The ability to compare two degenerate probability distributions (ie two probability

distributions supported on two distinct low-dimensional manifolds living in a much higher-

dimensional space) is a crucial problem arising in the estimation of generative models for …

[CITATION] Sinkhorn-autodiff: Tractable wasserstein learning of generative models

A Genevay, G Peyré, M Cuturi - arXiv preprint arXiv:1706.00292, 2017

Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - Advances in Neural Information Processing …, 2017 - papers.nips.cc

Abstract We introduce a novel framework for statistical analysis of populations of non-

degenerate Gaussian processes (GPs), which are natural representations of uncertain

curves. This allows inherent variation or uncertainty in function-valued data to be properly

2017

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BD Froese - Geophysics, 2017 - library.seg.org 2017

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function

is known to suffer from cycle-skipping issues which increases the risk of computing a local

rather than the global minimum of the misfit. The quadratic Wasserstein metric has been

On reproduction of On the regularization of Wasserstein GANs

J Seo, T Jeon - arXiv preprint arXiv:1712.05882, 2017 - arxiv.org

… Optimizing the Wasserstein-2 distance are out of our reproduction scope.… for Wasserstein

distance an

In intrinsic parallel transport in Wasserstein space

J Lott - arXiv preprint arXiv:1701.02297, 2017 - arxiv.org

Abstract: If M is a smooth compact connected Riemannian manifold, let P (M) denote the

Wasserstein space of probability measures on M. We describe a geometric construction of

parallel transport of some tangent cones along geodesics in P (M). We show that when

An intrinsic parallel transport in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact connected Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. We describe a geometric construction

of parallel transport of some tangent cones along geodesics in $ P (M) $. We show that

when everything is smooth, the geometric parallel transport agrees with earlier formal

calculations.

<——2017———————2017 -30—

Regularized Barycenters in the Wasserstein Space

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

Abstract This paper is an overview of results that have been obtain in 2 on the convex

regularization of Wasserstein barycenters for random measures supported on\mathbb R^ d.

We discuss the existence and uniqueness of such barycenters for a large class of

Regularized Barycenters in the Wasserstein Space

MR3637959 Lott, John On tangent cones in Wasserstein space. Proc. Amer. Math. Soc. 145 (2017), no. 7, 3127–3136. (Reviewer: Baris Coskunuzer) 49Q20 (51K99 53C23)

Journal Article 3 Citations

On tangent cones in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

Abstract: If $ M $ is a smooth compact Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. If $ S $ is an embedded submanifold of

$ M $, and $\mu $ is an absolutely continuous measure on $ S $, then we compute the

MR3682182 Kang, Kyungkeun; Kim, Hwa Kil Existence of weak solutions in Wasserstein space for a chemotaxis model coupled to fluid equations. SIAM J. Math. Anal. 49 (2017), no. 4, 2965–3004. 92B05 (35K55 35Q35 35Q84)

Journal Article

Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to Fluid Equations

K Kang, HK Kim - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider a coupled system of Keller--Segel-type equations and the incompressible

Navier--Stokes equations in spatial dimension two and three. We first establish the existence

of a weak solution of a Fokker--Plank equation in the Wasserstein space under the

HYPERSPECTRAL AND MULTISPECTRAL WASSERSTEIN BARYCENTER FOR IMAGE FUSION

J Mifdal, B Coll, N Courty, J Froment… - IGARSS …, 2017 - hal.archives-ouvertes.fr

… Index Terms— Image Fusion, Optimal Transport, Wasser- stein Barycenter 1. INTRODUCTION …

This regularization is carried out by penalizing the entropy of the joint coupling φ … Convolutional

wasserstein distances: Efficient optimal transportation on geometric do- mains …

Dynamic models of wasserstein-1-type unbalanced transport

Authors:Schmitzer B., Wirth B.
Article, 2017
Publication:arXiv, 2017 05 12
Publisher:2017

An elementary proof for the structure of Wasserstein derivatives

Authors:Wu C., Zhang J.
Article, 2017
Publication:arXiv, 2017 05 22
Publisher:2017

arXiv:1712.06446 [pdf, other]

A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

Clément Cancès, Daniel Matthes, Flore Nabet

Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)Investigators from University of Lille Have Reported New Data on Mechanical Engineering

(A Two-phase Two-fluxes Degenerate Cahn-hilliard Model As Constrained Wasserstein...

Journal of Engineering, 08/2019

NewsletterFull Text Online

Engineering - Mechanical Engineering; Investigators from University of Lille Have Reported New Data on Mechanical Engineering (A Two-phase Two-fluxes Degenerate Cahn-hilliard Model As Constrained Wasserstein...

Journal of Engineering, Aug 5, 2019, 1257

Newspaper ArticleFull Text Online

A two-phase two-fluxes degenerate cahn-hilliard model as constrained wasserstein gradient flow

arXiv:1712.06050 [pdf, other]

Wasserstein Distributional Robustness and Regularization in Statistical Learning

Rui Gao, Xi Chen, Anton J. Kleywegt

Subjects: Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)

A central question in statistical learning is to design algorithms that not only perform well on training data, but also generalize to new and unseen data. In...

arXiv:1712.05882 [pdf, other]

On reproduction of On the regularization of Wasserstein GANs

Junghoon Seo, Taegyun Jeon

Comments: 9 pages, 9 figures, ICLR 2018 reproducibility challenge

Subjects: Learning (cs.LG); Machine Learning (stat.ML)

Wasserstein Generative Adversarial Networks

[edit]Martin Arjovsky, Soumith Chintala, Léon Bottou ;

Proceedings of the 34th International Conference on Machine Learning, PMLR 70:214-223, 2017.

Abstract We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide

meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep

connections to different distances between distributions.

Wasserstein Distributional Robustness and Regularization in Statistical Learning

by R Gao Xi Chen Anton J. Kleywegt 2017

arXiv:1712.06050 [cs.LG]

<——2017————————2017 ————40—

MR3733412 Agredo, J.; Fagnola, F. On quantum versions of the classical Wasserstein distance. Stochastics 89 (2017), no. 6-7, 910–922. (Reviewer: Horacio Grinberg) 81S20 (49Q20)

Journal Article

On quantum versions of the classical Wasserstein distance

by J Agredo - ‎2017 - ‎Related articles

Stochastics An International Journal of Probability and Stochastic Processes

Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015

Dec 22, 2016 - We investigate a definition of quantum Wasserstein distance of two states based on their couplings on the product algebra as in the classical case. A detailed analysis of the two qubit model leads to a formal definition fulfilling some minimal requirements. It also shows that a clear-cut definition, by direct ...

Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric spie

by D Cheng - ‎2017

It is known in the standard l² distance that the closest Parseval frame to a given frame {Φi}^mi=1 ⊂ ℜ ^d is {S^-1/2(Φi)}^mi=1 where S is the frame operator of the original frame. We show this is also the case for probabilistic frames in the 2-Wasserstein distance. In the process we develop some regularity properties for the map ...

By: Cheng, Desai; Okoudjou, Kasso A.

Edited by: Lu, YM; VanDeVille, D; Papadakis, M

Conference: Conference on Wavelets and Sparsity XVII Location: San Diego, CA Date: AUG 06-09, 2017

Sponsor(s): SPIE

WAVELETS AND SPARSITY XVII Book Series: Proceedings of SPIE Volume: 10394 Article Number: 103940N Published: 2017

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning arXiv

MA Schmitz, M Heitz, N Bonneel, FMN Mboula… - arXiv preprint arXiv …, 2017

Abstract: This article introduces a new non-linear dictionary learning method for histograms

in the probability simplex. The method leverages optimal transport theory, in the sense that

our aim is to reconstruct histograms using so called displacement interpolations (aka

MR3590527 Prelim Kim, Young-Heon; Pass, Brendan; Wasserstein barycenters over Riemannian manifolds. Adv. Math. 307 (2017), 640–683.

Wasserstein barycenters over Riemannian manifolds - ScienceDirect

YH Kim, B Pass -

Volume 307, 5 February 2017, Pages 640-683. Advances in Mathematics. Wasserstein barycenters over Riemannian manifolds☆.

This paper is dedicated to the fond memory of our colleague and friend Martial Agueh, one of the originators of the theory of Wasserstein barycenters. Author links open overlay ...

Abstract We study barycenters in the space of probability measures on a Riemannian

manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we

establish absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on

MR3729384 Al Reda, F.; Maury, B. Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance. Topological optimization and optimal transport, 400–416, Radon Ser. Comput. Appl. Math., 17, De Gruyter, Berlin, 2017. 60J60 (35K08 35Q84 60B10 60J27 65M08 94C15)

Series Chapter

Zbl 06817170 Al Reda, F.; Maury, B.

Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance. (English)

Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 978-3-11-043926-7/hbk; 978-3-11-043041-7/ebook). Radon Series on Computational and Applied Mathematics 17, 400-416 (2017).

MSC: 60J60 94C15 35K05 35K08 65N08 60J27 60J28

Wasserstein blue noise sampling ACM

by Qin, Hongxing; Chen, Yi; He, Jinlong; More...

ACM Transactions on Graphics (TOG), 10/2017, Volume 36, Issue 5 07/2017, Volume 36, Issue 4

In this article, we present a multi-class blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density...

Journal Article: Full Text Online

Wasserstein Blue Noise Sampling - slides.games-cn.org

non convex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions: NONCONVEX GRADIENT FLOW IN THE WASSERSTEIN METRIC

by Craig, Katy

Proceedings of the London Mathematical Society, 01/2017

MR3653077 Craig, Katy Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions. Proc. Lond. Math. Soc. (3) 114 (2017), no. 1, 60–102. (Reviewer: Christopher P. Grant) 35Q82 (35A15 35B30 35K55 35Q92 47J25)

Journal Article 3 Citations

Nonconvex gradient flow in the Wasserstein metric and applications to ...

by K Craig - ‎2017 - ‎Cited by 8 - ‎Related articles

Jan 10, 2017 - Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more generally, semiconvex) energies has led to advances in several areas of partial differential equations and analysis. In this work, we extend the well-posedness theory for Wasserstein gradient flows to energies that are ...

A Wasserstein gradient flow approach to Poisson−Nernst−Planck equations

by D Kinderlehrer - ‎2017 - ‎Cited by 4 - ‎Related articles

Abstract. The Poisson−Nernst−Planck system of equations used to model ionic transport is inter- preted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global ...

Wasserstein gr

[PDF] arxiv.org

Face Super-Resolution Through Wasserstein Gadient flow approach to Poisson−Nernst−Planck equations

by Kinderlehrer, David; Monsaingeon, Léonard; Xu, Xiang

ESAIM: Control, Optimisation and Calculus of Variations, 01/2017, Volume 23, Issue 1

Journal Article: Full Text Online

The quasineutral limit of the Vlasov–Poisson equation in Wasserstein metric pdf

by Han-Kwan, Daniel; Iacobelli, Mikaela

Communications in Mathematical Sciences, 2017, Volume 15, Issue 2

MR3671564 Azzam, Jonas; David, Guy; Toro, Tatiana Wasserstein distance and the rectifiability of doubling measures: part II. Math. Z. 286 (2017), no. 3-4, 861–891. 28A75 (28A12)

Journal Article 1 Citation

Wasserstein distance and the rectifiability of doubling measures: part II

by Azzam, Jonas; David, Guy; Toro, Tatiana

Mathematische Zeitschrift, 08/2017, Volume 286, Issue 3

We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $$L^1$$
<——2017———————2017 ——— -50—

MR3647070 Li, Xinpeng; Lin, Yiqing Generalized Wasserstein distance and weak convergence of sublinear expectations. J. Theoret. Probab. 30 (2017), no. 2, 581–593. (Reviewer: Hong Zhang) 60A10 (60B10)

Journal Article

Generalized Wasserstein Distance and Weak Convergence of Sublinear Expectations

by Li, Xinpeng; Lin, Yiqing

Journal of Theoretical Probability, 10/2015, Volume 30, Issue 2

In this paper, we define the generalized Wasserstein distance for sets of Borel probability measures and demonstrate that weak convergence of sublinear...

Perturbation theory for Markov chains via Wasserstein distance arXiv

by Rudolf, Daniel; Schweizer, Nikolaus

Bernoulli, 03/2017

Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in...

MR3624887 Dedecker, Jérôme; Merlevède, Florence Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary

α-dependent sequences. Bernoulli 23 (2017), no. 3, 2083–2127. (Reviewer: Xinxin Jiang) 60B10 (60F05 60F17 60G10)

Journal Article 1 Citation

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences

by Dedecker, Jérôme; Merlevède, Florence

BERNOULLI Volume: 23 Issue: 3 Pages: 2083-2127 Published: AUG 2017

We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary α-dependent sequences. We prove

Wasserstein GAN arXiv

by Arjovsky, Martin; Chintala, Soumith; Bottou, Léon 01/2017

Abstract: We introduce a new algorithm named WGAN, an alternative to traditional GAN

training. In this new model, we show that we can improve the stability of learning, get rid of

problems like mode collapse, and provide meaningful learning curves useful for debugging

All 7 versions [PDF] springer.com

arXiv:1701.07875 (stat)

Submission history

From: Martin Arjovsky [view email]

[v1] Thu, 26 Jan 2017 21:10:29 UTC (8,090 KB)

[v2] Thu, 9 Mar 2017 23:12:26 UTC (8,042 KB)

[v3] Wed, 6 Dec 2017 20:01:54 UTC (8,042 KB)

Wasserstein gan

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017 - arxiv.org

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In

this new model, we show that we can improve the stability of learning, get rid of problems

like mode collapse, and provide meaningful learning curves useful for debugging and …

Cited by 5830 Related articles All 10 versions

Order-Preserving Wasserstein Distance for Sequence Matching IEEE

by Su, Bing; Hua, Gang Page(s):2906 - 2914

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017

We present a new distance measure between sequences that can tackle local temporal distortion and periodic sequences with arbitrary starting points. Through...

Order-Preserving Wasserstein Distance for Sequence Matching

2017 [PDF] archives-ouvertes.fr

Hyperspectral and multispectral Wasserstein barycenter for image fusion

J Mifdal, B Coll, N Courty, J Froment… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

The fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows

the extraction of relevant information from the fused image. Fusion consists of the

combination of the spectral information of the hypespectral image (h) and the spatial …

MR3621265 Legendre, Guillaume; Turinici, Gabriel Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces. C. R. Math. Acad. Sci. Paris 355 (2017), no. 3, 345–353. 65M99

Journal Article 2 Citations

Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces HAL

by Legendre, Guillaume; Turinici, Gabriel

Comptes Rendus Mathematique, 02/2017, Volume 355, Issue 3

Abstract The time discretization of gradient flows in metric spaces uses variants of the

celebrated implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in

this Note a different approach, which allows us to construct two second-order in time

MR3608466 Ramdas, Aaditya; García Trillos, Nicolás; Cuturi, Marco On Wasserstein two-sample testing and related families of nonparametric tests. Entropy 19 (2017), no. 2, Paper No. 47, 15 pp. (Reviewer: Marco Marozzi) 62G10

Journal Article 1 Citation

On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests arXiv

by Ramdas, Aaditya; Trillos, Nicolás; Cuturi, Marco

Entropy, 01/2017, Volume 19, Issue 2

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without...

The Steeest Descent Algorithm in Wasserstein Metric for the Sandpile Model of Self-Organized Criticality SIAM

by Barbu, Viorel

SIAM Journal on Control and Optimization, 01/2017, Volume 55, Issue 1

Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

by Mohajerin Esfahani, P; Kuhn, Daniel

Mathematical Programming, 2017

Abstract. We consider stochastic programs where the distribution of the uncertain

parameters is only observable through a finite training dataset. Using the Wasserstein

metric, we construct a ball in the space of (multivariate and non-discrete) probability

Data-driven distributionally robust optimization using the Wasserstein ...

https://link.springer.com/article/10.1007/s10107-017-1172-1

Jul 7, 2017 ... In this paper we study distributionally robust optimization problems with a Wasserstein ambiguity set centered at the uniform distribution ...
<——2017————2017 —————— -60—

Wasserstein Introspective Neural Networks arXiv

by Lee, Kwonjoon; Xu, Weijian; Fan, Fan; More... 11/2017

We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant...

Wasserstein introspective neural networks

Matricial Wasserstein-1 Distance

Authors:Yongxin Chen, Tryphon T. Georgiou, Lipeng Ning, Allen Tannenbaum
Article, 2017
Publication:IEEE control systems letters, 1, 2017, 14
Publisher:2017

Wasserstein Identity Testing - arXiv

by Deng, Shichuan; Li, Wenzheng; Wu, Xuan 10/2017

Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing...

Journal Article: Full Text Online

Journal of Machine Learning Research 1 (2017) 1-48

asserstein identity testing

Learning Wasserstein Embeddings arXiv

by Courty, Nicolas; Flamary, Rémi; Ducoffe, Mélanie 10/2017

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing...

Learning wasserstein embeddings

Parallel Streaming Wasserstein Barycenters

by Staib, Matthew; Claici, Sebastian; Solomon, Justin; More... 05/2017

Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These...

Parallel streaming wasserstein barycenters

Nuit Blanche: Wasserstein GAN - implementation -

Feb 7, 2017 - My name is Igor Carron ... Here is an implementation of it that I found on GitXiv, the most awesomest website on the interweb: https://github.com/martinarjovsky/WassersteinGAN. ... It's a problem when the critic fails to be close to optimum, and hence it's error stops being a good Wasserstein estimate. Known ...

Nuit Blanche: Improved Training of Wasserstein GANs - implementation -

Apr 4, 2017 - Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes significant progress toward stable training of GANs, but can still generate low-quality samples or fail to converge in some settings. We find ...

by Igor Carron Nuit Blanche, 04/2017

Thanks Alex for the heads-up ! We propose an alternative method for enforcing the Lipschitz constraint: instead of clipping weights, penalize the norm of the...

Cited by 4216 Related articles All 10 versions

Nuit Blanche: Wasserstein GAN / Towards Principled Methods for ...

Jan 30, 2017 - We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore ...

Bayes and maximum likelihood for L1-Wasserstein deconvolution of Laplace mixtures

Author:Scricciolo C.
Article, 2017
Publication:arXiv, 2017 08 17
Publisher:2017

Improved training of wasserstein gans

I Gulrajani, F Ahmed, M Arjovsky… - Advances in neural …, 2017 - proceedings.neurips.cc

Abstract Generative Adversarial Networks (GANs) are powerful generative models, but suffer

from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress

toward stable training of GANs, but sometimes can still generate only poor samples or fail to

converge. We find that these problems are often due to the use of weight clipping in WGAN

to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We

propose an alternative to clipping weights: penalize the norm of gradient of the critic with …

Save Cite Cited by 6883 Related articles All 12 versions

[CITATION] Aaron Courville. Improved Training of Wasserstein GANs

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin - Computer Science: Machine Learning, 2017

Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction

<--—2017—————2017—-70—

基于Wasserstein距离概率分布模型的非线性降维 [Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction]

by 曹小鹿辛云宏

计算机应用, 2017, Volume 37, Issue 10 Chinese

X CAO, Y XIN - Journal of Computer Applications, 2017 - en.cnki.com.cn

… In this paper,Wasserstein distance was introduced to dimensionality reduction,and a

novel method named Wasserstein Embedded Map( W-map) was presented for high-dimensional

data reduction and visualization. W-map converts dimensionality reduction problem into …

Visual Feature Attribution using Wasserstein GANs arXiv

by Baumgartner, Christian F; Koch, Lisa M; Tezcan, Kerem Can; More... 11/2017

Attributing the pixels of an input image to a certain category is an important and well-studied problem in computer vision, with applications ranging from...
Visual Feature Attribution using Wasserstein GANs

paperswithcode.com › paper › review

Visual Feature Attribution using Wasserstein GANs. Attributing the pixels of an input image to a certain ... Train, Test, Validation, Total. Num. Imag.

Papers With Code · Ross Tayl

Correcting Nuisance Variation using Wasserstein Distance arXiv

by Tabak, Gil; Fan, Minjie; Yang, Samuel J; More... 11/2017

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One...

2017

On the regularization of Wasserstein GANs

by Petzka, Henning; Fischer, Asja; Lukovnicov, Denis 09/2017

Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data....

Dimension-free Wasserstein contraction of nonlinear filters

arxiv.org › math

Aug 4, 2017 - Contraction estimates are obtained from an h-process representation of ... Cite as: arXiv:1708.01582 [math.ST]. (or arXiv:1708.01582v4 [math.

by N Whiteley - ‎2017 - ‎Cited by 1 - ‎Related articles

Dimension-free Wasserstein contraction of nonlinear filters

Sliced Wasserstein Kernel for Persistence Diagrams arXiv

by Carrière, Mathieu; Cuturi, Marco; Oudot, Steve 06/2017 arXiv

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of...

sliced Wasserstein estimation of mixtures r-b;oggers

by Christian P. Robert

Xi'an's Og, 11/2017

A paper by Soheil Kolouri and co-authors was arXived last week about using Wasserstein distance for inference on multivariate Gaussian mixtures. The basic...

sliced Wasserstein estimation of mixtures | Xi'an's Og

Relaxed Wasserstein with Applications to GANs nuit-blanche

May 26, 2017 - Generative Adversarial Networks (GANs) provide a versatile class of models for generative modeling. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Wasserstein distance rather than Jensen-Shannon

Relaxed Wasserstein with Applications to GANs arXiv

by X Guo - ‎2017 - ‎Cited by 4 - ‎Related articles

May 19, 2017 - In comparison to the existing literature in GANs, which are ad-hoc in the choices of cost functions, this new conceptual framework not only provides great flexibility in designing general cost functions, e.g., for applications to GANs, but also allows different cost functions implemented and compared under a ...

Relaxed Wasserstein with Applications to GANs - Semantic Scholar

We propose a novel class of statistical divergences called Relaxed Wasserstein (RW) divergence. RW divergence generalizes Wasserstein distance and is parametrized by strictly convex, differentiable functions. We establish for RW several key probabilistic properties, which are critical for the success of Wasserstein ...

Xin Guo, Johnny Hong, Tianyi Lin, Nan Yang

Relaxed Wasserstein with Applications to GANs - ResearchGate

https://www.researchgate.net/.../317062321_Relaxed_Wasserstein_with_Applications_to...

Request (PDF) | Relaxed Wasserstein... | Generative Adversarial Networks (GANs) provide a versatile class of models for generative modeling. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Wasserstein distance rather than ...

Xin Guo

Face Super-Resolution Through Wasserstein GANs arXiv

by Z Chen - ‎2017 - ‎Cited by 1 - ‎Related articles

May 6, 2017 - Face Super-Resolution Through Wasserstein GANs. Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide range of problems. Despite its great potential, GANs are difficult to train.

by Chen, Zhimin; Tong, Yuguang 05/2017

Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide...

Strongly Polynomial 2-Approximations of Discrete Wasserstein Barycenters arXiv

by S Borgwardt - ‎2017 - ‎Related articles

Apr 18, 2017 - We discuss approximation algorithms that trade a small error for a significant reduction in computational effort. ... After a finite number of iterations, it terminates with a 2-approximation that retains the favorable properties of a barycenter, namely a sparse support and no mass split at the

Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals. These arise in applications from economics to...

<——2017——————2017 ———— -80—

A canonical barycenter via Wasserstein regularization arXiv

by Kim, Young-Heon; Pass, Brendan 03/2017 MR

We introduce a weak notion of barycenter of a probability measure \mu on a metric measure space (X, d, {\bf m}), with the metric d and reference measure {\bf...
A canonical barycenter via Wasserstein regularization

Extremal flows on Wasserstein space arXiv

by Conforti, Giovanni; Pavon, Michele 12/2017

We develop an intrinsic geometric approach to calculus of variations on Wasserstein space. We show that the flows associated to the Schroedinger bridge with...

Inference in generative models using the Wasserstein distance arXiv

by Christian P. Robert Xi'an's Og, 01/2017

Today, Pierre Jacob posted on arXiv a paper of ours on the use of the Wasserstein distance in statistical inference, which main focus is exploiting this...

Nuit Blanche: Wasserstein Training of Restricted Boltzmann Machines nuit-blanche.

Feb 1, 2017 - We propose in this work a novel approach for Boltzmann machine training which assumes that a meaningful metric between observations is given. This metric can be represented by the Wasserstein distance between distributions, for which we derive a gradient with respect to the model

基于LBP特征和熵正则化Wasserstein距离的人脸表情识别

[Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance]

by 郑昌金章登义苏科华武小平洪程

计算机与数字工程, 2017, Volume 45, Issue 2 Chinese

A bound on the 2-Wasserstein distance between linear combinations of independent random variables

Authors:Arras B., Azmoodeh E., Poly G., Swan Y.
Article, 2017
Publication:arXiv, 2017 04 05
Publisher:2017

Manifold-valued Image Generation with Wasserstein Adversarial Networks arXiv

by Huang, Zhiwu; Wu, Jiqing; Van Gool, Luc 12/2017

Unsupervised image generation has recently received an increasing amount of attention thanks to the great success of generative adversarial networks (GANs),...

The Pontryagin Maximum Principle in the Wasserstein Space arXiv

by Bonnet, Benoît; Rossi, Francesco 11/2017

We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation...

All 33 versions [PDF] kyoto-u.ac.jp

The pontryagin maximum principle in the wasserstein space

Sliced Wasserstein Distance for Learning Gaussian Mixture Models grabdAI

Sliced Wasserstein Distance for Learning Gaussian Mixture Models arXiv

by Kolouri, Soheil; Rohde, Gustavo K; Hoffmann, Heiko 11/2017

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is...

Journal Article: Full Text Online

Sliced wasserstein distance for learning gaussian mixture models

Aggregated Wasserstein Metric and State Registration for Hidden Markov Models arXiv

by Chen, Yukun; Ye, Jianbo; Li, Jia 11/2017

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional...

Aggregated wasserstein metric and state registration for hidden markov models

<——2017———————2017 —————— -90—

Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

by Zhang, Ning; Yan, Junchi; Zhou, Yuchen 11/2017

Separating audio mixtures into individual tracks has been a long standing challenging task. We introduce a novel unsupervised audio source separation approach...

Abstract: Separating audio mixtures into individual instrument tracks has been a long

standing challenging task. We introduce a novel unsupervised audio source separation

approach based on deep adversarial learning. Specifically, our loss function adopts the

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

Learning to solve inverse problems using Wasserstein loss (PDF

by Adler, Jonas; Ringh, Axel; Öktem, Ozan; More... 10/2017

We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed...

The quadratic Wasserstein metric for earthquake location arXiv

by J Chen - ‎2017

Oct 28, 2017 - The quadratic Wasserstein metric for earthquake location. In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric was successfully introduced to the full waveform inversion.

The quadratic wasserstein metric for earthquake location

APPROXIMATION OF STABLE LAW IN WASSERSTEIN-1 DISTANCE BY STEIN’S METHOD

Author:Lihu X.U.
Article, 2017
Publication:arXiv, 2017 09 04
Publisher:2017

Cadlag stability and approximation of reversible coalescing-fragmentating Wasserstein dynamics arXiv

by Konarovskyi, Vitalii 11/2017

We construct coalescing-fragmentating Wasserstein dynamics [arXiv:1709.02839] for any initial condition and interacting potential by a finite particle...

Learning to solve inverse problems using Wasserstein loss arXiv

by Adler, Jonas; Ringh, Axel; Öktem, Ozan; More...10/2017

We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed...

The quadratic Wasserstein metric for earthquake location arXiv

by Chen, Jing; Chen, Yifan; Wu, Hao; More... 10/2017

In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric was successfully introduced to the full waveform inversion. We apply this method to...

Construction of Non-asymptotic Confidence Sets in 2 -Wasserstein Space

Authors:Ebert J., Spokoiny V., Suvorikova A.
Article, 2017
Publication:arXiv, 2017 03 10
Publisher:2017

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting arXiv

by Grimm, Christopher; Song, Yuhang; Littman, Michael L 09/2017

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely...

Journal Article: Full Text Online

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting arXiv

by Grimm, Christopher; Song, Yuhang; Littman, Michael L

09/2017 Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely...

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting

Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line arXiv

by Konarovskyi, Vitalii; von Renesse, Max 09/2017

We introduce a family of reversib

le fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on th

<——2017———————2017 —— -100—

Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line arXiv

by Konarovskyi, Vitalii; von Renesse, Max 09/2017

We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the...

Wasserstein CNN: Learning Invariant Features for NIR-VIS Face Recognition arXiv

by He, Ran; Wu, Xiang; Sun, Zhenan; More... 08/2017

Heterogeneous face recognition (HFR) aims to match facial images acquired from different sensing modalities with mission-critical applications in forensics,...

Wasserstein CNN: Learning invariant features for NIR-VIS face recognition

Wasserstein Distance Guided Representation Learning for Domain Adaptation arXiv

by Shen, Jian; Qu, Yanru; Zhang, Weinan; More... 07/2017

Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a...

Outlier Detection Using Distributionally Robust Optimization under the Wasserstein Metric arXiv

by Chen, Ruidi; Paschalidis, Ioannis Ch 06/2017

he Cramer Distance as a Solution to Biased Wasserstein ...The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence,...

We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability...

May 30, 2017

The Cramer Distance as a Solution to Biased Wasserstein Gradients arXiv

by Bellemare, Marc G; Danihelka, Ivo; Dabney, Will; More... 05/2017

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly...

… the Cramér distance is not a metric proper. However, its square root is, and is a member of the

lp family of metrics lp(P, Q) := (∫ FP (x) − FQ(x)|pdx )1/p . The lp and Wasserstein metrics are

identical at p = 1, but are otherwise distinct. Like the Wasser- stein metrics, the lp …

Convergence of the Population Dynamics algorithm in the Wasserstein metric arXiv

by Olvera-Cravioto, Mariana 05/2017

We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates...

Convergence of the Population Dynamics algorithm in the Wasserstein metric

Minimax Statistical Learning and Domain Adaptation with Wasserstein Distances arXiv

by Lee, Jaeho; Raginsky, Maxim 05/2017

As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set...

Ambiguity set and learning via Bregman and Wasserstein arXiv

by Guo, Xin; Hong, Johnny; Yang, Nan 05/2017

Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing...

Wasserstein loss arXiv

by Xiao, Shuai; Farajtabar, Mehrdad; Ye, Xiaojing; More... Cited by 3 - 05/2017

Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a...

Optimal Ballistic Transport and Hopf-Lax Formulae on Wasserstein Space arXiv

by Ghoussoub, Nassif 05/2017

Abstract: We investigate the optimal mass transport problem associated to the following"

ballistic" cost functional on phase space $ M\times M^* $, b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt;\gamma\in C^ 1 ([0, T), M);\gamma

Optimal Ballistic Transport and Hopf-Lax Formulae on Wasserstein Space
<——2017———————2017 ————110—

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

Inference in generative models using the Wasserstein distance arXiv

by Bernton, Espen; Jacob, Pierre E; Gerber, Mathieu; More... 01/2017

A growing range of generative statistical models are such the numerical evaluation of their likelihood functions is intractable. Approximate Bayesian...

Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein's method I arXiv

by Gaunt, Robert E 11/2017

The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions....

Wasserstein and Kolmogorov error bounds for variance ...

Nov 20, 2017 - We apply this theory to obtain Wasserstein or Kolmogorov error bounds for SVG approximation in four settings: comparison of VG and SVG ...

A partial Laplacian as an infinitesimal generator on the Wasserstein space ResearchGate

A partial Laplacian as an infinitesimal generator on the Wasserstein space arXiv

by Chow, Yat Tin; Gangbo, Wilfrid

10/2017 We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion...

arXiv:1710.10536v1

A partial Laplacian as an infinitesimal generator on the Wasserstein space

A Central Limit Theorem for Wasserstein type distances between two different laws arXiv

by Berthet, Philippe; Fort, Jean-Claude; Klein, Thierry 10/2017

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions F and G on \mathbb Cited by 9 Related articles All 5 versions
A central limit theorem for wasserstein type distances between two different laws

2017

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds arXiv

by Li, Songzi; Li, Xiang-Dong 10/2017

Abstract: In this survey paper, we give an overview of our recent works on the study of the $

W $-entropy for the heat equation associated with the Witten Laplacian on super-Ricci flows

and the Langevin deformation on Wasserstein space over Riemannian manifolds. Inspired

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

Wasserstein and total variation distance between marginals of L\'evy processes arXiv

by Mariucci, Ester; Reiß, Markus 10/2017

We present upper bounds for the Wasserstein distance of order p between the marginals of L\'evy processes, including Gaussian approximations for jumps of...

Journal Article: Full Text Online

Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment arXiv

by Hühnerbein, Ruben; Savarino, Fabrizio; Åström, Freddie; More... 10/2017 MR

We introduce a novel approach to Maximum A Posteriori inference based on discrete graphical models. By utilizing local Wasserstein distances for co

Accelerated Discrete Distribution Clustering under Wasserstein Distance arXive 2017

J Ye, P Wu, JZ Wang, J Li - arXiv preprint arXiv:1510.00012, 2015 - arxiv.org

Abstract: In a variety of research areas, the bag of weighted vectors and the histogram are

widely used descriptors for complex objects. Both can be expressed as discrete

distributions. D2-clustering pursues the minimum total within-cluster variation for a set of ...

Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem arXiv

Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem ResearchGate

by Amari, Shun-ichi; Karakida, Ryo; Oizumi, Masafumi 09/2017

Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is...

Journal Article: Full Text Online

Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem

S Amari, R Karakida, M Oizumi - arXiv preprint arXiv:1709.10219, 2017 - arxiv.org

Two geometrical structures have been extensively studied for a manifold of probability

distributions. One is based on the Fisher information metric, which is invariant under

reversible transformations of random variables, while the other is based on the Wasser

Information geometry connecting wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed

Log-PCA versus Geodesic PCA of histograms in the Wasserstein space arXiv

by Cazelles, Elsa; Seguy, Vivien; Bigot, Jérémie; More... 08/2017

This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation...

Journal Article: Full Text Online

Log-PCA versus geodesic PCA of histograms in the wasserstein space

MR3715379 Mora, Maria Giovanna; Peletier, Mark A.; Scardia, Lucia Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement. SIAM J. Math. Anal. 49 (2017), no. 5, 4149–4205. (Reviewer: Marc Oliver Rieger) 49J45 (70G75 74C05 94A08)

Journal Article 3 Citations

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement arXiv

by Mora, Maria Giovanna; Peletier, Mark; Scardia, Lucia 08/2017

We consider systems of n parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled...

Wasserstein stability of the entropy power inequality for log-concave random vectors IEEE

by Thomas A. Courtade; Max Fathi; Ashwin Pananjady

The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings, 01/2017

Conference Title: 2017 IEEE International Symposium on Information Theory (ISIT) Conference Start Date: 2017, June 25 Conference End Date: 2017, June 30...

Conference Proceeding: Citation Online

<——2017————2017 —120—

Enhancing diffusion MRI measures by integrating grey and white matter morphometry with hyperbolic wasserstein distance IEEE

by Wen Zhang; Jie Shi; Jun Yu; More...

The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings, 01/2017

Conference Title: 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017) Conference Start Date: 2017, April 18 Conference End Date:

Conference Proceeding:

By: Zhang, Wen; Shi, Jie; Yu, Jun; et al.

Book Group Author(s): IEEE

Conference: IEEE 14th International Symposium on Biomedical Imaging (ISBI) - From Nano to Macro Location: Melbourne, AUSTRALIA Date: APR 18-21,

Sponsor(s): IEEE; EMB; IEEE Signal Proc Soc

2017 IEEE 14TH INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING (ISBI 2017) Pages: 520-524 Published: 2017

MR3729381 Laborde, Maxime On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. Topological optimization and optimal transport, 304–332, Radon Ser. Comput. Appl. Math., 17, De Gruyter, Berlin, 2017. 35K45 (35K59 49J40)

Series Chapter 2 Citations

Zbl 06817167 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. (English) Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 978-3-11-043926-7/hbk; 978-3-11-043041-7/ebook). Radon Series on Computational and Applied Mathematics 17, 304-332 (2017).

Topological Optimization and Optimal Transport, 2017

Book Chapter: All 3 versions [PDF] ams.org

12. On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

Reports from University of British Columbia Highlight Recent Findings in Mathematics (Wasserstein barycenters over Riemannian manifolds)

Journal of Technology & Science, 10/2017

Newsletter: Full Text Online

Findings on Mathematics Discussed by Investigators at University of Edinburgh (Wasserstein distance and the rectifiability of doubling measures: part II)

Journal of Technology & Science, 08/2017

Newsletter: Full Text Online

Mathematics; Findings on Mathematics Discussed by Investigators at University of Edinburgh (Wasserstein distance and the rectifiability of doubling measures: part II)

Journal of Technology & Science, Aug 27, 2017, 140

Newspaper Article: Full Text Online

Wasserstein distance and the rectifiability of doubling measures

by J Azzam - ‎2017 - ‎Cited by 2 - ‎Related articles

Nov 8, 2016 - Wasserstein distance and the rectifiability of doubling measures: part II. Authors; Authors and affiliations. Jonas Azzam Email author; Guy David

Investigators at Tohoku University Discuss Findings in Algebra (Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices)

Journal of Technology & Science, 11/2017

Newsletter: Full Text Online

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices, and consider the problem of differentiability of the corresponding Cartan barycentric trajectory. As a consequence we have a version of Lie–Trotter formula and a related unitarily invariant norm inequality. Furthermore, a fixed point theorem related to the Karcher equation and the Cartan barycentric trajectory is also presented as an application.

New Algorithms Study Findings Have Been Reported from Tsinghua University (Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric)

Journal of Technology & Science, 11/2017

Newsletter: Full Text Online

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and energy loads, as well as their multi-energy interactions and dependencies, have negligible effects on the operation and analyses of integrated energy systems. Determining how to model the probability characteristics of such systems with high calculation accuracy using limited scenarios is a major difficulty of uncertainty description. This study proposes the use of an optimum quantile method based on the Wasserstein distance metric to generate a …

Findings in Mathematical Sciences Reported from University of Paris Saclay (The Quasineutral

The Wasserstein geometry of nonlinear sigma models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Nonlinear sigma models are quantum field theories describing, in the large deviation sense,

random fluctuations of harmonic maps between a Riemann surface and a Riemannian

manifold. Via their formal renormalization group analysis, they provide a framework for

possible generalizations of the Hamilton–Perelman Ricci flow. By exploiting the heat kernel

embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of

the space of probability measures over Riemannian metric measure spaces provides a …

Limit Of The Vlasov-poisson Equation In Wasserstein Metric)

Journal of Technology & Science, 04/2017

Newsletter: Full Text Online

The quasineutral limit of the Vlasov–Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - Communications in Mathematical Sciences, 2017 - intlpress.com

In this work, we study the quasineutral limit of the one-dimensional Vlasov–Poisson

equation for ions with massless thermalized electrons. We prove new weak-strong stability

estimates in the Wasserstein metric that allow us to extend and improve previously known …

arXiv 2014

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more generally, semiconvex) energies has led to advances in several areas of partial differential equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

Coalescing-fragmentating Wasserstein dynamics: particle approach

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - arxiv.org

We construct a family of semimartingales which describe the behavior of a particle system

with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warren

flow, an infinite system of diffusion particles on the real line which sticky-reflect from each …

<——2017——————2017 ———130—

indings in Computer Graphics Reported from Shandong ...

(2017-11-29), Findings in Computer Graphics Reported from Shandong University (Wasserstein Blue Noise Sampling), Computer Weekly News , 279, ISSN: 1944-1606, BUTTER® ID: 014750427 DOI Information The direct object identifier (DOI) for that additional information is: https://doi.org/10.1145

Wasserstein Blue Noise Sampling - ACM Digital Library

https://dl.acm.org › doi

In this article, we present a multi-class blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density ..
Cited by 17 Related articles All 5 versions

Mathematics; Reports from University of British Columbia Highlight Recent Findings in Mathematics (Wasserstein barycenters over Riemannian manifolds)

Journal of Technology & Science, Oct 8, 2017, 523

Newspaper Article: Full Text Online

Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we establish absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on Wasserstein space, extending on one hand, results in the Euclidean case (for barycenters between finitely many measures) of Agueh and Carlier [1] to the Riemannian setting, and on the other hand, results in the Riemannian case of Cordero-Erausquin, McCann, Schmuckenschläger …

Cited by 35 Related articles

Wasserstein距離にまつわる確率解析1桒田和正

(Kuwada, Kazumasa)2(お茶の水女子大学(Ochanomizu University))1 What is Wasserstein distance?

robability analysis of Wasserstein distance]

On interpolation and curvature via Wasserstein geodesics

Kell, M

ADVANCES IN CALCULUS OF VARIATIONS

2017 v. 10 no. 2 pp. 125–167

Journal Article

Mathematics - Calculus; Findings on Calculus from M. Kell and Colleagues Provide New Insights (On interpolation and curvature via Wasserstein geodesics)

Mathematics Week, May 9, 2017, 4

According to news reporting out of Leipzig, Germany, by VerticalNews editors, the research stated, "In this article, a proof of the interpolation inequality...

Newspaper Article: Citation Online

Patent US20170083608 - Accelerated discrete distribution clustering under wasserstein distance - Google patents

Accelerated discrete distribution clustering under wasserstein distance. US 20170083608 A1. Abstract. Computationally efficient accelerated D2-clustering algorithms are disclosed for clustering discrete distributions under the Wasserstein distance with improved scalability. Three first-order methods include subgradient ...

2017

Mathematics - Algebra; Investigators at Tohoku University Discuss Findings in Algebra (Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices)

Journal of Technology & Science, Nov 12, 2017, 223

Newspaper Article: Full Text Online

MR3695901 Hiai, Fumio; Lim, Yongdo Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices. Linear Algebra Appl. 533 (2017), 118–131. (Reviewer: Sanne ter Horst) 47L07 (15A42 15B48 47A64 47B65)

Journal Article 2 Citations

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices arXiv

By: Hiai, Fumio; Lim, Yongdo

LINEAR ALGEBRA AND ITS APPLICATIONS Volume: 533 Pages: 118-131 Published: NOV 15 2017

Abstract: We introduce a class of flows on the Wasserstein space of probability measures

with finite first moment on the Cartan-Hadamard Riemannian manifold of positive definite

matrices, and consider the problem of differentiability of the corresponding Cartan

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

Energy Volume 135, 15 September 2017, Pages 153-170 XueqianFu^aQinglaiGuo^aHongbinSun^aZhaoguangPan^aWenXiong^bLiWang^b

Abstract The stochastic fluctuation characteristics of intermittent renewable energy sources

and energy loads, as well as their multi-energy interactions and dependencies, have

negligible effects on the operation and analyses of integrated energy systems. Determining

Detecting changes in forced climate attractors with Wasserstein distance

by Y Robin - ‎2017 - ‎Related articles

NONLINEAR PROCESSES IN GEOPHYSICS Volume: 24 Issue: 3 Pages: 393-405 Published: JUL 31 2017

Jul 31, 2017 - Citation: Robin, Y., Yiou, P., and Naveau, P.: Detecting changes in forced climate attractors with Wasserstein distance, Nonlin. ... If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified.

Climate Change; Data on Climate Change Discussed by Researchers at National Center for Scientific Research (CNRS) (Detecting changes in forced climate attractors with Wasserstein...

Global Warming Focus, Aug 28, 2017, 36

Newspaper Article: Full Text Online

[pdf] Detecting changes in forced climate attractors with Wasserstein distance

Order-preserving wasserstein distance for sequence matching

B Su, G Hua - Proceedings of the IEEE Conference on …, 2017 - openaccess.thecvf.com

We present a new distance measure between sequences that can tackle local temporal

distortion and periodic sequences with arbitrary starting points. Through viewing the

instances of sequences as empirical samples of an unknown distribution, we cast the …

<——2017———2017–——140—

WGAN을 이용한 Data Augmentation 기법 - 대한전자공학회 : 논문

Technology; Recent Studies by J.Y. Guo and Co-Authors Add New Data to Technology Findings (Automatic Color Correction for Multisource Remote Sensing Images with Wasserstein CNN)

https://www.dbpia.co.kr › articleDetail · Translate this page

최근 영상 dataset을 이용하여 network를 학습시키는 연구가 활발히 진행되면서 ... WGAN을 이용한 Data Augmentation 기법. Data Augmentation method using WGAN.

[CITATION] WGAN 을 이용한 Data Augmentation 기법

임세호， 신용구， 유철환， 이한규， 고성제 - 대한전자공학회 학술대회, 2017

[Korean Data Augmentation Technique Using WGAN

Se-Ho Lim, Shin-Koo Yoo, Chul-Hwan Yoo, Han-Gyu Lee, and Sung-Je Goh-Korean Institute of Electronics Engineers]

Journal of Engineering, Jun 26, 2017, 1098

According to news originating from Beijing, People's Republic of China, by VerticalNews correspondents, research stated, "In this paper a non-parametric model...

Newspaper Article: Citation Online

Science - Mathematical Sciences; Reports on Mathematical Sciences Findings from University of Paris-Sud Provide New Insights ({Euclidean, metric, and Wasserstein} gradient flows: an overview)

Journal of Technology & Science, May 14, 2017, 437

According to news reporting originating from Orsay, France, by VerticalNews editors, the research stated, "This is an expository paper on the theory of...

Newspaper Article: Full Text Online

[HTML] {Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - Bulletin of Mathematical Sciences, 2017 - Springer

This is an expository paper on the theory of gradient flows, and in particular of those PDEs which can be interpreted as gradient flows for the Wasserstein metric on the space of probability measures (a distance induced by optimal transport). The starting point is the Euclidean theory, and then its generalization to metric spaces, according to the work of Ambrosio, Gigli and Savaré. Then comes an independent exposition of the Wasserstein theory, with a short introduction to the optimal transport tools that are needed and to the …

Cited by 62 Related articles

Mathematics; Investigators at PSL Research University Report Findings in Mathematics (Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces)

Journal of Technology & Science, Apr 30, 2017, 328

According to news reporting originating from Paris, France, by VerticalNews correspondents, research stated, "The time discretization of gradient flows in...

Newspaper Article: Full Text Online

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

The time discretization of gradient flows in metric spaces uses variants of the celebrated implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in this Note a different approach, which allows us to construct two second-order in time numerical schemes. In a metric space framework, we show that the schemes are well defined and prove the convergence for one of them under some regularity assumptions. For the particular case of a Fokker–Planck gradient flow in the Wasserstein space, we obtain …

Entropy; Research Conducted at University of California Has Provided New Information about Entropy (On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests)

Journal of Technology & Science, Apr 16, 2017, 1930

According to news reporting originating from Berkeley, California, by VerticalNews correspondents, research stated, "Nonparametric two-sample or homogeneity...

Newspaper Article:Full Text Online

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being designed and analyzed, both for the unidimensional and the multivariate setting. In this short survey, we focus on test statistics that involve the Wasserstein distance. Using an entropic smoothing of the Wasserstein distance, we connect …

Cited by 66 Related articles

Probability Research; Study Results from University of Bordeaux Broaden Understanding of Probability Research (Geodesic PCA in the Wasserstein space by convex PCA)

Journal of Robotics & Machine Learning, Apr 10, 2017, 424

According to news reporting originating from Talence, France, by VerticalNews correspondents, research stated, "We introduce the method of Geodesic Principal...

Newspaper Article: Citation Online

Mathematics - Mathematical Physics; Findings from M. Carfora et al Has Provided New Information about Mathematical Physics (The Wasserstein geometry of nonlinear sigma models and the...

Journal of Technology & Science, Mar 26, 2017, 125

According to news reporting originating in Pavia, Italy, by VerticalNews editors, the research stated, "Nonlinear sigma models are quantum field theories...

Newspaper Article: Full Text Online

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Nonlinear sigma models are quantum field theories describing, in the large deviation sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton–Perelman Ricci flow. By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a …

Gromov-Hausdorff limit of Wasserstein spaces on point clouds arXiv

Wasserstein GAN / Towards Principled Methods for Training Generative Adversarial Networks Nuit Blanche,

by Igor Carron

Nuit Blanche, 01/2017

We mentioned GANs before. Here are contributions on how to use Earth Mover's distances to improve their training (Cedric Villani is mentioned in the references...

by NG Trillos - ‎2017 - ‎Related articles

Feb 11, 2017 We show that as long as decays towards zero slower than an explicit rate depending on the level of uniformity of , then the space converges in the Gromov-Hausdorff sense towards the space of probability measures on endowed with the Wasserstein distance.

by Trillos, Nicolas Garcia

We consider a point cloud X_n := \{ x_1, \dots, x_n \} uniformly distributed on the flat torus \mathbb{T}^d : = \mathbb{R}^d / \mathbb{Z}^d , and construct a...

Gromov-Hausdorff limit of Wasserstein spaces on point clouds

NG Trillos - arXiv preprint arXiv:1702.03464, 2017 - arxiv.org

We consider a point cloud $ X_n:=\{x_1,\dots, x_n\} $ uniformly distributed on the flat torus $\mathbb {T}^ d:=\mathbb {R}^ d/\mathbb {Z}^ d $, and construct a geometric graph on the cloud by connecting points that are within distance $\epsilon $ of each other. We let $\mathcal {P}(X_n) $ be the space of probability measures on $ X_n $ and endow it with a discrete Wasserstein distance $ W_n $ as introduced independently by Maas and Zhou et al. for general finite Markov chains. We show that as long as $\epsilon=\epsilon_n $ decays …

Gromov-Hausdorff limit of wasserstein spaces on point clouds

<——2017—————2017 ————150—

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations ISAIM

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

Abstract The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is

All 15 versions [PDF] arxiv.org

A new approach for the construction of a Wasserstein diffusion arXiv

by Marx, Victor 10/2017

We propose in this paper a construction of a diffusion process on the space \mathcal {P}_2(\mathbb{R}) of probability measures with a second-order moment. This...

Journal Article: Full Text Online

A new approach for the construction of a Wasserstein diffusion qrXiv

by Marx, Victor 10/2017

We propose in this paper a construction of a diffusion process on the space \mathcal {P}_2(\mathbb{R}) of probability measures with a second-order moment. This...

Journal Article: Full Text Online

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

We propose in this paper a construction of a diffusion process on the space $\mathcal P_2

(\mathbb R) $ of probability measures with a second-order moment. This process was

introduced in several papers by Konarovskyi (see eg [12]) and consists of the limit as $ N …

A new approach for the construction of a Wasserstein diffusion

Exponential Ergodicity for SDEs Driven by α-Stable Processes with Markovian Switching in Wasserstein Distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2017 - Springer

… Keywords Exponential ergodicity · Symmetric α-stable process · Markovian switching · M-matrix ·

Wasserstein distance · Coupling method … To get the exponential ergodicity in Wasserstein

distances, we use the coupling method to deal with the Markov chain …

Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation using Holistic Convolutional Networks

by Fidon, Lucas; Li, Wenqi; Garcia-Peraza-Herrera, Luis C; More... 07/2017

The Dice score is widely used for binary segmentation due to its robustness to class imbalance. Soft generalisations of the Dice score allow it to be used as a...

Journal Article: Full Text Online

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

… BrainLes 2017: Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain

Injuries pp 64-76 | Cite as. Generalised Wasserstein Dice Score for Imbalanced

Multi-class Segmentation Using Holistic Convolutional Networks …

[PDF] Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric

Y Zhao, Y Liu, J Zhang, X Yang - pdfs.semanticscholar.org

Reward-risk ratio (RR) is a very important stock market definition. In order to capture the

situation that the investor does not have complete information on the distribution of the

underlying uncertainty, people extend RR model to distributionally robust reward-risk ratio …

Cited by 3854 Related articles

I Gulrajani, F Ahmed, M Arjovsky… - Advances in Neural …, 2017 - papers.nips.cc

Abstract Generative Adversarial Networks (GANs) are powerful generative models, but suffer

from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress

toward stable training of GANs, but sometimes can still generate only poor samples or fail to …

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

Markov Type constants, flat tori and Wasserstein spaces - PDF Free ...

Jan 20, 2017 - bi-Lipschitz embeddability of snowflakes into such Wasserstein ...... of Computing, STOC '03, pages 463â€...

Gromov-Wasserstein averaging of kernel and distance matrices

G Peyré, M Cuturi, J Solomon - International Conference on …, 2016 - proceedings.mlr.press

This paper presents a new technique for computing the barycenter of a set of distance or

kernel matrices. These matrices, which define the inter-relationships between points

sampled from individual domains, are not required to have the same size or to be in row-by …

Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms

Max Sommerfeld

Georg-August-Universität Göttingen, 2017

Wasserstein distances or, more generally, distances that quantify the optimal transport between probability measures on metric spaces have long been established as an important tool in probability theory.
Zbl 1392.62005 book

2917 thesis

Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms

<——2017—————2017——160—

Fréchet Means in Wasserstein Space: Theory and Algorithms

Yoav Zemel - 2017 - ‎No preview

Mots-clés de l'auteur: Fréchet mean ; functional data analysis ; geodesic variation ; optimal transportation ; phase variation ; point process ; random measure ; registration ; warping ; Wasserstein distance.

On the total variation Wasserstein gradient flow and the TV-JKO scheme

by G Carlier - ‎2017 - ‎Cited by 2 - ‎Related articles

Mar 1, 2017 - On the total variation Wasserstein gradient flow and the TV-JKO scheme. We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a form of maximum principle and in some cases, a minimum principle as well).

2017 [HTML] sciencedirect.com

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

… set of all geodesics connecting x and y. Moreover, the set { γ ( 1 2 ) | γ ∈ Geod x , y } will be called

the set of midpoints of the couple ( x , y ) and will be denoted x + y 2 (see [7, Chapter 2] for a

definition in general metric spaces and [1] in the particular case of Wasserstein spaces …

Investigators at PSL Research University Report Findings in Mathematics (Second-order in time schemes for gradient flows in Wasserstein...

Journal of Technology & Science, 04/2017

Newsletter: Full Text Online

Findings in Mathematical Sciences Reported from University of Paris Saclay (The Quasineutral Limit Of The Vlasov-poisson Equation In Wasserstein...

Journal of Technology & Science, 04/2017

Newsletter: Full Text Online

Science - Mathematical Sciences; Findings in Mathematical Sciences Reported from University of Paris Saclay (The Quasineutral Limit Of The Vlasov-poisson Equation In Wasserstein Metric)

Journal of Technology & Science, Apr 16, 2017, 381

Newspaper Article: Full Text Online

The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation for ions with massless thermalized electrons. We prove new weak-strong stability estimates in the Wasserstein metric that allow us to extend and improve previously known convergence results. In particular, we show that given a possibly unstable analytic initial profile, the formal limit holds for sequences of measure initial data converging sufficiently fast in the Wasserstein metric to this profile. This is achieved without assuming uniform …

On wasserstein two-sample testing and related families of nonparametric tests

Research Conducted at University of California Has Provided New Information about Entropy (On Wasserstein...

Journal of Technology & Science, 04/2017

Newsletter: Full Text Online

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

… Using an entropic smoothing of the Wasserstein distance, we connect these to … mean discrepancy and univariate methods like the Kolmogorov–Smirnov test, probability or … Given nonparametric two-sample testing's classical and continued importance, we aim to provide useful …

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On Wasserstein Two-Sample Testing ...

Entropy 2017, 19(2), 47; full text free

by Ramdas · ‎2017 · ‎Cited by 102 · ‎Related articles

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without ...
[PDF] mdpi.com

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

… A remarkable feature of Wasserstein distances is that Definition 1 applies to all measures

regardless of their absolute continuity with respect to the Lebesgue measure: The same definition

works for both empirical measures and for their densities if they exist …

Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

Wasserstein barycenters over Riemannian manifolds ...

www.sciencedirect.com › science › article › pii

Feb 5, 2017 — We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric.

by YH Kim · ‎2017 · ‎Cited by 44 · ‎Related articles

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and

energy loads, as well as their multi-energy interactions and dependencies, have negligible

effects on the operation and analyses of integrated energy systems. Determining how to …

Arrears prediction for electricity customer through Wgan-

Arrears prediction for electricity customer through Wgan-Gp

W Fu, D Zhang, Y Fu, J Li, Y Xie - … , Networking, Electronic and …, 2017 - ieeexplore.ieee.org

It is not common for electric company that arrears can be found accurately and in time. This

phenomenon leads to shortage of arrears data. It also cause process of predicting arrears

can not be further developed. Stratified sampling has become a general solution to the …

New Algorithms Study Findings Have Been Reported from Tsinghua University (Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein...

Journal of Technology & Science, 11/2017

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MR3595479 Carfora, Mauro The Wasserstein geometry of nonlinear

σ models and the Hamilton-Perelman Ricci flow. Rev. Math. Phys. 29 (2017), no. 1, 1750001, 71 pp. 53C44 (58D25 58D30 81T17)

The Wasserstein geometry of nonlinear σ models ... - World Scientific

by M Carfora - ‎2017 - ‎Cited by 7 - ‎Related articles

By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over ...

MR3764530 Pending Bhattacharya, Anirban; Pati, Debdeep Posterior contraction in Gaussian process regression using Wasserstein approximations. Inf. Inference 6 (2017), no. 4, 416–440. 62F15 (60G15 94A15)

Journal Article

Posterior contraction in Gaussian process regression using Wasserstein approximations.

by A Bhattacharya - ‎2017 - ‎Cited by 1 - ‎Related articles

We study posterior rates of contraction in Gaussian process regression with potentially unbounded covariate domain. Our argument relies on developing.

MR3737716 Conforti, Giovanni; Pavon, Michele Extremal curves in Wasserstein space. Geometric science of information, 91–99, Lecture Notes in Comput. Sci., 10589, Springer, Cham, 2017. (Reviewer: Vassili N. Kolokolʹtsov) 58E30 (49Q20 76Y05 94A08)

Series Chapter 1 Citation

Extremal Curves in Wasserstein Space | SpringerLink

by G Conforti - ‎2017 - ‎Cited by 2 - ‎Related articles

Oct 24, 2017 - We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges and the classic Madelung fluid can be derived from ...

Extremal Curves in Wasserstein Space
<——2017———————2017 ——170—

MR3737715 Cazelles, Elsa; Bigot, Jérémie; Papadakis, Nicolas Regularized barycenters in the Wasserstein space. Geometric science of information, 83–90, Lecture Notes in Comput. Sci., 10589, Springer, Cham, 2017. 62G99 (60B10 60G57 94A17)

Series Chapter 1 Citation

Regularized Barycenters in the Wasserstein Space | SpringerLink

by E Cazelles - ‎2017 - ‎Cited by 1 - ‎Related articles

Oct 24, 2017 - A stability result of regularized barycenters in terms of Bregman distance associated to the convex regularization term is also given. ... In this setting, we propose an efficient minimization algorithm based on accelerated gradient descent for the computation of regularized Wasserstein barycenters.

MR3693149 Jiang, Yin Absolute continuity of Wasserstein barycenters over Alexandrov spaces. Canad. J. Math. 69 (2017), no. 5, 1087–1108. (Reviewer: Bożena Piątek) 53C45 (49K30 51K05)

Journal Article

Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we prove that on a compact, $ n $-dimensional Alexandrov space with curvature at least− 1, the Wasserstein barycenter of Borel probability measures ${{\mu} _ {1}},\ldots,{{\mu} _ {m}} $ is absolutely continuous with respect to the $ n $-dimensional Hausdorff measure if one of them is.

MR3673057 Agueh, Martial; Carlier, Guillaume Vers un théorème de la limite centrale dans l'espace de Wasserstein? (French) [Towards a central limit theorem in the Wasserstein space?] C. R. Math. Acad. Sci. Paris 355 (2017), no. 7, 812–818. 60F05 (28A33)

Journal Article

Vers un théorème de la limite centrale dans l'espace de Wasserstein ...

by M Agueh - ‎2017 - ‎Cited by 4 - ‎Related articles

Nous conjecturons que ces barycentres obéissent à un théorème de la limite centrale que nous démontrons dans quelques cas (très) particuliers.

‎Cited by 13 · ‎Related articles

MR3663634 Le Gouic, Thibaut; Loubes, Jean-Michel Existence and consistency of Wasserstein barycenters. Probab. Theory Related Fields 168 (2017), no. 3-4, 901–917. 60D05 (62G20 62H10)

Journal Article 4 Citations

Existence and consistency of Wasserstein barycenters | SpringerLink

by T Le Gouic - ‎2017 - ‎Cited by 26 - ‎Related articles

Section 2 presents general definitions and states a general theorem that ensures the existence of a barycenter of probability measures in the Wasserstein space. In Sect. 3, a consistency result is proven. Section 4 is devoted to some statistical applications.

Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant ...

[PDF] Steepest descend algorithm in the Wasserstein metric for a sandpile model

V Barbu - www-dimat.unipv.it

For n= 2, equation (1) describes the dynamic of the sandpile model of self-organized

criticality which we briefly present below. If ρ= ρ (t, x1, x2) is the energy (or mass density)

assigned to the site x=(x1, x2) of a square lattice at time t, then, if ρ (t, x1, x2) exceeds the …

MR3631386 Lai, Rongjie; Zhao, Hongkai Multiscale nonrigid point cloud registration using rotation-invariant sliced-Wasserstein distance via Laplace-Beltrami eigenmap. SIAM J. Imaging Sci. 10 (2017), no. 2, 449–483. 94A08 (58J50 65N25 68U05)

Journal Article 2 Citations

by R Lai - ‎2017 - ‎Cited by 12 - ‎Related articles

MR3631299 Han-Kwan, Daniel; Iacobelli, Mikaela Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in higher dimension. J. Differential Equations 263 (2017), no. 1, 1–25. 35Q83 (35B25 35B35)

Journal Article 2 Citations

Quasineutral limit for Vlasov–Poisson via Wasserstein stability ...

by D Han-Kwan - ‎2017 - ‎Cited by 10 - ‎Related articles

Jul 5, 2017 - This work is concerned with the quasineutral limit of the Vlasov–Poisson system in two and three dimensions. We justify the formal limit for very ...

MR3630091 Kell, Martin On interpolation and curvature via Wasserstein geodesics. Adv. Calc. Var. 10 (2017), no. 2, 125–167. (Reviewer: Valeri Obukhovskiĭ) 58E35 (28C15)

Journal Article 5 Citations

On interpolation and curvature via Wasserstein geodesics : Advances ...

by M Kell - ‎2017 - ‎Cited by 8 - ‎Related articles

In this article, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given. ... Both, the BBL inequality and the curvature condition, rely on geodesics in the 2-Wasserstein space, which was a natural candidate because of its connection to convex analysis in the Euclidean setting.

MR3625852 Santambrogio, Filippo {Euclidean, metric, and Wasserstein} gradient flows: an overview. Bull. Math. Sci. 7 (2017), no. 1, 87–154. (Reviewer: Benoît Kloeckner) 34G25 (35Q84 49J45 49M29 49Q20)

Journal Article 4 Citations

Euclidean, metric, and Wasserstein} gradient flows: an overview ...

by F Santambrogio - ‎2017 - ‎Cited by 27 - ‎Related articles

MR3620566 Han-Kwan, Daniel; Iacobelli, Mikaela The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric. Commun. Math. Sci. 15 (2017), no. 2, 481–509. (Reviewer: Juhi Jang) 35Q83 (35B35)

Journal Article 4 Citations

<——2017——————— -180 —

MR3620352 Ye, Jianbo; Wu, Panruo; Wang, James Z.; Li, Jia Fast discrete distribution clustering using Wasserstein barycenter with sparse support. IEEE Trans. Signal Process. 65 (2017), no. 9, 2317–2332. 94A12

Journal Article 1 Citation

Fast Discrete Distribution Clustering Using Wasserstein Barycenter ...

by J Ye - ‎2017 - ‎Cited by 30 - ‎Related articles

May 1, 2017 - Fast Discrete Distribution Clustering Using Wasserstein Barycenter With Sparse Support, 2017 Article. orig-research. Bibliometrics Data ...

‎Abstract · ‎Authors · ‎References · ‎Cited By

MR3606732 Bigot, Jérémie; Gouet, Raúl; Klein, Thierry; López, Alfredo Geodesic PCA in the Wasserstein space by convex PCA. Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017), no. 1, 1–26. 62G05 (60B10 62G20 62H25)

Journal Article 3 Citations

Geodesic PCA in the Wasserstein space by convex PCA - Project Euclid

by J Bigot - ‎2017 - ‎Cited by 30 - ‎Related articles

We introduce the method of Geodesic Principal Component Analysis (GPCA) on ... Keywords: Wasserstein space; Geodesic and Convex Principal Component ...

MR3606415 Barbu, Viorel The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality. SIAM J. Control Optim. 55 (2017), no. 1, 413–428. (Reviewer: Koji Kikuchi) 35K59 (35A15 35K15 35R70 60J60)

Journal Article 1 Citation

The Steepest Descent Algorithm in Wasserstein Metric for the ...

by V Barbu - ‎2017 - ‎Cited by 2 - ‎Related articles

MR3601616 Berckmoes, Ben; Hellemans, Tim; Sioen, Mark; Van Casteren, Jan An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric. J. Math. Anal. Appl. 449 (2017), no. 2, 1770–1789. (Reviewer: Mona Khare) 54B30 (54E05)

Journal Article 1 Citation

An application of approach theory to the relative Hausdorff measure of ...

by B Berckmoes - ‎2017 - ‎Cited by 1 - ‎Related articles

In this paper, we will use approach theory to study the relative Hausdorff measure of non-compactness for the well-known Wasserstein metric [40] on the space ...

Peer-reviewed
An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

Authors:Ben Berckmoes, Tim Hellemans, Mark Sioen, Jan Van Casteren
Summary:After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in 1989, we show that this theory is intimately related to the well-known Wasserstein metric on the space of probability measures with a finite first moment on a complete and separable metric space. More precisely, we introduce a canonical approach structure, called the contractive approach structure, and prove that it is metrized by the Wasserstein metric. The key ingredients of the proof of this result are Dini's Theorem, Ascoli's Theorem, and the fact that the class of real-valued contractions on a metric space has some nice stability properties. We then combine the obtained result with Prokhorov's Theorem to establish inequalities between the relative Hausdorff measure of non-compactness for the Wasserstein metric and a canonical measure of non-uniform integrabilityShow more

MR3601019 Kinderlehrer, David; Monsaingeon, Léonard; Xu, Xiang A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations. ESAIM Control Optim. Calc. Var. 23 (2017), no. 1, 137–164. (Reviewer: Juha K. Kinnunen) 35M31 (35K65 47J30)

Journal Article 3 Citations

A Wasserstein gradient flow approach to Poisson−Nernst−Planck ...

by D Kinderlehrer - ‎2017 - ‎Cited by 15 - ‎Related articles

A Wasserstein gradient flow approach to Poisson−Nernst−Planck equations. ... The Poisson−Nernst−Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment.

MR3598633 Xiang, Jim X. Sample size determination of a nonparametric test based on weighted

L2-Wasserstein distance. Statist. Probab. Lett. 123 (2017), 160–164. 62G10 (62G20)

Journal Article

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

In this paper we derive a formula for the sample size of a nonparametric test based on

weighted L 2-Wasserstein distance with a known alternative. As an example we apply the

formula to determine the sample size for a hypothesis testing from the Tukey's contaminated

distribution model. The reliability of the sample size formula is evaluated in terms of type I

errors and the powers of the test. The Monte Carlo simulation results show that the test

based on the weighted L 2-Wasserstein distance performs equally well as the Anderson …

Sample size determination of a nonparametric test based on weighted ...

by JX Xiang - ‎2017 - ‎Related articles

Abstract. In this paper we derive a formula for the sample size of a nonparametric test based on weighted L 2 -Wasserstein distance with a known alternative.

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

In this paper we derive a formula for the sample size of a nonparametric test based on weighted L 2-Wasserstein distance with a known alternative. As an example we apply the formula to determine the sample size for a hypothesis testing from the Tukey's contaminated distribution model. The reliability of the sample size formula is evaluated in terms of type I errors and the powers of the test. The Monte Carlo simulation results show that the test based on the weighted L 2-Wasserstein distance performs equally well as the Anderson …

Low Dose CT Image Denoising Using a Generative Adversarial ...

by Q Yang - ‎2017 - ‎Cited by 48 - ‎Related articles

Aug 3, 2017 - Abstract: In this paper, we introduce a new CT image denoising method based on the generative adversarial network (GAN) with Wasserstein ...

On the Bures-Wasserstein distance between positive definite matrices arXiv

by Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo 12/2017

The metric d(A,B)=\left[ \tr\, A+\tr\, B-2\tr(A^{1/2}BA^{1/2})^{1/2}\right]^{1/2} on the manifold of n\times n positive definite matrices arises in various...

[PDF] On the Bures-Wasserstein Distance between positive definite matrices

The metric d (A, B)=[tr A+ tr B− 2tr (A1/2BA1/2) 1/2] 1/2 on the manifold of n× n positive

definite matrices arises in various optimisation problems, in quantum information and in the

theory of optimal transport. It is also related to Riemannian geometry. In the first part of this …

n the bures-wasserstein distance between positive definite matrices

2017

Proof that the optimal transport cost is lower semicontinuous

https://math.stackexchange.com › questions › proof-tha...

Sep 5, 2017 — the Wasserstein distance is lower semicontinuous on P(X) (just like the optimal transport cost C, for any lower semicontinuous cost function c; recall the ...

2 answers

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

… In this paper, we present a specific implementa- tion in which a variational autoencoder (VAE [1]) assumes the inference task and a Wasserstein generative adversarial network (W-GAN [2]) undertakes speech synthesis … Red arrows represent inference …

Cited by 141 Related articles
<-—2017—————2017 ——— -190—

2017 see 2019

From GAN to WGAN - Lil'Log

Aug 20, 2017 - Improved GAN Training; Wasserstein GAN (WGAN). What is Wasserstein distance? Why Wasserstein is better than JS or KL divergence?

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Y Tin Chow, W Gangbo - arXiv preprint arXiv:1710.10536, 2017 - adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion and plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, and we use it to define heat flow on the Wasserstein space. We verify a distinctive smoothing effect of this flow for a particular class of initial conditions. To this end, we will develop a theory of Fourier analysis and conic surfaces in metric spaces. We …

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric

C Duan, W Fang, L Jiang, L Yao, J Liu - arXiv preprint arXiv:1706.05538, 2017 - arxiv.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In presence of VRE

uncertainties, this paper discusses a distributionally robust chance constrained approximate …

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the

discrete and continuous multi-armed bandit settings with entropy regularisation. We show

that in the small steps limit with respect to the Wasserstein distance $ W_2 $, policy

dynamics are governed by the Fokker-Planck (heat) equation, following the Jordan …

arXiv:1712.07185 [pdf, ps, other]

On Wasserstein Reinforcement Learning and the Fokker-Planck equation

Pierre H. Richemond, Brendan Maginnis

Subjects: Learning (cs.LG) 2017Cited by 6 Related articles All 3 versions

[PDF] SENSITIVITY OF THE COMPLIANCE AND OF THE WASSERSTEIN DISTANCE WITH RESPECT TO A VARYING SOURCE

GUY BOUCHITTÉ, I FRAGALA, I LUCARDESI - 2017 - cvgmt.sns.it

We show that the compliance functional in elasticity is differentiable with respect to

horizontal variations of the load term, when the latter is given by a possibly concentrated

measure; moreover, we provide an integral representation formula for the derivative as a …

Optimal Transport Relaxations with Application to Wasserstein GANs

S Mahdian, J Blanchet, P Glynn - arXiv preprint arXiv:1906.03317, 2019 - arxiv.org

… For instance, min-max representation justifies understanding our relax- ation as a regularization …

We derive a confidence interval for G0(µ0,ν) through the use of … Data-driven distributionally robust

opti- mization using the wasserstein metric: Performance guarantees and tractable …

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance arXiv pdf

Maya Briani, Emiliano Cristiani, Elisa Iacomini

Arrears Prediction For Electricity Customer Through Wgan-Gp

By: Fu, Weiwei; Li, Jianyuan; Zhang, Dezheng; et al.

Conference: IEEE 2nd Information Technology, Networking, Electronic and Automation Control Conference (ITNEC) Location: Chengdu, PEOPLES R CHINA Date: DEC 15-17, 2017

Sponsor(s): IEEE PRESS

PROCEEDINGS OF 2017 IEEE 2ND INFORMATION TECHNOLOGY, NETWORKING, ELECTRONIC AND AUTOMATION CONTROL CONFERENCE (ITNEC) Pages: 1667-1670 Published: 2017

100 WGaN, HEMT modeling

By: Tajima, Yusuke

MICROWAVE JOURNAL Volume: 50 Issue: 5 Pages: 204-+ Published: MAY 2007

Times Cited: 1

[PDF] Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

GA Hanasusanto, D Kuhn - 2017 - pdfs.semanticscholar.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

<——2017—————2017——-200 —

Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant Sliced-Wasserstein Distance via Laplace--Beltrami Eigenmap

R Lai, H Zhao - SIAM Journal on Imaging Sciences, 2017 - SIAM

In this work, we propose computational models and algorithms for point cloud registration

with nonrigid transformation. First, point clouds sampled from manifolds originally embedded

in some Euclidean space are transformed to new point clouds embedded in R^n by the …

[C] Wasserstein distance for clustering interval data

2917 ZZZZ

A Irpino, R Verde - GFKL 2007, 2007 - iris.unicampania.it

IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili … Wasserstein …

[CITATION] Wasserstein distance for clustering interval data

A Irpino, R Verde - GFKL 2007, 2007 - iris.unicampania.it

IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti

della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati

della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili … Wasserstein …

Wasserstein distance for clustering interval data - Luigi Vanvitelli

iris.unicampania.it › handle

Titolo: Wasserstein distance for clustering interval data. Autori: IRPINO, Antonio · VERDE, Rosanna. Data di pubblicazione: 2007. Handle ...

by A Irpino · ‎2007

arXiv:1712.07528 [pdf, ps, other]

Harmonic mappings valued in the Wasserstein space

Hugo Lavenant (LM-Orsay)

Subjects: Analysis of PDEs (math.AP)

Harmonic mappings valued in the Wasserstein space

Authors:Hugo Lavenant (LM-Orsay). (Submitted on 20 Dec 2017 (v1), last revised 28 May 2019 (this ...

arXiv:1712.07528 [pdf, ps, other]

Harmonic mappings valued in the Wasserstein space

Hugo Lavenant (LM-Orsay)

Subjects: Analysis of PDEs (math.AP)

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Oct 28, 2017 - Abstract: We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is ...

by YT Chow - ‎2017 - ‎Cited by 11 - ‎Related articles

[PDF] imperial.ac.uk 2018

[PDF] Bregman and Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond

GANR Wasserstein - wwwf.imperial.ac.uk

Page 1. Bregman Divergence Function Generative Adversarial Networks (GANs) Wasserstein

Divergence and GANs Relaxed Wasserstein Empirical Results Conclusions Bregman and

Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond Xin Guo …

Wasserstein gan

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017 - arxiv.org

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and …

Cited by 5097 Related articles All 10 versions View as HTML

Cited by 5401 Related articles All 10 versions View as HTML

Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein...

by Reda, F. Al; Maury, B

Topological Optimization and Optimal Transport, 2017

Book ChapterFull Text Online

Семинар Добрушинской математической лаборатории ИППИ РАН

19 сентября 2017 г. 16:00, г. Москва, комн. 307 ИППИ РАН (Большой Каретный пер., 19)

Условие выживаемости в пространстве Васерштейна

Ю. В. Авербух

Институт математики и механики им. Н. Н. Красовского Уральского отделения РАН, г. Екатеринбург

Аннотация: В докладе рассматривается управляемая система "среднего поля" т.е. динамическая система в пространстве вероятностей (пространстве Васерштейна), описывающая эволюцию большого числа агентов, взаимодействующих через "среднее поле" и управляемых одним лицом. Исследуется вопрос о выживаемости. В общем случае, говорят, что множество в заданном метрическом пространстве является выживающим относительно динамической системы, если для любой точки из этого множества, существует выходящее из нее движение в силу динамической системы полностью содержащееся в множестве. Впервые понятие выживаемости было предложено для конечномерных пространств. Позже было показано что в терминах выживаемости можно сформулировать понятие вязкостного решения уравнения Гамильтона-Якоби первого порядка и дать характеризацию функции цены в задаче управления. Выживаемость в пространстве Васерштейна также предполагается использовать при исследовании задач управления в пространстве вероятностей. В конечном случае теорема о выживаемости связывает понятие выживаемости со свойствами конуса касательных направлений к заданному множеству. В случае пространства Васерштейна мы вводим касательное направление как распределение в касательном пространстве. В этом случае теорема о выживаемости формулируется в классическом виде: заданное множество вероятностей выживает относительно данной системы "среднего поля" тогда и только тогда, когда множество касательных распределений пересекается с множеством распределений, возможных в силу динамики.

Manifold-valued Image Generation with Wasserstein Generative Adversarial Nets

2017 arXiv: Computer Vision and Pattern Recognition

2017 cited by many

Wasserstein Auto-Encoders

126 citations*

2017 arXiv: Machine Learning

Wasserstein Auto-Encoders

Wasserstein Auto-Encoders

by I Tolstikhin · 2017 · Cited by 542 — We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a ...

[CITATION] Wasserstein Auto-Encoders. arXiv e-prints, art

I Tolstikhin, O Bousquet, S Gelly, B Schoelkopf - arXiv preprint arXiv:1711.01558, 2017

by Tolstikhin, Ilya; Bousquet, Olivier; Gelly, Sylvain; More... 11/2017

We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the...

[CITATION] Wasserstein Auto-Encoders. arXiv e-prints, art

I Tolstikhin, O Bousquet, S Gelly, B Schoelkopf - arXiv preprint arXiv:1711.01558, 2017

Arrears prediction for electricity customer through Wgan-Gp

W Fu, D Zhang, Y Fu, J Li, Y Xie - 2017 IEEE 2nd Information …, 2017 - ieeexplore.ieee.org

It is not common for electric company that arrears can be found accurately and in time. This

phenomenon leads to shortage of arrears data. It also cause process of predicting arrears

can not be further developed. Stratified sampling has become a general solution to the …

基于 Wasserstein 距离和分裂 Bregman 方法的图像分割算法

<—-2017———————2017 —— 210—

王瑜，闫沫 - 电子设计工程, 2017 - cqvip.com

针对基于CV 模型的活动轮廓分割算法无法应用于灰度非均匀图像分割的问题.

采用Wasserstein 距离作为区域直方图相似性测度, 提出基于该测度的非参数活动轮廓分割模型.

在模型求解时引入全局凸分割和分裂Bregman 方法, 减少了计算量. 大量实验结果表明该模型不 …

[Chinese Image segmentation algorithm based on Wasserstein distance and split Bregman method]

Wasserstein gan

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017 - arxiv.org

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In

this new model, we show that we can improve the stability of learning, get rid of problems

like mode collapse, and provide meaningful learning curves useful for debugging and …

Cited by 5872 Related articles All 10 versions

2017 [PDF] nips.cc [cited by many #2]

Improved training of wasserstein gans

I Gulrajani, F Ahmed, M Arjovsky… - Advances in neural …, 2017 - papers.nips.cc

Abstract Generative Adversarial Networks (GANs) are powerful generative models, but suffer

from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress

toward stable training of GANs, but sometimes can still generate only poor samples or fail to …
Cited by 6980 Related articles All 12 versions

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

Learning wasserstein embeddings

[PDF] {Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - Bulletin of Mathematical Sciences, 2017 - Springer

This is an expository paper on the theory of gradient flows, and in particular of those PDEs

which can be interpreted as gradient flows for the Wasserstein metric on the space of

probability measures (a distance induced by optimal transport). The starting point is the …

N Courty, R Flamary, M Ducoffe - arXiv preprint arXiv:1710.07457, 2017 - arxiv.org

The Wasserstein distance received a lot of attention recently in the community of machine

learning, especially for its principled way of comparing distributions. It has found numerous

applications in several hard problems, such as domain adaptation, dimensionality reduction …
Cited by 33 Related articles All 6 versions

2017 SEE 2018 [PDF] mdpi.com

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that

involves identifying differences between two random variables without making parametric

aCited by 263 Related articles All 6 versions

ithin-cluster variation for a set of discrete distributions …

2017

Fast discrete distribution clustering using Wasserstein barycenter with sparse support

J Ye, P Wu, JZ Wang, J Li - IEEE Transactions on Signal …, 2017 - ieeexplore.ieee.org

In a variety of research areas, the weighted bag of vectors and the histogram are widely

used descriptors for complex objects. Both can be expressed as discrete distributions. D2-

clustering pursues the minimum total within-cluster variation for a set of discrete distributions …

Wasserstein learning of deep generative point process models

S Xiao, M Farajtabar, X Ye, J Yan, L Song… - Advances in neural …, 2017 - papers.nips.cc

Point processes are becoming very popular in modeling asynchronous sequential data due

to their sound mathematical foundation and strength in modeling a variety of real-world

phenomena. Currently, they are often characterized via intensity function which limits …

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging

but highly valuable in real application scenarios. In most situations, the source and the target

speakers do not repeat the same texts or they may even speak different languages. In this …

[CITATION] Y. Tsao in H.-M. Wang,“Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks,”

CC Hsu, HT Hwang, YC Wu - arXiv preprint arXiv:1704.00849, 20

,<<——2017———————2017 —— 220—

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

Parallel streaming Wasserstein barycenters

M Staib, S Claici, JM Solomon… - Advances in Neural …, 2017 - papers.nips.cc

Efficiently aggregating data from different sources is a challenging problem, particularly

when samples from each source are distributed differently. These differences can be

inherent to the inference task or present for other reasons: sensors in a sensor network may …

Existence and consistency of Wasserstein barycenters

T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual

notion of statistical mean. We prove the existence of Wasserstein barycenters of random

probabilities defined on a geodesic space (E, d). We also prove the consistency of this …

Sliced wasserstein kernel for persistence diagrams

M Carriere, M Cuturi, S Oudot - arXiv preprint arXiv:1706.03358, 2017 - arxiv.org

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they

are routinely used to describe topological properties of complicated shapes. PDs enjoy

strong stability properties and have proven their utility in various learning contexts. They do …

CITATION] Sliced Wasserstein Kernel for Persistence Diagrams

S Oudot - ICML, 2017 - openreview.net

OpenReview is created by the Information Extraction and Synthesis Laboratory, College of Information

and Computer Science, University of Massachusetts Amherst. We gratefully acknowledge the

support of the OpenReview sponsors: Google, Facebook, NSF, the University of Massachusetts …

Relaxed wasserstein with applications to gans

X Guo, J Hong, T Lin, N Yang - arXiv preprint arXiv:1705.07164, 2017 - arxiv.org

Comparing probability distributions is an integral part of many modern data-driven

applications, such as generative adversarial networks (GANs) and distributionally robust

optimization (DRO). We propose a novel class of statistical divergences called\textit …

Face super-resolution through wasserstein gans

Z Chen, Y Tong - arXiv preprint arXiv:1705.02438, 2017 - arxiv.org

Generative adversarial networks (GANs) have received a tremendous amount of attention in

the past few years, and have inspired applications addressing a wide range of problems.

Despite its great potential, GANs are difficult to train. Recently, a series of papers (Arjovsky & …

Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

We study barycenters in the space of probability measures on a Riemannian manifold,

equipped with the Wasserstein metric. Under reasonable assumptions, we establish

absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on Wasserstein …

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

The Dice score is widely used for binary segmentation due to its robustness to class

imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for

training convolutional neural networks (CNN). Although CNNs trained using mean-class …

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

hat the combination of the proposed generalised Wasserstein Dice score and our …

Save Cite Cited by 129 Related articles All 11 versions

Reversible coalescing-fragmentating Wasserstein dynamics on the real line

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1709.02839, 2017 - arxiv.org

We introduce a family of reversible fragmentating-coagulating processes of particles of

varying size-scaled diffusivity with strictly local interaction on the real line. The construction

is based on a new family of measures on the set of real increasing functions as reference …

<——2017———————2017 —— 230 —

Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - Advances in Neural Information Processing …, 2017 - papers.nips.cc

We introduce a novel framework for statistical analysis of populations of non-degenerate

Gaussian processes (GPs), which are natural representations of uncertain curves. This

allows inherent variation or uncertainty in function-valued data to be properly incorporated in …

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu, Y Zhang - IET Generation, Transmission …, 2017 - IET

In order to address the wind power uncertainty in the security constrained economic

dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve

and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

MG Mora, MA Peletier, L Scardia - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider systems of n parallel edge dislocations in a single slip system, represented by

points in a two-dimensional domain; the elastic medium is modeled as a continuum. We

formulate the energy of this system in terms of the empirical measure of the dislocations and …

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

A framework for Wasserstein-1-type metrics

B Schmitzer, B Wirth - arXiv preprint arXiv:1701.01945, 2017 - arxiv.org

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy

measure between nonnegative measures of different mass. This generalization inherits the

convexity and computational efficiency from the Wasserstein-1 metric, and it includes …

Cited by 14 Related articles All 4 versions
<—2017———————2017 —— -240 —

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

[PDF] pku.edu.cn

Wasserstein blue noise sampling

H Qin, Y Chen, J He, B Chen - ACM Transactions on Graphics (TOG), 2017 - dl.acm.org

In this article, we present a multi-class blue noise sampling algorithm by throwing samples

as the constrained Wasserstein barycenter of multiple density distributions. Using an

entropic regularization term, a constrained transport plan in the optimal transport problem is …

Matricial wasserstein-1 distance

Y Chen, TT Georgiou, L Ning… - IEEE control systems …, 2017 - ieeexplore.ieee.org

We propose an extension of the Wasserstein 1-metric (W 1) for density matrices, matrix-

valued density measures, and an unbalanced interpretation of mass transport. We use

duality theory and, in particular, a “dual of the dual” formulation of W 1. This matrix analog of …

[PDF] Detecting changes in forced climate attractors with Wasserstein distance.

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - d-nb.info

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

Extremal curves in Wasserstein space

G Conforti, M Pavon - International Conference on Geometric Science of …, 2017 - Springer

We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges

and the classic Madelung fluid can be derived from variational principles on Wasserstein

space. The second order differential equations are accordingly obtained by annihilating the …

2017

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the

electrons f ( t , x , v ) , for t ∈ R + , ( x , v ) ∈ T d × R d where T d is the d-dimensional torus and

d = 2 , 3 . As usual, f ( t , x , v ) d x d v can be interpreted as the probability of finding particles

with position and velocity close to the point ( x , v ) in the phase space at time t. We also define …

[HTML] Vers un théorème de la limite centrale dans l'espace de Wasserstein?

M Agueh, G Carlier - Comptes Rendus Mathématique, 2017 - Elsevier

Résumé Les barycentres dans l'espace de Wasserstein constituent une manière naturelle

d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines

appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons …

Automatic color correction for multisource remote sensing images with Wasserstein CNN

J Guo, Z Pan, B Lei, C Ding - Remote Sensing, 2017 - mdpi.com

In this paper a non-parametric model based on Wasserstein CNN is proposed for color

correction. It is suitable for large-scale remote sensing image preprocessing from multiple

sources under various viewing conditions, including illumination variances, atmosphere …

<——2017———————2017 —— 250—

[PDF] mjstaib.com

[PDF] Wasserstein k-means++ for cloud regime histogram clustering

M Staib, S Jegelka - Climate informatics, 2017 - mjstaib.com

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

k-means clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

The time discretization of gradient flows in metric spaces uses variants of the celebrated

implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in this Note a

different approach, which allows us to construct two second-order in time numerical …

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

On interpolation and curvature via Wasserstein geodesics

M Kell - Advances in Calculus of Variations, 2017 - degruyter.com

In this article, a proof of the interpolation inequality along geodesics in p-Wasserstein

spaces is given. This interpolation inequality was the main ingredient to prove the Borel–

Brascamp–Lieb inequality for general Riemannian and Finsler manifolds and led Lott …

Multilevel clustering via Wasserstein means

N Ho, XL Nguyen, M Yurochkin, HH Bui… - arXiv preprint arXiv …, 2017 - arxiv.org

We propose a novel approach to the problem of multilevel clustering, which aims to

simultaneously partition data in each group and discover grouping patterns among groups

in a potentially large hierarchically structured corpus of data. Our method involves a joint …

Data-driven distributed optimization using Wasserstein ambiguity sets

A Cherukuri, J Cortés - 2017 55th Annual Allerton Conference …, 2017 - ieeexplore.ieee.org

This paper considers a general class of stochastic optimization problem for multiagent

systems. We assume that the probability distribution of the uncertain parameters is unknown

to the agents and instead, each agent gathers a certain number of samples of it. The …

Weakly supervised audio source separation via spectrum energy preserved wasserstein learning

N Zhang, J Yan, Y Zhou - arXiv preprint arXiv:1711.04121, 2017 - arxiv.org

Separating audio mixtures into individual instrument tracks has been a long standing

challenging task. We introduce a novel weakly supervised audio source separation

approach based on deep adversarial learning. Specifically, our loss function adopts the …

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost

functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

Log-PCA versus Geodesic PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - arXiv preprint arXiv …, 2017 - arxiv.org

This paper is concerned by the statistical analysis of data sets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the PCA of histograms with respect to the 2-Wasserstein …

On tangent cones in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact Riemannian manifold, let $ P (M) $ denote the Wasserstein

space of probability measures on $ M $. If $ S $ is an embedded submanifold of $ M $, and

$\mu $ is an absolutely continuous measure on $ S $, then we compute the tangent cone of …

<——2017———————2017 —— 260—

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Nonlinear sigma models are quantum field theories describing, in the large deviation sense,

random fluctuations of harmonic maps between a Riemann surface and a Riemannian

manifold. Via their formal renormalization group analysis, they provide a framework for …

Correcting nuisance variation using wasserstein distance

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - arXiv preprint arXiv …, 2017 - arxiv.org

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological

information resulting from various factors affecting the cells. One motivating application is

drug development: morphological cell features can be captured from images, from which …

[CITATION] Correcting Nuisance Variation using Wasserstein Distance. arXiv

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - 2017 - Nov

MAP image labeling using Wasserstein messages and geometric assignment

F Åström, R Hühnerbein, F Savarino… - … Conference on Scale …, 2017 - Springer

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by

following the Riemannian gradient flow of a given objective function on the so-called

assignment manifold. The approach evaluates user-defined data term and additionally …

A Central Limit Theorem for Wasserstein type distances between two different laws

P Berthet, JC Fort, T Klein - arXiv preprint arXiv:1710.09763, 2017 - arxiv.org

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

12 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

M Laborde - Topological Optimization and Optimal Transport: In …, 2017 - books.google.com

This chapter presents existence and uniqueness results for a class of parabolic systems with

nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular

perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic …

2017 [PDF] projecteuclid.org

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary -dependent sequences

J Dedecker, F Merlevède - Bernoulli, 2017 - projecteuclid.org

We study the Wasserstein distance of order 1 between the empirical distribution and the

marginal distribution of stationary $\alpha $-dependent sequences. We prove some

moments inequalities of order $ p $ for any $ p\geq1 $, and we give some conditions under …

Information geometry of wasserstein divergence

R Karakida, S Amari - International Conference on Geometric Science of …, 2017 - Springer

There are two geometrical structures in a manifold of probability distributions. One is

invariant, based on the Fisher information, and the other is based on the Wasserstein

distance of optimal transportation. We propose a unified framework which connects the …

[PDF] Cadlág stability and approximation of reversible coalescing-fragmentating Wasserstein dynamics

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - researchgate.net

We construct coalescing-fragmentating Wasserstein dynamics [27] for any initial condition

and interacting potential by a finite particle approximation. We show that such a model

admits a description by a family of continuous semimartingales, where every semimartingale …

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite

first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices,

and consider the problem of differentiability of the corresponding Cartan barycentric …

Construction of non-asymptotic confidence sets in 2-Wasserstein space

J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658, 2017 - arxiv.org

In this paper, we consider a probabilistic setting where the probability measures are

considered to be random objects. We propose a procedure of construction non-asymptotic

confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea …

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

[CITATION] Construction of non-asymptotic confidence sets in 2-Wasserstein space (2017)

J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658

ited by 19 Related articles All 7 versions
<——2017———————2017 —— 270—

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

An elementary proof for the structure of Wasserstein derivatives

C Wu, J Zhang - arXiv preprint arXiv:1705.08046, 2017 - arxiv.org

Let $ F:\mathbb {L}^ 2 (\Omega,\mathbb {R})\to\mathbb {R} $ be a law invariant and

continuously Fréchet differentiable mapping. Based on Lions\cite {Lions}, Cardaliaguet\cite

{Cardaliaguet}(Theorem 6.2 and 6.5) proved that:\bea\label {Derivative} DF (\xi)= g (\xi),\eea …

On quantum versions of the classical Wasserstein distance

J Agredo, F Fagnola - Stochastics, 2017 - Taylor & Francis

We investigate a definition of quantum Wasserstein distance of two states based on their

couplings on the product algebra as in the classical case. A detailed analysis of the two

qubit model leads to a formal definition fulfilling some minimal requirements. It also shows …

Regularized barycenters in the Wasserstein space

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

This paper is an overview of results that have been obtain in 2 on the convex regularization

of Wasserstein barycenters for random measures supported on\mathbb R^ d. We discuss

the existence and uniqueness of such barycenters for a large class of regularizing functions …

Effective Lipschitz constraint enforcement for Wasserstein GAN training

S Cui, Y Jiang - 2017 2nd IEEE International Conference on …, 2017 - ieeexplore.ieee.org

Generative Adversarial Networks (GANs) are efficient frameworks for estimating generative

model via adversarial process. However, GAN has known for suffering from training

instability. Wasserstein GAN (WGAN) improves the training stability significantly but also …

2017

Wasserstein identity testing

S Deng, W Li, X Wu - arXiv preprint arXiv:1710.10457, 2017 - arxiv.org

Uniformity testing and the more general identity testing are well studied problems in

distributional property testing. Most previous work focuses on testing under $ L_1 $-

distance. However, when the support is very large or even continuous, testing under $ L_1 …

[PDF] Wasserstein distance on finite spaces: Statistical inference and algorithms

M Sommerfeld - 2017 - d-nb.info

Wasserstein distances or, more generally, distances that quantify the optimal transport

between probability measures on metric spaces have long been established as an important

tool in probability theory. More recently, it has found its way into statistical theory …

[HTML] Energy-relaxed Wasserstein gans (energywgan): towards more stable and high resolution image generation

J Wu, Z Huang, J Thoma, L Van Gool - arXiv preprint arXiv:1712.01026, 2017 - deepai.org

2 Background Imagine there are two players in a game. One player (Generator) intends to generate visually plausible images, aiming to fool its opponent, while the opponent (Discriminator) attempts to discriminate real images from synthetic images. Such adversarial …

[HTML] Manifold-valued image generation with wasserstein adversarial networks

EW GANs - 2017 - deepai.org

Unsupervised image generation has recently received an increasing amount of attention thanks

to the great success of generative adversarial networks (GANs), particularly Wasserstein

GANs. Inspired by the paradigm of real-valued image generation, this paper makes the first attempt …

An intrinsic parallel transport in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact connected Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. We describe a geometric construction

of parallel transport of some tangent cones along geodesics in $ P (M) $. We show that …

<——2017———————2017 —— 270 —

A simulated annealing based inexact oracle for Wasserstein loss minimization

J Ye, JZ Wang, J Li - International Conference on Machine …, 2017 - proceedings.mlr.press

Learning under a Wasserstein loss, aka Wasserstein loss minimization (WLM), is an

emerging research topic for gaining insights from a large set of structured objects. Despite

being conceptually simple, WLM problems are computationally challenging because they …

Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to Fluid Equations

K Kang, HK Kim - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider a coupled system of Keller--Segel-type equations and the incompressible

Navier--Stokes equations in spatial dimension two and three. We first establish the existence

of a weak solution of a Fokker--Plank equation in the Wasserstein space under the …

Generalized Wasserstein distance and weak convergence of sublinear expectations

X Li, Y Lin - Journal of Theoretical Probability, 2017 - Springer

Recently, Peng establishes a theory of time-consistent sublinear expectations in [5, 6], ie, the

G-expectation theory. This new theory provides with several important models and tools for studying

robust hedging and utility maximization problems in the financial markets under Knightian uncertainty …

Absolute continuity of Wasserstein barycenters over Alexandrov spaces

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we prove that on a compact, $ n $-dimensional Alexandrov space with

curvature at least− 1, the Wasserstein barycenter of Borel probability measures ${{\mu} _

{1}},\ldots,{{\mu} _ {m}} $ is absolutely continuous with respect to the $ n $-dimensional …

Hyperspectral and multispectral Wasserstein barycenter for image fusion

J Mifdal, B Coll, N Courty, J Froment… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

The fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows

the extraction of relevant information from the fused image. Fusion consists of the

2017

[PDF] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - core.ac.uk

This work studies the problem of statistical inference for Fréchet means in the Wasserstein

space of measures on Euclidean spaces, W2 (Rd). This question arises naturally from the

problem of separating amplitude and phase variation in point processes, analogous to a …

Fréchet means in Wasserstein space

[CITATION] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - Ecole Polytechnique Fédérale de …

Y Zemel - 2017 - infoscience.epfl.ch

… This work studies the problem of statistical inference for Fréchet means in the Wasserstein … Our techniques are specific to the Wasserstein space, because Hessian-type arguments …

[PDF] Quantum Wasserstein-1 Distance

Y Chen, TT Georgiou, L Ning… - arXiv preprint arXiv …, 2017 - researchgate.net

In this note, we propose an extension of the Wasserstein 1-metric (W1) for matrix probability

densities, matrix-valued density measures, and an unbalanced interpretation of mass

transport. The key is using duality theory, in particular, a “dual of the dual” formulation of W1 …

15 Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

F Al Reda, B Maury - … Optimization and Optimal Transport: In the …, 2017 - books.google.com

This paper establishes a link between some space discretization strategies of the finite

volume type for the Fokker–Planck equation in general meshes (Voronoï tesselations) and

gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein …

2017

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

A Robust Learning Algorithm for Regression Models Using Distributionally Robust Optimization under the Wasserstein Metric

R Chen, IC Paschalidis - arXiv preprint arXiv:1706.02412, 2017 - arxiv.org

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified

regression plane in a linear regression setting, when the observed samples are potentially

contaminated with adversarially corrupted outliers. Our approach mitigates the impact of …

<—2017———2017———————— 280 —

Wasserstein distance and the rectifiability of doubling measures: part II

J Azzam, G David, T Toro - Mathematische Zeitschrift, 2017 - Springer

We study the structure of the support of a doubling measure by analyzing its self-similarity

properties, which we estimate using a variant of the$L^ 1$ Wasserstein distance. We show

that a measure satisfying certain self-similarity conditions admits a unique (up to …

Dimension-free Wasserstein contraction of nonlinear filters

N Whiteley - arXiv preprint arXiv:1708.01582, 2017 - arxiv.org

For a class of partially observed diffusions, sufficient conditions are given for the map from

initial condition of the signal to filtering distribution to be contractive with respect to

Wasserstein distances, with rate which has no dependence on the dimension of the state …

Posterior contraction in Gaussian process regression using Wasserstein approximations

A Bhattacharya, D Pati - Information and Inference: A Journal of …, 2017 - academic.oup.com

We study posterior rates of contraction in Gaussian process regression with potentially

unbounded covariate domain. Our argument relies on developing a Gaussian

approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of …

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting

C Grimm, Y Song, ML Littman - arXiv preprint arXiv:1709.06533, 2017 - arxiv.org

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving

density estimation problems---using data to assess how likely samples are to be drawn from

the same distribution. Instead of explicitly computing these probabilities, GANs learn a …

Aggregated Wasserstein Metric and State Registration for Hidden Markov Models

Y Chen, J Ye, J Li - arXiv preprint arXiv:1711.05792, 2017 - arxiv.org

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time position follows a …

On reproduction of On the regularization of Wasserstein GANs

J Seo, T Jeon - arXiv preprint arXiv:1712.05882, 2017 - arxiv.org

This report has several purposes. First, our report is written to investigate the reproducibility

of the submitted paper On the regularization of Wasserstein GANs (2018). Second, among

the experiments performed in the submitted paper, five aspects were emphasized and …

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

Cited by 62 Related articles

[PDF] WASSERSTEIN k-MEANS+ HISTOGRAM CLUSTERING

M Staib, S Jegelka - NCAR Technical Notes NCAR/TN536+ PROC - par.nsf.gov

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

kmeans clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

Wasserstein GAN

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017 - arxiv.org

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In

this new model, we show that we can improve the stability of learning, get rid of problems

like mode collapse, and provide meaningful learning curves useful for debugging and …

[CITATION] Wasserstein gan (2017)

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017 - Available

[CITATION] Wasserstein gan

A Martin, C Soumith, B Léon - arXiv preprint arXiv:1701.07875, 2017

[CITATION] Wasserstein gan. arXiv preprint arXiv: 170107875

M Arjovsky, S Chintala, L Bottou - 2017

[PDF] optimization-online.org

[PDF] Distributionally robust reward–risk ratio programming with Wasserstein metric

Y Zhao, Y Liu, J Zhang, X Yang - 2017 - optimization-online.org

Reward-risk ratio (RR) is a very important stock market definition. In order to capture the

situation that the investor does not have complete information on the distribution of the

underlying uncertainty, people extend RR model to distributionally robust reward-risk ratio …

<——2017———————2017 —— 290 —

Exponential convergence in the Wasserstein metric for one dimensional diffusions

L Cheng, R Li, L Wu - arXiv preprint arXiv:1703.00507, 2017 - arxiv.org

In this paper, we find some general and efficient sufficient conditions for the exponential

convergence $ W_ {1, d}(P_t (x,\cdot), P_t (y,\cdot))\le Ke^{-\delta t} d (x, y) $ for the

semigroup $(P_t) $ of one-dimensional diffusion. Moreover some sharp estimates of the …

The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality

V Barbu - SIAM Journal on Control and Optimization, 2017 - SIAM

The nonlinear diffusion equation \rho_t-Δ(ρH(ρ-\rho_c))=0 in (0,∞)*R^n, ρ(0,x)=\rho_0(x),

where H is the Heaviside function, describes the sandpile model P. Bak, C. Tang, and K.

Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and IM Janosi, Phys. A, 185 (1992) …

2017 [PDF] arxiv.org

Reversible coalescing-fragmentating Wasserstein dynamics on the real line

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1709.02839, 2017 - arxiv.org

We introduce a family of reversible fragmentating-coagulating processes of particles of

varying size-scaled diffusivity with strictly local interaction on the real line. The construction

is based on a new family of measures on the set of real increasing functions as reference …

Tractable Wasserstein Learning of Generative Models

https://www.semanticscholar.org › paper › Sinkhorn-Auto...

Jun 1, 2017 — This paper presents the first tractable computational method to train large scale generative models using an optimal transport loss, .

[CITATION] Sinkhorn-autodiff: Tractable Wasserstein learning of generative models

A Genevay, G Peyré, M Cuturi - arXiv preprint arXiv:1706.00292, 2017

Cited by 27 Related articles

Ambiguity set and learning via Bregman and Wasserstein

X Guo, J Hong, N Yang - arXiv preprint arXiv:1705.08056, 2017 - arxiv.org

Construction of ambiguity set in robust optimization relies on the choice of divergences

between probability distributions. In distribution learning, choosing appropriate probability

distributions based on observed data is critical for approximating the true distribution. To …

2017

[PDF] rwth-aachen.de

[PDF] Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

M Kampschulte, M Westdickenberg, RL Jerrard… - 2017 - publications.rwth-aachen.de

The main aim of this thesis is to explore a possible approach to gradient flows for Cartesian

(and other) currents. We will do so using the method of minimizing movements. The key

ingredient for this turns out to be the right choice of metric. For this we propose a …

[PDF] cnrs.fr

[PDF] Wasserstein Dictionary Learning

MA Schmitz, M Heitz, N Bonneel, F Ngolè, D Coeurjolly… - perso.liris.cnrs.fr

Page 1. Wasserstein Dictionary Learning Morgan A. Schmitz * , Matthieu Heitz, Nicolas Bonneel,

Fred Ngolè, David Coeurjolly, Marco Cuturi, Gabriel Peyré, Jean-Luc Starck * * CosmoStat,

Astrophysics Dept., IRFU, CEA Saclay | morgan.schmitz@cea.fr Introduction • Optimal Transport …

[PDF] A particle model for Wasserstein type diffusion

V Konarovskyi, M von Renesse - math.uni-leipzig.de

A particle model for Wasserstein type diffusion … ∂tµt = β 2 ∆µt + ∇ · ( µt∇ δF(µt) δµt … –

Dean-Kawasaki equation The equation appears in macroscopic fluctuation theory and glass

dynamic models D. Dean '96, K. Kawasaki, E. Vanden-Eijnden, A. Donev, B. Derrida, J …

Gradient flows in uncertainty propagation and filtering of linear Gaussian systems

[PDF] The WASSERSTEIN DISTANCE AS A UNIVARIATE NEUROIMAGING BIOMARKER FOR FDG-PET ANALYSIS

L Mi, W Zhang, J Zhang, Y Fan, D Goradia, K Chen… - gsl.lab.asu.edu

We propose a univariate biomarker of the FDGPET images by using the Wasserstein

distance. We apply the biomarker to the Alzheimer's disease (AD) analysis. The

experimental results demonstrate the robustness of our biomarker in distinguishing AD from …

A Halder, TT Georgiou - 2017 IEEE 56th Annual Conference …, 2017 - ieeexplore.ieee.org

The purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop …

<——2017———————2017 —— 300 —

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

[PDF] gatech.edu

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too

large and complex for easy computation. Because continuous transport problems are

generally solved by conversion to either discrete or semi-discrete forms, I focused on …

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

In this paper we derive a formula for the sample size of a nonparametric test based on

weighted L 2-Wasserstein distance with a known alternative. As an example we apply the

formula to determine the sample size for a hypothesis testing from the Tukey's contaminated …

Coalescing-fragmentating Wasserstein dynamics: particle approach

2017 [PDF] arxiv.org

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - arxiv.org

We construct a family of semimartingales which describe the behavior of a particle system

with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warren

flow, an infinite system of diffusion particles on the real line which sticky-reflect from each …

2017

Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction

X CAO, Y XIN - Journal of Computer Applications, 2017 - en.cnki.com.cn

Dimensionality reduction plays an important role in big data analysis and visualization.

Many dimensionality reduction techniques with probabilistic distribution models rely on the

optimizaition of cost function between low-dimensional model distribution and high …

[CITATION] Wasserstein Training of Deep Boltzmann Machines

C Wang, T Tong, Y Zou

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Y Tin Chow, W Gangbo - arXiv, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on he Wasserstein space

[PDF] An Informal Introduction to the Maths Behind Wasserstein GAN

Q Bai - 2017 - pdfs.semanticscholar.org

Briefly speaking,[1] explains from a theoretical perspective why training GAN is hard, and [2]

suggests a solution from the perspective of geometric foundation of generative modeling,

which is more fundamental than GAN itself. The algorithm suggested by [2] ends up being …

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a

variational model for nonuniform illumination correction, that incorporates a penalty term that …

A degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

<——2017———————2017 —— 310 —

2017 see 2019

C CANCES - dogbe.users.lmno.cnrs.fr

We derive a phase field model for incompressible immiscible two-phase flows as the

Wasserstein gradient flow of the Cahn-Hilliard energy. The cost of each phase motion is

related to a classical squared Wasserstein distance, and a constraint enforces the sum of the …

[CITATION] A degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

[CITATION] A degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

by I Gulrajani · 2017 · Cited by 4532 — Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only low-quality samples or fail to converge.

[CITATION] Improved training of Wasserstein GANs. arXiv e-prints

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - Online

[CITATION] Improved training of wasserstein GANs. ArXiv e-prints (2017)

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017

[CITATION] Improved training of wasserstein gans. CoRR abs/1704.00028 (2017)

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - pdfs.semanticscholar.org

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

A Stochastic gradient method to compute Wasserstein barycenters of distributions

2017

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

D Cheng, KA Okoudjou - Wavelets and Sparsity XVII, 2017 - spiedigitallibrary.org

It is known in the standard l 2 distance that the closest Parseval frame to a given frame {Φ i}

mi= 1⊂ ℜ d is {S-1/2 (Φ i)} mi= 1 where S is the frame operator of the original frame. We

show this is also the case for probabilistic frames in the 2-Wasserstein distance. In the …

Finding the closest probabilistic Parseval frame in the 2-Wasserstein ...

- by D Cheng - ‎2017 - ‎Related articles

We show this is also the case for probabilistic frames in the 2-Wasserstein .....
Aug 24, 2017

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that

involves identifying differences between two random variables without making parametric

assumptions about their underlying distributions. The literature is old and rich, with a wide …

2017

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

In this paper we derive a formula for the sample size of a nonparametric test based on

weighted L 2-Wasserstein distance with a known alternative. As an example we apply the

formula to determine the sample size for a hypothesis testing from the Tukey's contaminated …

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN

method is proposed based on LBP features and entropy-regularized Wasserstein distance,

by combining the mathematical properties of Wasserstein distance in optimal mass …

<——2017———————2017 —— 320—

[PDF] SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole, D Coeurjolly… - perso.liris.cnrs.fr

SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based

unsupervised non-linear dictionary learning∗ … Morgan A. Schmitz† , Matthieu Heitz‡ , Nicolas

Bonneel‡ , Fred Ngol`e§ , David Coeurjolly‡ , Marco Cuturi¶, Gabriel Peyré , and Jean-Luc …

[CITATION] Distributionally

Wasserstein GAN [C/OL]DC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao, J Liu - arXiv preprint arXiv:1706.05538, 2017

[CITATION] Wasserstein GAN. CoRR abs/1701.07875 (2017)

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017

Sharp asymptotic and finite-sample rates of convergence of ...

ttps://arxiv.org › cs

Learning to solve inverse problems using Wasserstein loss

by J Adler · 2017 · Cited by 27 — We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme ...

[CITATION] Learning to solve inverse problems using Wasserstein loss, ArXiv, 1710.10898 (2017)

J Adler, A Ringh, O Öktem, J Karlsson - Poster in NIPS, 2017

by J Weed · 2017 · Cited by 171 — Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning.

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary

1 August 2017

α-dependent sequences

Jérôme Dedecker, Florence Merlevède

Bernoulli Vol. 23, Issue 3 (Aug 2017), pg(s) 2083-2127

KEYWORDS: central limit theorem, empirical process, Intermittency, moments inequalities, Stationary sequences, Wasserstein distance

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN

method is proposed based on LBP features and entropy-regularized Wasserstein distance,

by combining the mathematical properties of Wasserstein distance in optimal mass …

2017

Sampling of probability measures in the convex order by Wasserstein projection - Project Euclid

https://projecteuclid.org › euclid.aihp

by A Alfonsi · 2020 · Cited by 19 — We prove convergence of the Wasserstein projection based sampling methods as the sample sizes tend to infinity and illustrate them by numerical experiments.

Submission history

From: Aurelien Alfonsi [view email]

[v1] Fri, 15 Sep 2017 16:00:08 UTC (249 KB)

[v2] Thu, 16 Nov 2017 13:46:26 UTC (327 KB)

[v3] Fri, 8 Feb 2019 09:10:45 UTC (218 KB)

[CITATION] Sampling of probability measures in the convex order by Wasserstein projection. arXiv e-prints, page

A Alfonsi, J Corbetta, B Jourdain - arXiv preprint arXiv:1709.05287, 2017

A Central Limit Theorem for Wasserstein type distances between two different laws

2017 [PDF] arxiv.org

P Berthet, JC Fort, T Klein - arXiv preprint arXiv:1710.09763, 2017 - arxiv.org

… the distance between two different distributions with respect to a class of Wasserstein costs

… From these samples we estimate the Wasserstein distances or costs between F and G and …

A framework for Wasserstein-1-type metrics

B Schmitzer, B Wirth - arXiv preprint arXiv:1701.01945, 2017 - arxiv.org

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy

measure between nonnegative measures of different mass. This generalization inherits the

convexity and computational efficiency from the Wasserstein-1 metric, and it includes …

基于 Wasserstein 距离和分裂 Bregman 方法的图像分割算法

王瑜，闫沫 - 电子设计工程, 2017 - cqvip.com

针对基于CV 模型的活动轮廓分割算法无法应用于灰度非均匀图像分割的问题.

采用Wasserstein 距离作为区域直方图相似性测度, 提出基于该测度的非参数活动轮廓分割模型.

在模型求解时引入全局凸分割和分裂Bregman 方法, 减少了计算量. 大量实验结果表明该模型不 …

[Chinese Image segmentation algorithm based on Wasserstein distance and split Bregman method]

<——2017———————2017 —— 330—

inference with Wasserstein distance | Xi'an's Og

... use of the Wasserstein distance in statistical inference, which main focus is exploiting this ... Which is why ...

Jan 23, 2017

[PDF] asso-afig.fr

[CITATION] Barycentres de Wasserstein pour les diagrammes de persistance

J Tierny

Approximation of stable law in Wasserstein-1 distance by Stein's method. Accepted by Annals of Applied Probability

L Xu - arXiv preprint arXiv:1709.00805, 2017

[CITATION] Approximation of stable law in Wasserstein-1 distance by Stein's method. Accepted by Annals of Applied Probability

L Xu - arXiv preprint arXiv:1709.00805, 2017

multivariate CLT in Wasserstein distance with near optimal ...

2017

https://www.researchgate.net › ... › Convergence

A multivariate CLT in Wasserstein distance with near optimal convergence rate ... Authors: Alex Zhai ... March 2017 · Probability Theory and Related Fields.

2017

Sharp asymptotic and finite-sample rates of ... - NASA/ADS

https://ui.adsabs.harvard.edu › abs › abstract

by J Weed · 2017 · Cited by 171 — The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine ...

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

rongly Polynomial 2-Approximations of Discrete ...

https://www.researchgate.net › ... › Polynomials

Download Citation | Strongly Polynomial 2-Approximations of Discrete Wasserstein Barycenters | Wasserstein barycenters correspond to optimal solutions of ...

[CITATION] Strongly Polynomial 2-Approximations for Discrete Wasserstein Barycenters. eprint

S Borgwardt - arXiv preprint arXiv:1704.05491, 2017

Cited by 2 Related article

Evolution of the Wasserstein distance between the marginals ...

https://project.inria.fr › files › 2017/04 › jourdainsophia

Mar 31, 2017 — Evolution of the Wasserstein distance between the marginals of two Markov processes. Benjamin Jourdain (ENPC CERMICS and INRIA ...

[CITATION] Evolution of the Wasserstein distance between the marginals of two Markov processes

J Corbetta - 2017 see 2016 and 2018

(PDF) Correcting Nuisance Variation using Wasserstein ...

https://www.researchgate.net › publication › 320867145_...

Nov 2, 2017 — Correcting Nuisance Variation using Wasserstein Distance ... Removal of batch eﬀects using distribution-matching residual networks.

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Davis, G Tabak, M Fan, S Yang, S Hoyer - 2017

[res and entropy regularization Wasserstein distance]

焦艳艳 - 2017 - cdmd.cnki.com.cn

随着科学技术的飞速发展及3D 技术的提高, 人们在数据采集和图形建模领域取得了很大的进步.

基于数字分析的应用领域有很多, 如: 分子生物学, 人脸识别, 模式识别等.

图形匹配是计算机视觉, 计算机图形学, 机器人学等领域的基本问题之一, 也是数字分析的重要 …
[Chinese 3D graphics matching method based on Gromov-Wasserstein distance]

[PDF] 709journal.com

[PDF] 基于 LBP 特征和熵正则化 Wasserstein 距离的人脸表情识别

郑昌金，章登义，苏科华，武小平，洪程 - 计算机与数字工程, 2017 - jsj.709journal.com

摘! 要! 针对U 最近邻分类中相似度量的量化问题# 结合最优传输理论中G3CC-. C,-16

距离数学特性# 提出G 种基于WR@ 特征和正则化G3CC-. C,-16 距离的U 近邻分类方法$

首先对人脸表情图像进行预处理# 然后使用WR@ 算子对图像进行特征提取获得WR …

[PDF] 基于 Wasserstein 距离概率分布模型的非线性降维

曹小鹿，辛云宏 - 计算机应用, 2017 - joca.cn

降维是大数据分析和可视化领域中的核心问题, 其中基于概率分布模型的的降维算法通过最优化

高维数据模型和低维数据模型之间的代价函数来实现降维. 这种策略的核心在于构建最能体现

数据特征的概率分布模型. 基于此, 本文将Wasserstein 距离引入降维, 提出一个基于 …

[Chinese Nonlinear dimensionality reduction based on Wasserstein distance probability distribution model[

<——2017—————2017 ——340—

2017 zzz 32

[CITATION] RATIONALES WITH WASSERSTEIN GANS

T LIKE

Geodesic PCA in the Wasserstein space by convex PCA

J Bigot, R Gouet, T Klein, A López - Annales de l'Institut Henri …, 2017 - projecteuclid.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

Aggregated Wasserstein Metric and State Registration for Hidden Markov Models

Y Chen, J Ye, J Li - arXiv preprint arXiv:1711.05792, 2017 - arxiv.org

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time position follows a …

Posterior contraction in Gaussian process regression using Wasserstein approximations

A Bhattacharya, D Pati - Information and Inference: A Journal of …, 2017 - academic.oup.com

We study posterior rates of contraction in Gaussian process regression with potentially

unbounded covariate domain. Our argument relies on developing a Gaussian

approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of …
Cited by 5 Related articles All 4 versions

Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

We study barycenters in the space of probability measures on a Riemannian manifold,

equipped with the Wasserstein metric. Under reasonable assumptions, we establish

absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on Wasserstein …

2017

Wasserstein GAN and the Kantorovich-Rubinstein Duality

Feb 24, 2017 — This is our case of the Kantorovich-Rubinstein duality. It actually holds for other metrics than just the Euclidian metric we used. But the ...

[CITATION] Wasserstein gan and the kantorovich-rubinstein duality

V Herrmann - … : https://vincentherrmann. github. io/blog/wasserstein, 2017

Wasserstein GAN and the Kantorovich-Rubinstein Duality ...

https://vincentherrmann.github.io › blog › wasserstein

Feb 24, 2017 — Wasserstein GAN and the Kantorovich-Rubinstein Duality ... For discrete probability distributions, the Wasserstein distance is also descriptively ...

[CITATION] Wasserstein gan and the kantorovich-rubinstein duality

V Herrmann - … : https://vincentherrmann. github. io/blog/wasserstein, 2017

15 Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

F Al Reda, B Maury - … Optimization and Optimal Transport: In the …, 2017 - books.google.com

This paper establishes a link between some space discretization strategies of the finite

volume type for the Fokker–Planck equation in general meshes (Voronoï tesselations) and

gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein …

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

2017

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

<--—2017————2017——- 350-

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Nonlinear sigma models are quantum field theories describing, in the large deviation sense,

random fluctuations of harmonic maps between a Riemann surface and a Riemannian

manifold. Via their formal renormalization group analysis, they provide a framework for …

Effective Lipschitz constraint enforcement for Wasserstein GAN training

S Cui, Y Jiang - 2017 2nd IEEE International Conference on …, 2017 - ieeexplore.ieee.org

Generative Adversarial Networks (GANs) are efficient frameworks for estimating generative

model via adversarial process. However, GAN has known for suffering from training

instability. Wasserstein GAN (WGAN) improves the training stability significantly but also …

[PDF] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - core.ac.uk

This work studies the problem of statistical inference for Fréchet means in the Wasserstein

space of measures on Euclidean spaces, W2 (Rd). This question arises naturally from the

problem of separating amplitude and phase variation in point processes, analogous to a …

Fréchet means in Wasserstein space

2017

Y Zemel - 2017 - infoscience.epfl.ch

This work studies the problem of statistical inference for Fréchet means in the Wasserstein

space of measures on Euclidean spaces, W2 (Rd). This question arises naturally from the

problem of separating amplitude and phase variation in point processes, analogous to a …

2017

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

A partial Laplacian as an infinitesimal generator on the Wasserstein space

2017

Y Tin Chow, W Gangbo - arXiv, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

2017

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Nonlinear sigma models are quantum field theories describing, in the large deviation sense,

random fluctuations of harmonic maps between a Riemann surface and a Riemannian

manifold. Via their formal renormalization group analysis, they provide a framework for …

2017

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

<——2017———————2017 —— 360—

2017

A simulated annealing based inexact oracle for Wasserstein loss minimization

J Ye, JZ Wang, J Li - International Conference on Machine …, 2017 - proceedings.mlr.press

Learning under a Wasserstein loss, aka Wasserstein loss minimization (WLM), is an

emerging research topic for gaining insights from a large set of structured objects. Despite

being conceptually simple, WLM problems are computationally challenging because they …

2017

Wasserstein learning of deep generative point process models

S Xiao, M Farajtabar, X Ye, J Yan, L Song… - Advances in neural …, 2017 - papers.nips.cc

Point processes are becoming very popular in modeling asynchronous sequential data due

to their sound mathematical foundation and strength in modeling a variety of real-world

phenomena. Currently, they are often characterized via intensity function which limits …

2017

Weakly supervised audio source separation via spectrum energy preserved wasserstein learning

N Zhang, J Yan, Y Zhou - arXiv preprint arXiv:1711.04121, 2017 - arxiv.org

Separating audio mixtures into individual instrument tracks has been a long standing

challenging task. We introduce a novel weakly supervised audio source separation

approach based on deep adversarial learning. Specifically, our loss function adopts the …

Fast discrete distribution clustering using Wasserstein barycenter with sparse support

J Ye, P Wu, JZ Wang, J Li - IEEE Transactions on Signal …, 2017 - ieeexplore.ieee.org

In a variety of research areas, the weighted bag of vectors and the histogram are widely

used descriptors for complex objects. Both can be expressed as discrete distributions. D2-

clustering pursues the minimum total within-cluster variation for a set of discrete distributions …

2017 [PDF] archives-ouvertes.fr

Hyperspectral and multispectral Wasserstein barycenter for image fusion

J Mifdal, B Coll, N Courty, J Froment… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

The fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows

the extraction of relevant information from the fused image. Fusion consists of the

combination of the spectral information of the hypespectral image (h) and the spatial …

Existence and consistency of Wasserstein barycenters

T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual

notion of statistical mean. We prove the existence of Wasserstein barycenters of random

probabilities defined on a geodesic space (E, d). We also prove the consistency of this …

2017 [PDF] nips.cc

Parallel streaming Wasserstein barycenters

M Staib, S Claici, JM Solomon… - Advances in Neural …, 2017 - papers.nips.cc

Efficiently aggregating data from different sources is a challenging problem, particularly

when samples from each source are distributed differently. These differences can be

inherent to the inference task or present for other reasons: sensors in a sensor network may …

Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

We study barycenters in the space of probability measures on a Riemannian manifold,

equipped with the Wasserstein metric. Under reasonable assumptions, we establish

absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on Wasserstein …

2017 [PDF] researchgate.net

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

Absolute continuity of Wasserstein barycenters over Alexandrov spaces

2017

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we prove that on a compact, $ n $-dimensional Alexandrov space with

curvature at least− 1, the Wasserstein barycenter of Borel probability measures ${{\mu} _

{1}},\ldots,{{\mu} _ {m}} $ is absolutely continuous with respect to the $ n $-dimensional …

Strongly Polynomial 2-Approximations of Discrete Wasserstein ...

www.researchgate.net › publication › 316270669_Strongl...

Download Citation | Strongly Polynomial 2-Approximations of Discrete Wasserstein Barycenters | Wasserstein barycenters correspond to optimal solutions of ...

Strongly Polynomial 2-Approximations of Discrete ...

www.semanticscholar.org › paper › Strongly-Polynomial-...

Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, which arise in a wide range of fields. In many ...

.CITATION] Strongly Polynomial 2-Approximations for Discrete Wasserstein Barycenters.

eprint

S Borgwardt - arXiv preprint arXiv:1704.05491, 2017

[CITATION] Strongly polynomial 2-approximations of discrete Wasserstein barycenters

S Borgwardt - arXiv preprint arXiv:1704.05491, 2017
Cite Cited by 5 Related articles

year 2017

[CITATION] Strongly polynomial 2-approximations of discrete Wasserstein barycenters

S Borgwardt - arXiv preprint arXiv:1704.05491, 2017

Strongly polynomial 2-approximations of discrete wasserstein barycenters

year 2017 [PDF] nfu.edu.tw

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

… Hence, we proposed some different machine learning approaches for analyzing multivalued

data. We transform daily weather data into a distribution-valued data and histogram data then

adopt a Wasserstein-based distance for weather distribution-valued data …

Related articles
<——2017———————2017 —— 380—

2017 [PDF] core.ac.uk

[PDF] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - core.ac.uk

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces, W2 (Rd). This question arises naturally from the problem of separating amplitude and phase variation in point processes, analogous to a …

[CITATION] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - Ecole Polytechnique Fédérale de …

Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to Fluid Equations

2017

K Kang, HK Kim - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider a coupled system of Keller--Segel-type equations and the incompressible Navier--Stokes equations in spatial dimension two and three. We first establish the existence of a weak solution of a Fokker--Plank equation in the Wasserstein space under the …

2017 zzz 33 see 2015 2018

[CITATION] Differential forms and symplectic geometry on Wasserstein space

T Pacini - 2012 - open.library.ubc.ca

2017 zzz 34 see 2018

[CITATION] Wide Consensus aggregation in the Wasserstein Space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2017

[CITATION] Wide Consensus aggregation in the Wasserstein Space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2017

see 2015, 2018

Extremal curves in Wasserstein space

G Conforti, M Pavon - International Conference on Geometric Science of …, 2017 - Springer

We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges

and the classic Madelung fluid can be derived from variational principles on Wasserstein

space. The second order differential equations are accordingly obtained by annihilating the …

2017

Information geometry of wasserstein divergence

R Karakida, S Amari - International Conference on Geometric Science of …, 2017 - Springer

There are two geometrical structures in a manifold of probability distributions. One is invariant, based on the Fisher information, and the other is based on the Wasserstein distance of optimal transportation. We propose a unified framework which connects the …

2017

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Dimension-free Wasserstein contraction of nonlinear filters

N Whiteley - arXiv preprint arXiv:1708.01582, 2017 - arxiv.org

For a class of partially observed diffusions, sufficient conditions are given for the map from

initial condition of the signal to filtering distribution to be contractive with respect to

Wasserstein distances, with rate which has no dependence on the dimension of the state …

Wasserstein Convergence Rate for Empirical Measures on Noncompact Manifolds

FY Wang - arXiv preprint arXiv:2007.14667, 2020 - arxiv.org

Let $ X_t $ be the (reflecting) diffusion process generated by $ L:=\Delta+\nabla V $ on a

complete connected Riemannian manifold $ M $ possibly with a boundary $\partial M $,

where $ V\in C^ 1 (M) $ such that $\mu (dx):= e^{V (x)} dx $ is a probability measure. We …

2017

Matricial wasserstein-1 distance

Y Chen, TT Georgiou, L Ning… - IEEE control systems …, 2017 - ieeexplore.ieee.org

We propose an extension of the Wasserstein 1-metric (W 1) for density matrices, matrix-

valued density measures, and an unbalanced interpretation of mass transport. We use

<——2017———————2017 —— 390———

2017 [PDF] researchgate.net

[PDF] Quantum Wasserstein-1 Distance

Y Chen, TT Georgiou, L Ning… - arXiv preprint arXiv …, 2017 - researchgate.net

In this note, we propose an extension of the Wasserstein 1-metric (W1) for matrix probability

densities, matrix-valued density measures, and an unbalanced interpretation of mass

transport. The key is using duality theory, in particular, a “dual of the dual” formulation of W1 …

1 Related articles

2017

Approximation of stable law in Wasserstein-1 distance by ...

by L Xu · 2017 · Cited by 19 — Approximation of stable law in Wasserstein-1 distance by Stein's method. can be interpreted as an L^{1} Stein discrepancy. As an application, we prove a general theorem of stable law convergence rate when \zeta_{n,i} are i.i.d. and the distribution falls in the normal domain of attraction of \mu.

[CITATION] Approximation of stable law in Wasserstein-1 distance by Stein's method. Accepted by Annals of Applied Probability

L Xu - arXiv preprint arXiv:1709.00805, 2017

Information geometry of wasserstein divergence

2017

R Karakida, S Amari - International Conference on Geometric Science of …, 2017 - Springer

There are two geometrical structures in a manifold of probability distributions. One is

invariant, based on the Fisher information, and the other is based on the Wasserstein

distance of optimal transportation. We propose a unified framework which connects the …

L Xu - arXiv preprint arXiv:1709.00805, 2017

Sliced wasserstein kernel for persistence diagrams

M Carriere, M Cuturi, S Oudot - arXiv preprint arXiv:1706.03358, 2017 - arxiv.org

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they

are routinely used to describe topological properties of complicated shapes. PDs enjoy

strong stability properties and have proven their utility in various learning contexts. They do …

[CITATION] Sliced Wasserstein Kernel for Persistence Diagrams

S Oudot - ICML, 2017 - openreview.net

OpenReview is created by the Information Extraction and Synthesis Laboratory, College of Information

and Computer Science, University of Massachusetts Amherst. We gratefully acknowledge the

support of the OpenReview sponsors: Google, Facebook, NSF, the University of Massachusetts …

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

B Kloeckner - Journal of Topology and Analysis, 2012 - World Scientific

A Wasserstein space is a metric space of sufficiently concentrated probability measures over

a general metric space. The main goal of this paper is to estimate the largeness of

Wasserstein spaces, in a sense to be made precise. In the first part, we generalize the …

2017

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

A framework for Wasserstein-1-type metrics

B Schmitzer, B Wirth - arXiv preprint arXiv:1701.01945, 2017 - arxiv.org

… 1 Introduction 1.1 Motivation Optimal transport and Wasserstein metrics are becoming

increasingly popular tools in many applied fields … A significant practical limitation of

Wasserstein metrics is their high naive computational complexity …

Generalized Wasserstein distance and weak convergence of sublinear expectations

X Li, Y Lin - Journal of Theoretical Probability, 2017 - Springer

Recently, Peng establishes a theory of time-consistent sublinear expectations in [5, 6], ie, the

G-expectation theory. This new theory provides with several important models and tools for studying

robust hedging and utility maximization problems in the financial markets under Knightian uncertainty …

2017 [PDF] rwth-aachen.de

[PDF] Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

M Kampschulte, M Westdickenberg, RL Jerrard… - 2017 - publications.rwth-aachen.de

The main aim of this thesis is to explore a possible approach to gradient flows for Cartesian

(and other) currents. We will do so using the method of minimizing movements. The key

ingredient for this turns out to be the right choice of metric. For this we propose a …

Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - Advances in Neural Information Processing …, 2017 - papers.nips.cc

We introduce a novel framework for statistical analysis of populations of non-degenerate

Gaussian processes (GPs), which are natural representations of uncertain curves. This

allows inherent variation or uncertainty in function-valued data to be properly incorporated in …

Cited by 34 Related articles All 6 versions
<——2017———————2017 ——— 400—

Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

çƒ√Wasserstein space

J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658, 2017 - arxiv.org

In this paper, we consider a probabilistic setting where the probability measures are

considered to be random objects. We propose a procedure of construction non-asymptotic

confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea …

2017

D Cheng, KA Okoudjou - Wavelets and Sparsity XVII, 2017 - spiedigitallibrary.org

It is known in the standard l 2 distance that the closest Parseval frame to a given frame {Φ i}

mi= 1⊂ ℜ d is {S-1/2 (Φ i)} mi= 1 where S is the frame operator of the original frame. We

show this is also the case for probabilistic frames in the 2-Wasserstein distance. In the …

2017

Construction of non-asymptotic confidence sets in 2-Wasserstein space

J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658, 2017 - arxiv.org

In this paper, we consider a probabilistic setting where the probability measures are

considered to be random objects. We propose a procedure of construction non-asymptotic

confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea …

[CITATION] Construction of non-asymptotic confidence sets in 2-Wasserstein space (2017)

J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658

Разложения типа Денниса–Васерштейна

НА Вавилов, СС Синчук - Записки научных семинаров ПОМИ, 2010 - mathnet.ru

В работе доказывается обобщение разложения Денниса–Васерштейна для

произвольной пары максимальных параболических подгрупп $ P_r $ и $ P_s $ в полной

линейной группе $\mathrm {GL}(n, R) $, в предположении $ rs\geq\mathrm {sr}(R) …

基于 Gromov-Wasserstein 距离的 3D 图形匹配方法

焦艳艳 - 2017 - cdmd.cnki.com.cn

随着科学技术的飞速发展及3D 技术的提高, 人们在数据采集和图形建模领域取得了很大的进步.

基于数字分析的应用领域有很多, 如: 分子生物学, 人脸识别, 模式识别等.

图形匹配是计算机视觉, 计算机图形学, 机器人学等领域的基本问题之一, 也是数字分析的重要 …

[Chinese 3D graphics matching method based on Gromov-Wasserstein distance]

2017

From Monge Kantorovich to Gromov Wasserstein: Numerical ...

ins.sjtu.edu.cn › seminars › 2017/01/03 › from-monge-...

Jan 3, 2017 — From Monge Kantorovich to Gromov Wasserstein: Numerical Optimal Transport between Several Metric Spaces ... For instance, they allow for the first time to compute barycenters (according to OT distances) of pr

Learning wasserstein embeddings

N Courty, R Flamary, M Ducoffe - arXiv preprint arXiv:1710.07457, 2017 - arxiv.org

The Wasserstein distance received a lot of attention recently in the community of machine

learning, especially for its principled way of comparing distributions. It has found numerous

applications in several hard problems, such as domain adaptation, dimensionality reduction …

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

[PDF] Detecting changes in forced climate attractors with Wasserstein distance.

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - d-nb.info

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

MG Mora, MA Peletier, L Scardia - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider systems of n parallel edge dislocations in a single slip system, represented by

points in a two-dimensional domain; the elastic medium is modeled as a continuum. We

formulate the energy of this system in terms of the empirical measure of the dislocations and …

<--—2017———————2017—— 410-

Automatic color correction for multisource remote sensing images with Wasserstein CNN

J Guo, Z Pan, B Lei, C Ding - Remote Sensing, 2017 - mdpi.com

In this paper a non-parametric model based on Wasserstein CNN is proposed for color

correction. It is suitable for large-scale remote sensing image preprocessing from multiple

sources under various viewing conditions, including illumination variances, atmosphere …

2017 7 patent

A kind of empty convolution method based on WGAN models

CN CN108021978A 周智恒华南理工大学

Priority 2017-11-14 • Filed 2017-11-14 • Published 2018-05-11

1. a kind of empty convolution method based on WGAN models, it is characterised in that the empty convolution method includes following step Suddenly： S1, construction are originally generated confrontation network model, and generating image by maker inputs to arbiter progress network training； …

[PDF] Distributionally robust reward–risk ratio programming with Wasserstein metric

Y Zhao, Y Liu, J Zhang, X Yang - 2017 - optimization-online.org

Reward-risk ratio (RR) is a very important stock market definition. In order to capture the

situation that the investor does not have complete information on the distribution of the

underlying uncertainty, people extend RR model to distributionally robust reward-risk ratio …

[PDF] MGAN: TRAINING GENERATIVE ADVERSARIAL NETS WITH MULTIPLE GENERATORS

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

Q Hoang, TD Nguyen, T Le… - arXiv preprint arXiv …, 2017 - researchgate.net

We propose in this paper a new approach to train the Generative Adversarial Nets (GANs)

with a mixture of generators to overcome the mode collapsing problem. The main intuition is

to employ multiple generators, instead of using a single one as in the original GAN. The idea …

2017

Wasserstein learning of deep generative point process models

S Xiao, M Farajtabar, X Ye, J Yan… - Advances in neural …, 2017 - proceedings.neurips.cc

… 2.4 WGAN for Temporal Point Processes Equipped with a way to approximately compute

the Wasserstein distance, we will look for a model Pr that is close to the distribution of real …

asserstein learning of deep generative point process models

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost

functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

[PDF] kyoto-u.ac.jp

F] {Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - Bulletin of Mathematical Sciences, 2017 - Springer

This is an expository paper on the theory of gradient flows, and in particular of those PDEs

which can be interpreted as gradient flows for the Wasserstein metric on the space of

probability measures (a distance induced by optimal transport). The starting point is the …

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to Fluid Equations

K Kang, HK Kim - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider a coupled system of Keller--Segel-type equations and the incompressible

Navier--Stokes equations in spatial dimension two and three. We first establish the existence

of a weak solution of a Fokker--Plank equation in the Wasserstein space under the …

<——2017———————2017 ——— 420 —

Minimax Statistical Learning with Wasserstein Distances

Cited by 17 Related articles

by J Lee · 2017 · Cited by 72 — As an illustrative example, we provide generalization guarantees for transport-based domain adaptation problems where the Wasserstein distance ...

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

Cited by 17 Related articles

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

Cited by 4115 Related articles All 9 versions

I Gulrajani, F Ahmed, M Arjovsky… - Advances in neural …, 2017 - papers.nips.cc

Abstract Generative Adversarial Networks (GANs) are powerful generative models, but suffer

from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress

toward stable training of GANs, but sometimes can still generate only poor samples or fail to …

CITATION] Improved training of wasserstein gans Advances in Neural Information Processing Systems

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - 2017

On the regularization of wasserstein gans

H Petzka, A Fischer, D Lukovnicov - arXiv preprint arXiv:1709.08894, 2017 - arxiv.org

Since their invention, generative adversarial networks (GANs) have become a popular

approach for learning to model a distribution of real (unlabeled) data. Convergence

problems during training are overcome by Wasserstein GANs which minimize the distance …

Face super-resolution through wasserstein gans

Z Chen, Y Tong - arXiv preprint arXiv:1705.02438, 2017 - arxiv.org

Generative adversarial networks (GANs) have received a tremendous amount of attention in

the past few years, and have inspired applications addressing a wide range of problems.

Despite its great potential, GANs are difficult to train. Recently, a series of papers (Arjovsky & …

[HTML] Energy-relaxed Wasserstein gans (energywgan): towards more stable and high resolution image generation

J Wu, Z Huang, J Thoma, L Van Gool - arXiv preprint arXiv:1712.01026, 2017 - deepai.org

2 Background Imagine there are two players in a game. One player (Generator) intends to

generate visually plausible images, aiming to fool its opponent, while the opponent

(Discriminator) attempts to discriminate real images from synthetic images. Such adversarial …

On reproduction of On the regularization of Wasserstein GANs

J Seo, T Jeon - arXiv preprint arXiv:1712.05882, 2017 - arxiv.org

This report has several purposes. First, our report is written to investigate the reproducibility

of the submitted paper On the regularization of Wasserstein GANs (2018). Second, among

the experiments performed in the submitted paper, five aspects were emphasized and …

Effective Lipschitz constraint enforcement for Wasserstein GAN training

2017 zzz 35

[CITATION] RATIONALES WITH WASSERSTEIN GANS

T LIKE

S Cui, Y Jiang - 2017 2nd IEEE International Conference on …, 2017 - ieeexplore.ieee.org

Generative Adversarial Networks (GANs) are efficient frameworks for estimating generative

model via adversarial process. However, GAN has known for suffering from training

instability. Wasserstein GAN (WGAN) improves the training stability significantly but also …

[PDF] An Informal Introduction to the Maths Behind Wasserstein GAN

Q Bai - 2017 - pdfs.semanticscholar.org

Briefly speaking,[1] explains from a theoretical perspective why training GAN is hard, and [2]

suggests a solution from the perspective of geometric foundation of generative modeling,

which is more fundamental than GAN itself. The algorithm suggested by [2] ends up being …

<——2017—— —2017 ——— 430——

2017 zzz 35

[CITATION] Léon Bo ou. 2017. Wasserstein gan

M Arjovsky, S Chintala - arXiv preprint arXiv:1701.07875, 2017

2017 [PDF] researchgate.net

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given …

Order-preserving wasserstein distance for sequence matching

B Su, G Hua - Proceedings of the IEEE Conference on …, 2017 - openaccess.thecvf.com

We present a new distance measure between sequences that can tackle local temporal

distortion and periodic sequences with arbitrary starting points. Through viewing the

instances of sequences as empirical samples of an unknown distribution, we cast the …

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

[PDF] Detecting changes in forced climate attractors with Wasserstein distance.

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - d-nb.info

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and

energy loads, as well as their multi-energy interactions and dependencies, have negligible

effects on the operation and analyses of integrated energy systems. Determining how to …

Correcting nuisance variation using wasserstein distance

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - arXiv preprint arXiv …, 2017 - arxiv.org

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological

information resulting from various factors affecting the cells. One motivating application is

drug development: morphological cell features can be captured from images, from which …

CITATION] Correcting Nuisance Variation using Wasserstein Distance. arXiv

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - 2017 - Nov

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary -dependent sequences

J Dedecker, F Merlevède - Bernoulli, 2017 - projecteuclid.org

We study the Wasserstein distance of order 1 between the empirical distribution and the

marginal distribution of stationary $\alpha $-dependent sequences. We prove some

moments inequalities of order $ p $ for any $ p\geq1 $, and we give some conditions under …

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

On quantum versions of the classical Wasserstein distance

J Agredo, F Fagnola - Stochastics, 2017 - Taylor & Francis

We investigate a definition of quantum Wasserstein distance of two states based on their

couplings on the product algebra as in the classical case. A detailed analysis of the two

qubit model leads to a formal definition fulfilling some minimal requirements. It also shows …

Cited by 9 Related articles All 5 versions
<——2017—— —2017 ——— 440—

[PDF] Wasserstein distance on finite spaces: Statistical inference and algorithms

M Sommerfeld - 2017 - d-nb.info

Wasserstein distances or, more generally, distances that quantify the optimal transport

between probability measures on metric spaces have long been established as an important

tool in probability theory. More recently, it has found its way into statistical theory …

Generalized Wasserstein distance and weak convergence of sublinear expectations

X Li, Y Lin - Journal of Theoretical Probability, 2017 - Springer

Recently, Peng establishes a theory of time-consistent sublinear expectations in [5, 6], ie, the

G-expectation theory. This new theory provides with several important models and tools for studying

robust hedging and utility maximization problems in the financial markets under Knightian uncertainty …

Weakly supervised audio source separation via spectrum energy preserved Wasserstein learning

N Zhang, J Yan, Y Zhou - arXiv preprint arXiv:1711.04121, 2017 - arxiv.org

Separating audio mixtures into individual instrument tracks has been a long standing

challenging task. We introduce a novel weakly supervised audio source separation

approach based on deep adversarial learning. Specifically, our loss function adopts the …

Wasserstein distance and the rectifiability of doubling measures: part II

J Azzam, G David, T Toro - Mathematische Zeitschrift, 2017 - Springer

We study the structure of the support of a doubling measure by analyzing its self-similarity

properties, which we estimate using a variant of the$L^ 1$ Wasserstein distance. We show

that a measure satisfying certain self-similarity conditions admits a unique (up to …

[PDF] Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

Wasserstein Distance

SM Walczak - Metric Diffusion Along Foliations, 2017 - Springer

Abstract The Wasserstein distance of Borel probability measures will play the important role

in metric diffusion along foliations. We here present the Kantorovich Duality Theorem for

optimal transportation problem. We also recall the definition of the Wasserstein distance …

[PDF] rwth-aachen.de

M Kampschulte, M Westdickenberg, RL Jerrard… - 2017 - publications.rwth-aachen.de

The main aim of this thesis is to explore a possible approach to gradient flows for Cartesian

(and other) currents. We will do so using the method of minimizing movements. The key

ingredient for this turns out to be the right choice of metric. For this we propose a …

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

[PDF] The WASSERSTEIN DISTANCE AS A UNIVARIATE NEUROIMAGING BIOMARKER FOR FDG-PET ANALYSIS

L Mi, W Zhang, J Zhang, Y Fan, D Goradia, K Chen… - gsl.lab.asu.edu

We propose a univariate biomarker of the FDGPET images by using the Wasserstein

distance. We apply the biomarker to the Alzheimer's disease (AD) analysis. The

experimental results demonstrate the robustness of our biomarker in distinguishing AD from …

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too

large and complex for easy computation. Because continuous transport problems are

generally solved by conversion to either discrete or semi-discrete forms, I focused on …

Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction

X CAO, Y XIN - Journal of Computer Applications, 2017 - en.cnki.com.cn

Dimensionality reduction plays an important role in big data analysis and visualization.

Many dimensionality reduction techniques with probabilistic distribution models rely on the

optimizaition of cost function between low-dimensional model distribution and high …

<——2017——- —2017 ——— 450 —

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a

variational model for nonuniform illumination correction, that incorporates a penalty term that …

[PDF] Quantum Wasserstein-1 Distance

Y Chen, TT Georgiou, L Ning… - arXiv preprint arXiv …, 2017 - researchgate.net

… More specif- ically, several groups [5, 6, 18] independently developed quantum mechanical

frameworks for defining a Wasserstein distance on matrix-valued densities (normalized to have

trace 1), via a variational framework with a continuity equation constraint generalizing the …

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN

method is proposed based on LBP features and entropy-regularized Wasserstein distance,

by combining the mathematical properties of Wasserstein distance in optimal mass …

rxiv.org › math

Sharp asymptotic and finite-sample rates of convergence of ...

by J Weed · 2017 · Cited by 163 — We prove sharp asymptotic and finite-sample results for this rate of convergence for general measures on general compact metric spaces. Our finite-sample results show the existence of multi-scale behavior, where measures can exhibit radically different rates of convergence as n grows.

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Evolution of the Wasserstein distance between the ... - Inria

2017 see 2018

Mar 1, 2017 — Evolution of the Wasserstein distance between the marginals of two Markov processes. Benjamin Jourdain (ENPC CERMICS and INRIA Mathrisk).

[CITATION] Evolution of the Wasserstein distance between the marginals of two Markov processes

Correcting Nuisance Variation using Wasserstein Distance

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

by G Tabak · 2017 · Cited by 3 — In this case, the particular batch in which a set of experiments were ... should contain only the relevant biological information (e.g. drug effects). ... distances between marginal distributions (such as the Wasserstein distance) of ..

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Davis, G Tabak, M Fan, S Yang, S Hoyer - 2017

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Tabak, M Fan, S Yang, S Hoyer, G Davis - 2017

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - Advances in Neural Information Processing …, 2017 - papers.nips.cc

We introduce a novel framework for statistical analysis of populations of non-degenerate

Gaussian processes (GPs), which are natural representations of uncertain curves. This

allows inherent variation or uncertainty in function-valued data to be properly incorporated in …

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more

generally, semiconvex) energies has led to advances in several areas of partial differential

equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

<——2017—— —2017 ——460—

[PDF] Distributionally robust reward–risk ratio programming with Wasserstein metric

Y Zhao, Y Liu, J Zhang, X Yang - 2017 - optimization-online.org

Reward-risk ratio (RR) is a very important stock market definition. In order to capture

Exponential convergence in the Wasserstein metric for one dimensional diffusions

L Cheng, R Li, L Wu - arXiv preprint arXiv:1703.00507, 2017 - arxiv.org

In this paper, we find some general and efficient sufficient conditions for the exponential

convergence $ W_ {1, d}(P_t (x,\cdot), P_t (y,\cdot))\le Ke^{-\delta t} d (x, y) $ for the

semigroup $(P_t) $ of one-dimensional diffusion. Moreover some sharp estimates of the …

The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality

V Barbu - SIAM Journal on Control and Optimization, 2017 - SIAM

The nonlinear diffusion equation \rho_t-Δ(ρH(ρ-\rho_c))=0 in (0,∞)*R^n, ρ(0,x)=\rho_0(x),

where H is the Heaviside function, describes the sandpile model P. Bak, C. Tang, and K.

Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and IM Janosi, Phys. A, 185 (1992) …

Distributionally Robust Chance-Constrained Approximate AC ...

Jun 17, 2017 — Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric. Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE).

[CITATION] Distributionally robust chance-constrained voltage-concerned DC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao, J Liu - arXiv preprint arXiv:1706.05538, 2017

F [CITATION] Distributionally robust chance-constrained voltage-concerned DC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao, J Liu - arXiv preprint arXiv:1706.05538, 2017

Aggregated Wasserstein Metric and State Registration for Hidden Markov Models

Y Chen, J Ye, J Li - arXiv preprint arXiv:1711.05792, 2017 - arxiv.org

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time position follows a …

Dimension-free Wasserstein contraction of nonlinear filters

N Whiteley - arXiv preprint arXiv:1708.01582, 2017 - arxiv.org

For a class of partially observed diffusions, sufficient conditions are given for the map from

initial condition of the signal to filtering distribution to be contractive with respect to

Wasserstein distances, with rate which has no dependence on the dimension of the state …

Absolute continuity of Wasserstein barycenters over Alexandrov spaces

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we prove that on a compact, $ n $-dimensional Alexandrov space with

curvature at least− 1, the Wasserstein barycenter of Borel probability measures ${{\mu} _

{1}},\ldots,{{\mu} _ {m}} $ is absolutely continuous with respect to the $ n $-dimensional …

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

2017

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN

method is proposed based on LBP features and entropy-regularized Wasserstein distance,

by combining the mathematical properties of Wasserstein distance in optimal mass …

2017

[PDF] berkeley.edu

Wasserstein stability of the entropy power inequality for log-concave random vectors

TA Courtade, M Fathi… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

We establish quantitative stability results for the entropy power inequality (EPI) in arbitrary

dimension. Specifically, we show that if uniformly log-concave densities nearly saturate the

EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance …

On parameter estimation with the Wasserstein distance

E Bernton, PE Jacob, M Gerber, CP Robert - arXiv preprint arXiv …, 2017 - arxiv.org

Statistical inference can be performed by minimizing, over the parameter space, the

Wasserstein distance between model distributions and the empirical distribution of the data.

We study asymptotic properties of such minimum Wasserstein distance estimators …

n parameter estimation with the Wasserstein distance

<——2017—— —2017 ——— 470—

[PDF] Inference in generative models using the Wasserstein distance

…, PE Jacob, M Gerber, CP Robert - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given …

Cited by 57 Related articles All 2 versions
[CITATION] Inference in generative models using the Wasserstein distance

CP Robert see 2017

A Stochastic gradient method to compute Wasserstein barycenters of distributions

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

Approximation of stable law in Wasserstein-1 distance by ...

Report number: BCSim-2018-s08

[CITATION] Approximation of stable law in Wasserstein-1 distance by Stein's method. Accepted by Annals of Applied Probability

L Xu - arXiv preprint arXiv:1709.00805, 2017

An Informal Introduction to the Maths Behind Wasserstein GAN

2017 PDF

https://www.cs.bu.edu › publication › wgan_math

by Q Bai · 2017 — An Informal Introduction to the Maths Behind. Wasserstein GAN. Qinxun Bai. February, 2017. Briefly speaking, [1] explains from a theoretical perspective why ...

6 pages

[CITATION] An Informal Introduction to the Maths Behind Wasserstein GAN

Q Bai - 2017

year modified 2017

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

year modified 2017

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

2017

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction

2017

X CAO, Y XIN - Journal of Computer Applications, 2017 - en.cnki.com.cn

Dimensionality reduction plays an important role in big data analysis and visualization.

Many dimensionality reduction techniques with probabilistic distribution models rely on the

optimizaition of cost function between low-dimensional model distribution and high …

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that

involves identifying differences between two random variables without making parametric

assumptions about their underlying distributions. The literature is old and rich, with a wide …

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

<——2017—— —2017 ——— 480—

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost

functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a

variational model for nonuniform illumination correction, that incorporates a penalty term that …

Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction

X CAO, Y XIN - Journal of Computer Applications, 2017 - en.cnki.com.cn

Dimensionality reduction plays an important role in big data analysis and visualization.

Many dimensionality reduction techniques with probabilistic distribution models rely on the

optimizaition of cost function between low-dimensional model distribution and high …

2017

[CITATION] Sampling of probability measures in the convex order by Wasserstein projection. arXiv e-prints, page

A Alfonsi, J Corbetta, B Jourdain - arXiv preprint arXiv:1709.05287, 2017

Improved training of wasserstein gans

2017

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - arxiv.org

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from

training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward

stable training of GANs, but sometimes can still generate only low-quality samples or fail to …

Cited by 4544 Related articles All 10 versions

[CITATION] Improved training of wasserstein GANs (2017)

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - Available

2017

On the regularization of wasserstein gans

H Petzka, A Fischer, D Lukovnicov - arXiv preprint arXiv:1709.08894, 2017 - arxiv.org

Since their invention, generative adversarial networks (GANs) have become a popular

approach for learning to model a distribution of real (unlabeled) data. Convergence

problems during training are overcome by Wasserstein GANs which minimize the distance …

2017

Existence and consistency of Wasserstein barycenters

T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual

notion of statistical mean. We prove the existence of Wasserstein barycenters of random

probabilities defined on a geodesic space (E, d). We also prove the consistency of this …

2[PDF] arxiv.org

Existence and consistency of Wasserstein barycenters

T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual

notion of statistical mean. We prove the existence of Wasserstein barycenters of random

probabilities defined on a geodesic space (E, d). We also prove the consistency of this …

Learning from uncertain curves:The 2-Wasserstein metric for Gaussian processes

Authors:Guyon, I. (Contributor), Luxburg, U. V. (Contributor), Bengio, S. (Contributor), Wallach, H. (Contributor), Fergus, R. (Contributor), Vishwanathan, S. (Contributor), Garnett, R. (Contributor), Mallasto, Anton (Creator), Feragen, Aasa (Creator)Show more
Summary:We introduce a novel framework for statistical analysis of populations of nondegenerate

Gaussian processes (GPs), which are natural representations of uncertain

curves. This allows inherent variation or uncertainty in function-valued data to be

properly incorporated in the population analysis. Using the 2-Wasserstein metric we

geometrize the space of GPs with L2 mean and covariance functions over compact

index spaces. We prove uniqueness of the barycenter of a population of GPs, as well

as convergence of the metric and the barycenter of their finite-dimensional counterparts.

This justifies practical computations. Finally, we demonstrate our framework

through experimental validation on GP datasets representing brain connectivity and

climate development. A MATLAB library for relevant computations will be published

at https://sites.google.com/view/antonmallasto/softwareShow more
Downloadable Archival Material, 2017
English
Publisher:NIPS Proceedings, 2017

<——2017———2017——— 490—

An elementary proof for the structure of Wasserstein derivatives

C Wu, J Zhang - arXiv preprint arXiv:1705.08046, 2017 - arxiv.org

Let $ F:\mathbb {L}^ 2 (\Omega,\mathbb {R})\to\mathbb {R} $ be a law invariant and

continuously Fréchet differentiable mapping. Based on Lions\cite {Lions}, Cardaliaguet\cite

{Cardaliaguet}(Theorem 6.2 and 6.5) proved that:\bea\label {Derivative} DF (\xi)= g (\xi),\eea …

Information geometry of wasserstein divergence

R Karakida, S Amari - International Conference on Geometric Science of …, 2017 - Springer

There are two geometrical structures in a manifold of probability distributions. One is

invariant, based on the Fisher information, and the other is based on the Wasserstein

distance of optimal transportation. We propose a unified framework which connects the …

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

… is not surprising in view of the recent work of Sturm, Lott–Villani, and Gigli–Mantegazza on Ricci

flow in a metric space setting [26–30], nonetheless the explicit formulation of the nonlinear σ model

and of its relation with Ricci flow theory in terms of Wasserstein geometry is highly …

Absolute continuity of Wasserstein barycenters over Alexandrov spaces

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we prove that on a compact,-dimensional Alexandrov space with curvature at

least− 1, the Wasserstein barycenter of Borel probability measures is absolutely continuous

with respect to the-dimensional Hausdorff measure if one of them is.

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting

C Grimm, Y Song, ML Littman - arXiv preprint arXiv:1709.06533, 2017 - arxiv.org

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving

density estimation problems---using data to assess how likely samples are to be drawn from

the same distribution. Instead of explicitly computing these probabilities, GANs learn a …

2017

On reproduction of On the regularization of Wasserstein GANs

J Seo, T Jeon - arXiv preprint arXiv:1712.05882, 2017 - arxiv.org

This report has several purposes. First, our report is written to investigate the reproducibility

of the submitted paper On the regularization of Wasserstein GANs (2018). Second, among

the experiments performed in the submitted paper, five aspects were emphasized and …

[CITATION] Denis Lukovnicov On the regularization of Wasserstein GANs

H Petzka, A Fischer - arXiv preprint arXiv:1709.08894, 2017

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

… distribution-valued data. Finally, we used hierarchical clustering or principal

component analysis (PCA) to deal with clustering or dimension reduction under results

of Wasserstein distance, respectively. I. INTRODUCTION In the …

2017

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary -dependent sequences

J Dedecker, F Merlevede - Bernoulli, 2017 - projecteuclid.org

We study the Wasserstein distance of order 1 between the empirical distribution and the

marginal distribution of stationary $\alpha $-dependent sequences. We prove some

moments inequalities of order $ p $ for any $ p\geq1 $, and we give some conditions under …

[PDF] cmu.edu

[PDF] Wasserstein Training of Deep Boltzmann Machines

C Wang, T Tong, Y Zou - cs.cmu.edu

… Finally, we experimentally explored Wasserstein training of RBMs and DBMs for digit

generation with MNIST dataset, and showed the superiority of Wasserstein training

compared to traditional KL- divergence training. 1. Introduction …

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that

involves identifying differences between two random variables without making parametric

assumptions about their underlying distributions. The literature is old and rich, with a wide …

<——2017—— —2017 ——— 500—

[PDF] rwth-aachen.de

[PDF] Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

M Kampschulte, M Westdickenberg, RL Jerrard… - 2017 - publications.rwth-aachen.de

… The key idea to finding such a metric interestingly enough comes from a differ- ent direction,

namely the notion of Wasserstein-distance in optimal transport, or to be more specific a certain

way to formulate the Wasserstein-distance, which goes back to Benamou and Brenier …

2017 thesis
Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

Wasserstein learning of deep generative point process models

S Xiao, M Farajtabar, X Ye, J Yan, L Song… - arXiv preprint arXiv …, 2017 - arxiv.org

Point processes are becoming very popular in modeling asynchronous sequential data due

to their sound mathematical foundation and strength in modeling a variety of real-world

phenomena. Currently, they are often characterized via intensity function which limits …

2017

[1711.08875] Wasserstein Introspective Neural Networks - arXiv

by K Lee · 2017 · Cited by 40 — Abstract: We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model.

Posterior contraction in Gaussian process regression using Wasserstein approximations

A Bhattacharya, D Pati - Information and Inference: A Journal of …, 2017 - academic.oup.com

We study posterior rates of contraction in Gaussian process regression with potentially

unbounded covariate domain. Our argument relies on developing a Gaussian

approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of …

2017

Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems

A Alfonsi, J Corbetta, B Jourdain - Available at SSRN 3072356, 2017 - papers.ssrn.com

… U is sampled independently from X according to the uniform distribution on [0,1]. Let φ : R →

R be a convex … SAMPLING OF PROBABILITY MEASURES IN THE CONVEX ORDER … We assume

that µ ≤cx ν with µ, ν ∈ P1(R). We consider two iid samples X1,...,XI with distribution µ …

[CITATION] Sampling of probability measures in the convex order by Wasserstein projection. arXiv e-prints, page

A Alfonsi, J Corbetta, B Jourdain - arXiv preprint arXiv:1709.05287, 2017

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

[CITATION] The Cramer Distance as a Solution to Biased Wasserstein Gradients. arXiv 2017

MG Bellemare, I Danihelka, W Dabney, S Mohamed… - arXiv preprint arXiv:1705.10743

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

Enhancing diffusion MRI measures by integrating grey and white matter morphometry with hyperbolic wasserstein distance

W Zhang, J Shi, J Yu, L Zhan… - 2017 IEEE 14th …, 2017 - ieeexplore.ieee.org

In order to improve the preclinical diagnose of Alzheimer's disease (AD), there is a great

deal of interest in analyzing the AD related brain structural changes with magnetic

resonance image (MRI) analyses. As the major features, variation of the structural …

[PDF] A particle model for Wasserstein type diffusion

V Konarovskyi, M von Renesse - math.uni-leipzig.de

A particle model for Wasserstein type diffusion … ∂tµt = β 2 ∆µt + ∇ · ( µt∇ δF(µt) δµt … –

Dean-Kawasaki equation The equation appears in macroscopic fluctuation theory and glass

dynamic models D. Dean '96, K. Kawasaki, E. Vanden-Eijnden, A. Donev, B. Derrida, J …

Reversible coalescing-fragmentating Wasserstein dynamics on the real line

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1709.02839, 2017 - arxiv.org

We introduce a family of reversible fragmentating-coagulating processes of particles of

varying size-scaled diffusivity with strictly local interaction on the real line. The construction

is based on a new family of measures on the set of real increasing functions as reference …

<——2017—— —2017 ——— 510—

[PDF] {Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - Bulletin of Mathematical Sciences, 2017 - Springer

This is an expository paper on the theory of gradient flows, and in particular of those PDEs

which can be interpreted as gradient flows for the Wasserstein metric on the space of

probability measures (a distance induced by optimal transport). The starting point is the …

Coalescing-fragmentating Wasserstein dynamics: particle approach

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - arxiv.org

We construct a family of semimartingales which describe the behavior of a particle system

with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warren

flow, an infinite system of diffusion particles on the real line which sticky-reflect from each …

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more

generally, semiconvex) energies has led to advances in several areas of partial differential

equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

The time discretization of gradient flows in metric spaces uses variants of the celebrated

implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in this Note a

different approach, which allows us to construct two second-order in time numerical …

2017

[PDF] Cadlág stability and approximation of reversible coalescing-fragmentating Wasserstein dynamics

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - researchgate.net

We construct coalescing-fragmentating Wasserstein dynamics [27] for any initial condition

and interacting potential by a finite particle approximation. We show that such a model

admits a description by a family of continuous semimartingales, where every semimartingale …

The Wasserstein geometry of nonlinear models and the Hamilton–Perelman Ricci flow

M Carfora - Reviews in Mathematical Physics, 2017 - World Scientific

Nonlinear sigma models are quantum field theories describing, in the large deviation sense,

random fluctuations of harmonic maps between a Riemann surface and a Riemannian

manifold. Via their formal renormalization group analysis, they provide a framework for …

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite

first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices,

and consider the problem of differentiability of the corresponding Cartan barycentric …

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

<——2017—— —2017 ——— 520—

[PDF] rwth-aachen.de

[PDF] Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

M Kampschulte, M Westdickenberg, RL Jerrard… - 2017 - publications.rwth-aachen.de

The main aim of this thesis is to explore a possible approach to gradient flows for Cartesian

(and other) currents. We will do so using the method of minimizing movements. The key

ingredient for this turns out to be the right choice of metric. For this we propose a …

[PDF] A particle model for Wasserstein type diffusion

V Konarovskyi, M von Renesse - math.uni-leipzig.de

… There is known a “singular” Γ such that the DK equation has a solution µt on P2([0,1])

called the Wasserstein diffusion that is a Markov process and satisfies the Varadhan formula …

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

[HTML] Vers un théorème de la limite centrale dans l'espace de Wasserstein?

M Agueh, G Carlier - Comptes Rendus Mathématique, 2017 - Elsevier

Résumé Les barycentres dans l'espace de Wasserstein constituent une manière naturelle

d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines

appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons …

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging

but highly valuable in real application scenarios. In most situations, the source and the target

speakers do not repeat the same texts or they may even speak different languages. In this …

Geodesic PCA in the Wasserstein space by convex PCA

J Bigot, R Gouet, T Klein, A López - Annales de l'Institut Henri …, 2017 - projecteuclid.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

[PDF] neurips.cc

[PDF] Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - … of the 31st International Conference on …, 2017 - papers.neurips.cc

We introduce a novel framework for statistical analysis of populations of nondegenerate

Gaussian processes (GPs), which are natural representations of uncertain curves. This

allows inherent variation or uncertainty in function-valued data to be properly incorporated in …

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

Enhancing diffusion MRI measures by integrating grey and white matter morphometry with hyperbolic wasserstein distance

W Zhang, J Shi, J Yu, L Zhan… - 2017 IEEE 14th …, 2017 - ieeexplore.ieee.org

In order to improve the preclinical diagnose of Alzheimer's disease (AD), there is a great

deal of interest in analyzing the AD related brain structural changes with magnetic

resonance image (MRI) analyses. As the major features, variation of the structural …

Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant Sliced-Wasserstein Distance via Laplace--Beltrami Eigenmap

R Lai, H Zhao - SIAM Journal on Imaging Sciences, 2017 - SIAM

In this work, we propose computational models and algorithms for point cloud registration

with nonrigid transformation. First, point clouds sampled from manifolds originally embedded

in some Euclidean space are transformed to new point clouds embedded in R^n by the …

Cited by 20 Related articles

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost

functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

<——2017—————2017—————530—

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

Finsler structure in the p-Wasserstein space and gradient flows

M Agueh - Comptes Rendus Mathematique, 2012 - Elsevier

It is known from the work of F. Otto (2001)[9], that the space of probability measures

equipped with the quadratic Wasserstein distance, ie, the 2-Wasserstein space, can be

viewed as a Riemannian manifold. Here we show that when the quadratic cost is replaced …

Ambiguity set and learning via Bregman and Wasserstein

X Guo, J Hong, N Yang - arXiv preprint arXiv:1705.08056, 2017 - arxiv.org

Construction of ambiguity set in robust optimization relies on the choice of divergences

between probability distributions. In distribution learning, choosing appropriate probability

distributions based on observed data is critical for approximating the true distribution. To …

2017

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite

first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices,

and consider the problem of differentiability of the corresponding Cartan barycentric …

[1704.05491] An LP-based, Strongly-Polynomial 2 ... - arXiv.org

by S Borgwardt · 2017 · Cited by 3 — Discrete Wasserstein barycenters correspond to optimal solutions of transportation problems for a set of probability measures with finite support.

[CITATION] Strongly polynomial 2-approximations of discrete Wasserstein barycenters

S Borgwardt - arXiv preprint arXiv:1704.05491, 2017

Транспортная задача Монжа-Канторовича, пространство Васерштейна и его геометрия

2017

[Transportation prob;em of Monge-Kantorovich, the Vaserstein space and its geometry]

Андрей Соболевский

Семинар Добрушинской математической лаборатории [March 21, 2019[

17.03.2017 | Ефимова Мария Александровна 21 марта 2017 г.

[PDF]

2017

A Generalized Vaserstein symbol Tariq Syed Nov 23, 2017

arXiv:1711.08210 [pdf, ps, other]

A Generalized Vaserstein symbol

Tariq Syed

Comments: 36 pages

Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC); K-Theory and Homology (math.KT)

A generalized Vaserstein symbol

by Syed, Tariq 11/2017

Let $R$ be a ring with $2 \in R^{\times}$. Then the usual Vaserstein symbol is a map from the orbit space of unimodular rows of length $3$ under the action of...

Journal Article: Full Text Online

[711.08210] A generalized Vaserstein symbol - arXiv

Ivarsson, Björn; Kutzschebauch, Frank

2017

A solution of Gromov’s Vaserstein problem. (English. Abridged French version) Zbl 1160.32017

C. R., Math., Acad. Sci. Paris 346, No. 23-24, 1239-1243 (2008).

Reviewer: Eugen Pascu (Montréal)

MSC: 32H02 32E10

Full Text: DOI

[PDF] mjstaib.com

[PDF] Wasserstein k-means++ for cloud regime histogram clustering

M Staib, S Jegelka - Climate informatics, 2017 - mjstaib.com

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

k-means clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

Effective Lipschitz constraint enforcement for Wasserstein GAN training

2017

S Cui, Y Jiang - 2017 2nd IEEE International Conference on …, 2017 - ieeexplore.ieee.org

Generative Adversarial Networks (GANs) are efficient frameworks for estimating generative

model via adversarial process. However, GAN has known for suffering from training

instability. Wasserstein GAN (WGAN) improves the training stability significantly but also …

<——2017—— —2017 ——— 540—

[HTML] Energy-relaxed Wasserstein gans (energywgan): towards more stable and high resolution image generation

J Wu, Z Huang, J Thoma, L Van Gool - arXiv preprint arXiv:1712.01026, 2017 - deepai.org

2 Background Imagine there are two players in a game. One player (Generator) intends to

generate visually plausible images, aiming to fool its opponent, while the opponent

(Discriminator) attempts to discriminate real images from synthetic images. Such adversarial …

[PDF] WASSERSTEIN k-MEANS+ HISTOGRAM CLUSTERING

M Staib, S Jegelka - NCAR Technical Notes NCAR/TN536+ PROC - par.nsf.gov

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

kmeans clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

[PDF] Wasserstein Training of Deep Boltzmann Machines

C Wang, T Tong, Y Zou - cs.cmu.edu

Training various probabilistic graphical models, such as restricted Boltzmann machines

(RBMs), deep Boltzmann machines (DBMs), is usually done by maximum likelihood

estimation, or equivalently minimizing the Kullback-Leibler (KL) divergence between the …

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

Multilevel Clustering via Wasserstein Means

2017

Multilevel Clustering via Wasserstein Means arXiv

by Ho, Nhat; Nguyen, XuanLong; Yurochkin, Mikhail; More... 06/2017

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns...

This is "Multilevel Clustering via Wasserstein Means --- Nhat Ho, Long Nguyen, Mikhail Yurochkin ...

Oct 14, 2017 · Uploaded by TechTalksTV

Multilevel clustering via wasserstein means

MAP image labeling using Wasserstein messages and geometric assignment

F Åström, R Hühnerbein, F Savarino… - … Conference on Scale …, 2017 - Springer

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by following the Riemannian gradient flow of a given objective function on the so-called assignment manifold. The approach evaluates user-defined data term and additionally …

MAP Image Labeling Using Wasserstein Messages and Geometric Assignment

[PDF] uni-heidelberg.de

C Schnörr - Scale Space and Variational Methods in Computer …, 2017 - books.google.com

Hyperspectral and multispectral Wasserstein barycenter for image fusion

J Mifdal, B Coll, N Courty, J Froment… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

The fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows the extraction of relevant information from the fused image. Fusion consists of the combination of the spectral information of the hypespectral image (h) and the spatial …

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to image acquisition sensors' malfunction or external interference. In this paper we propose a variational model for nonuniform illumination correction, that incorporates a penalty term that …

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

2017

MAP image labeling using Wasserstein messages and geometric assignment

F Åström, R Hühnerbein, F Savarino… - … Conference on Scale …, 2017 - Springer

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by

following the Riemannian gradient flow of a given objective function on the so-called

assignment manifold. The approach evaluates user-defined data term and additionally …

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

2017

15 Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

F Al Reda, B Maury - … Optimization and Optimal Transport: In the …, 2017 - books.google.com

This paper establishes a link between some space discretization strategies of the finite

volume type for the Fokker–Planck equation in general meshes (Voronoï tesselations) and

gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein …

2017

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

2017

Fast discrete distribution clustering using Wasserstein barycenter with sparse support

J Ye, P Wu, JZ Wang, J Li - IEEE Transactions on Signal …, 2017 - ieeexplore.ieee.org

2017

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

2017

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

2017

[PDF] wiley.com

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu, Y Zhang - IET Generation, Transmission …, 2017 - IET

In order to address the wind power uncertainty in the security constrained economic dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

2017

Weakly supervised audio source separation via spectrum energy preserved Wasserstein learning

N Zhang, J Yan, Y Zhou - arXiv preprint arXiv:1711.04121, 2017 - arxiv.org

Separating audio mixtures into individual instrument tracks has been a long standing challenging task. We introduce a novel weakly supervised audio source separation approach based on deep adversarial learning. Specifically, our loss function adopts the …

2017

DF] Unsupervised Audio Source Separation via Spectrum ...

www.semanticscholar.org › paper › Unsupervised-Audio-...

Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning · Figures, Tables, and Topics from this paper · Figures and Tables.

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

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2017

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

MG Mora, MA Peletier, L Scardia - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider systems of n parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modeled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations and …

Generalized Wasserstein distance and weak convergence of sublinear expectations

X Li, Y Lin - Journal of Theoretical Probability, 2017 - Springer

Recently, Peng establishes a theory of time-consistent sublinear expectations in [5, 6], ie, the G-expectation theory. This new theory provides with several important models and tools for studying robust hedging and utility maximization problems in the financial markets under Knightian uncertainty …

Wasserstein stability of the entropy power inequality for log-concave random vectors

TA Courtade, M Fathi… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

We establish quantitative stability results for the entropy power inequality (EPI) in arbitrary dimension. Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance …

Exponential convergence in the Wasserstein metric for one dimensional diffusions

L Cheng, R Li, L Wu - arXiv preprint arXiv:1703.00507, 2017 - arxiv.org

In this paper, we find some general and efficient sufficient conditions for the exponential convergence $ W_ {1, d}(P_t (x,\cdot), P_t (y,\cdot))\le Ke^{-\delta t} d (x, y) $ for the semigroup $(P_t) $ of one-dimensional diffusion. Moreover some sharp estimates of the …

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN method is proposed based on LBP features and entropy-regularized Wasserstein distance, by combining the mathematical properties of Wasserstein distance in optimal mass …

Sharp asymptotic and finite-sample rates of convergence of ...

by J Weed · 2017 · Cited by 163 — Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning.

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Cited by 5 Related arti

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

2017

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

2017

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging but highly valuable in real application scenarios. In most situations, the source and the target speakers do not repeat the same texts or they may even speak different languages. In this …

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

<——2017—— —2017 ——— 570—

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices, and consider the problem of differentiability of the corresponding Cartan barycentric …

[PDF] Cadlág stability and approximation of reversible coalescing-fragmentating Wasserstein dynamics

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - researchgate.net

We construct coalescing-fragmentating Wasserstein dynamics [27] for any initial condition and interacting potential by a finite particle approximation. We show that such a model admits a description by a family of continuous semimartingales, where every semimartingale …

Wasserstein stability of the entropy power inequality for log-concave random vectors

TA Courtade, M Fathi… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

We establish quantitative stability results for the entropy power inequality (EPI) in arbitrary dimension. Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance …

2017 pink to pdf 2017

www.semanticscholar.org › paper › On-lower-bounds-for...

On lower bounds for theL2-Wasserstein metric in a Hilbert space ... Shape of a Distribution Through the L2-Wasserstein Distance · J. A. Cuesta-Albertos, Carlos ...

2017 modified

On lower bounds for the L -Wasserstein metric in a Hilbert space

personales.unican.es/cuestaj/BoundWasserstein...

We provide two families of lower bounds for the L2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and su cient condition for the supremum in it to be attained. In the nite dimensional case, we identify the basis which provides the most accurate lower bound in the family.

On the regularization of wasserstein gans

H Petzka, A Fischer, D Lukovnicov - arXiv preprint arXiv:1709.08894, 2017 - arxiv.org

Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance …

[CITATION] Denis Lukovnicov On the regularization of Wasserstein GANs

H Petzka, A Fischer - arXiv preprint arXiv:1709.08894, 2017

Reversible coalescing-fragmentating Wasserstein dynamics on the real line

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1709.02839, 2017 - arxiv.org

We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the real line. The construction is based on a new family of measures on the set of real increasing functions as reference …

On interpolation and curvature via Wasserstein geodesics

M Kell - Advances in Calculus of Variations, 2017 - degruyter.com

In this article, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel–Brascamp–Lieb inequality for general Riemannian and Finsler manifolds and led Lott …

On quantum versions of the classical Wasserstein distance

J Agredo, F Fagnola - Stochastics, 2017 - Taylor & Francis

We investigate a definition of quantum Wasserstein distance of two states based on their couplings on the product algebra as in the classical case. A detailed analysis of the two qubit model leads to a formal definition fulfilling some minimal requirements. It also shows …

12 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

M Laborde - Topological Optimization and Optimal Transport: In …, 2017 - books.google.com

This chapter presents existence and uniqueness results for a class of parabolic systems with nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic …

On tangent cones in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact Riemannian manifold, let $ P (M) $ denote the Wasserstein space of probability measures on $ M $. If $ S $ is an embedded submanifold of $ M $, and $\mu $ is an absolutely continuous measure on $ S $, then we compute the tangent cone of …

<——2017—— —2017 ——— 580—

[PDF] Wasserstein distance on finite spaces: Statistical inference and algorithms

M Sommerfeld - 2017 - d-nb.info

Wasserstein distances or, more generally, distances that quantify the optimal transport between probability measures on metric spaces have long been established as an important tool in probability theory. More recently, it has found its way into statistical theory …

On reproduction of On the regularization of Wasserstein GANs

J Seo, T Jeon - arXiv preprint arXiv:1712.05882, 2017 - arxiv.org

This report has several purposes. First, our report is written to investigate the reproducibility of the submitted paper On the regularization of Wasserstein GANs (2018). Second, among the experiments performed in the submitted paper, five aspects were emphasized and …

A partial Laplacian as an infinitesimal generator on the Wasserstein space

2017

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion and plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

Wasserstein distributional robustness and regularization in statistical learning

R Gao, X Chen, AJ Kleywegt - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

A central question in statistical learning is to design algorithms that not only perform well on training data, but also generalize to new and unseen data. In this paper, we tackle this question by formulating a distributionally robust stochastic optimization (DRSO) problem …

Cited by 81 Related articles

Minimax statistical learning with wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017 - arxiv.org

As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax …

[PDF] Wasserstein distance on finite spaces: Statistical inference and algorithms

M Sommerfeld - 2017 - d-nb.info

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

12 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

M Laborde - Topological Optimization and Optimal Transport: In …, 2017 - books.google.com

This chapter presents existence and uniqueness results for a class of parabolic systems with nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic …

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma (0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

<——2017—— —2017 ——— 590—

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too large and complex for easy computation. Because continuous transport problems are generally solved by conversion to either discrete or semi-discrete forms, I focused on …

2017 see 2018 [PDF] arxiv.org

On the regularization of wasserstein gans

H Petzka, A Fischer, D Lukovnicov - arXiv preprint arXiv:1709.08894, 2017 - arxiv.org

… We will denote by Lip1 the set of all 1-Lipschitz functions, ie, the set of all functions f such …

of Wasserstein GANs, we propose to use the following penalty term to enforce the Lipschitz …

metric introduces a new minimization problem, which requires the ...

[CITATION] On the regularization of Wasserstein GANs

S Augustin - Proc. Int. Conf. Learn. Representations, 2018

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

self-similarity conditions admits a unique (up to …

The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality

V Barbu - SIAM Journal on Control and Optimization, 2017 - SIAM

The nonlinear diffusion equation \rho_t-Δ(ρH(ρ-\rho_c))=0 in (0,∞)*R^n, ρ(0,x)=\rho_0(x),

where H is the Heaviside function, describes the sandpile model P. Bak, C. Tang, and K.

Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and IM Janosi, Phys. A, 185 (1992) …

[PDF] Wasserstein generative adversarial network

W Gong - Int Conf Mach Learn, 2017 - mlmi.eng.cam.ac.uk

Recent advances in deep generative models give us new perspective on modeling highdimensional, nonlinear data distributions. Especially the GAN training can successfully produce sharp, realistic images. However, GAN sidesteps the use of traditional maximum …

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in 1989, we show that this theory is intimately related to the well-known Wasserstein metric on the space of probability measures with a finite first moment on a complete and separable …

A Central Limit Theorem for Wasserstein type distances between two different laws

P Berthet, JC Fort, T Klein - arXiv preprint arXiv:1710.09763, 2017 - arxiv.org

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

A Central Limit Theorem for Wasserstein type distances ...

hal.archives-ouvertes.fr › document

by P Berthet · 2017 · Cited by 9 — The framework is very simple: two samples of i.i.d. real random variables taking values in R with continuous cumulative distribution function (c.d.f.) F and G are available. ... From these samples we estimate the Wasserstein distances or costs between F and G and we prove a central limit theorem (CLT).

2017

Wasserstein GAN and the Kantorovich-Rubinstein Duality ...

vincentherrmann.github.io › blog › wasserstein

Feb 24, 2017 — For discrete probability distributions, the Wasserstein distance is also descriptively called the earth mover's distance (EMD). If we imagine the ...

[CITATION] Wasserstein gan and the kantorovich-rubinstein duality

V Herrmann - … : https://vincentherrmann. github. io/blog/wasserstein, 2017

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

The Dice score is widely used for binary segmentation due to its robustness to class imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for training convolutional neural networks (CNN). Although CNNs trained using mean-class …

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and

energy loads, as well as their multi-energy interactions and dependencies, have negligible

effects on the operation and analyses of integrated energy systems. Determining how to …

<——2017—— —2017 ——— 600—

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

[PDF] Wasserstein Training of Deep Boltzmann Machines

C Wang, T Tong, Y Zou - cs.cmu.edu

Training various probabilistic graphical models, such as restricted Boltzmann machines (RBMs), deep Boltzmann machines (DBMs), is usually done by maximum likelihood estimation, or equivalently minimizing the Kullback-Leibler (KL) divergence between the …

2017

[PDF] fleuret.org

F Fleuret - fleuret.org

… (Arjovsky et al., 2017) In some way, the resulting Wasserstein GAN (WGAN) trades the difficulty to train G for the difficulty to train D. In practice, this weakness results in extremely long convergence time. François Fleuret AMMI – Introduction to Deep Learning / 10.2. Wasserstein …

2017

Wasserstein learning of deep generative point process models

S Xiao, M Farajtabar, X Ye, J Yan, L Song… - arXiv preprint arXiv …, 2017 - arxiv.org

Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity function which limits …

2017

The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality

V Barbu - SIAM Journal on Control and Optimization, 2017 - SIAM

The nonlinear diffusion equation \rho_t-Δ(ρH(ρ-\rho_c))=0 in (0,∞)*R^n, ρ(0,x)=\rho_0(x), where H is the Heaviside function, describes the sandpile model P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and IM Janosi, Phys. A, 185 (1992) …

A Stochastic gradient method to compute Wasserstein barycenters of distributions

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

2017

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

Parameter estimation in finite mixture models by regularized optimal transport: A unified framework for hard and soft clustering

A Dessein, N Papadakis, CA Deledalle - arXiv preprint arXiv:1711.04366, 2017 - arxiv.org

… Clustering with Optimal Transport Using the concept of Wasserstein barycenters [2,13, 22], there

exists many … P = {Pξ}ξ∈Ξ be a parametric statistical model on a measurable space (X, A … between

pairwise components and a convex and differentiable potential φ with penalty λ ≥ 0 …

2017

Regularized barycenters in the Wasserstein space

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

This paper is an overview of results that have been obtain in 2 on the convex regularization

of Wasserstein barycenters for random measures supported on\mathbb R^ d. We discuss

the existence and uniqueness of such barycenters for a large class of regularizing functions …

Extremal curves in Wasserstein space

G Conforti, M Pavon - International Conference on Geometric Science of …, 2017 - Springer

We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges

and the classic Madelung fluid can be derived from variational principles on Wasserstein

space. The second order differential equations are accordingly obtained by annihilating the …

Log-PCA versus geodesic PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - arXiv preprint arXiv …, 2017 - arxiv.org

This paper is concerned by the statistical analysis of data sets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the PCA of histograms with respect to the 2-Wasserstein …

<——2017—— —2017 ——— 610—

Regularized barycenters in the Wasserstein space

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

This paper is an overview of results that have been obtain in 2 on the convex regularization

of Wasserstein barycenters for random measures supported on\mathbb R^ d. We discuss

the existence and uniqueness of such barycenters for a large class of regularizing functions …

An intrinsic parallel transport in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact connected Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. We describe a geometric construction

of parallel transport of some tangent cones along geodesics in $ P (M) $. We show that …

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

Detecting changes in forced climate attractors with Wasserstein distance

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - npg.copernicus.org

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

WGAN 을 이용한 Data Augmentation 기법

임세호， 신용구， 유철환， 이한규， 고성제 - 대한전자공학회 학술대회, 2017 - dbpia.co.kr

최근 영상 dataset 을 이용하여 network 를 학습시키는 연구가 활발히 진행되면서 영상 dataset

구축의 중요성이 증가하고 있다. 이에 학습에 필요한 dataset 의수가 부족한 경우에는 기존

dataset 을 자르거나 회전시키는 등의 방법을 통해 인위적으로 dataset 의 수를늘리는 data …

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

[Korean Data Augmentation Technique Using WGAN ]

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

Coalescing-fragmentating Wasserstein dynamics: particle approach

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - arxiv.org

We construct a family of semimartingales which describe the behavior of a particle system

with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warren

flow, an infinite system of diffusion particles on the real line which sticky-reflect from each …

[PDF] Distributionally robust reward–risk ratio programming with Wasserstein metric

Y Zhao, Y Liu, J Zhang, X Yang - 2017 - optimization-online.org

Reward-risk ratio (RR) is a very important stock market definition. In order to capture the

situation that the investor does not have complete information on the distribution of the

underlying uncertainty, people extend RR model to distributionally robust reward-risk ratio …

A Robust Learning Algorithm for Regression Models Using Distributionally Robust Optimization under the Wasserstein Metric

R Chen, IC Paschalidis - arXiv preprint arXiv:1706.02412, 2017 - arxiv.org

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified

regression plane in a linear regression setting, when the observed samples are potentially

contaminated with adversarially corrupted outliers. Our approach mitigates the impact of …

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

<——2017—— —2017 ——— 620—

Wasserstein Distributionally Robust Optimization and Variation Regularization

R Gao, X Chen, AJ Kleywegt - arXiv preprint arXiv:1712.06050, 2017 - arxiv.org

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical

success for various applications in operations research and machine learning, owing partly

to its regularization effect. Although connection between Wasserstein DRO and …

www.researchgate.net › ... › Robustness

Jun 17, 2017 — Distributionally Robust Chance-Constrained Voltage-Concerned DC-OPF with Wasserstein Metric · Abstract and Figures · Citations (5) ...

[CITATION] Distributionally robust chance-constrained voltage-concerned DC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao, J Liu - arXiv preprint arXiv …, 2017 - Working paper

Absolute continuity of Wasserstein barycenters over Alexandrov spaces

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

The time discretization of gradient flows in metric spaces uses variants of the celebrated

implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in this Note a

different approach, which allows us to construct two second-order in time numerical …

2017

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we prove that on a compact,-dimensional Alexandrov space with curvature at

least− 1, the Wasserstein barycenter of Borel probability measures is absolutely continuous

with respect to the-dimensional Hausdorff measure if one of them is.

2017

Regularized barycenters in the Wasserstein space

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

This paper is an overview of results that have been obtain in 2 on the convex regularization

of Wasserstein barycenters for random measures supported on\mathbb R^ d. We discuss

the existence and uniqueness of such barycenters for a large class of regularizing functions …

A Stochastic gradient method to compute Wasserstein barycenters of distributions

2017

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

2017 Cited by 581
Wasserstein Distance Guided Representation Learning for ...

Wasserstein Distance Guided Representation Learning for ...

by J Shen · 2017 · Cited by 581 — Wasserstein Distance Guided Representation Learning for Domain Adaptation. Authors:Jian Shen, Yanru Qu, Weinan Zhang, Yong Yu ·

by J Shen · ‎2017 · ‎Cited by 227 · ‎Related articles

Jul 5, 2017 — WDGRL utilizes a neural network, denoted by the domain critic, to estimate empirical Wasserstein distance between the source and target ...

[CITATION] Yong Yu

J Shen, Y Qu, W Zhang - Wasserstein distance guided representation learning …, 2017

Relaxed Wasserstein with applications to GANs

X Guo, J Hong, T Lin, N Yang - arXiv preprint arXiv:1705.07164, 2017 - arxiv.org

Comparing probability distributions is an integral part of many modern data-driven

applications, such as generative adversarial networks (GANs) and distributionally robust

optimization (DRO). We propose a novel class of statistical divergences called\textit …

Improved training of wasserstein gans - ‎Gulrajani - Cited by 4310

Improving the improved training of wasserstein gans: A … - ‎Wei - Cited by 134

On the regularization of wasserstein gans - ‎Petzka - Cited by 105

[CITATION] Denis Lukovnicov On the regularization of Wasserstein GANs

H Petzka, A Fischer - arXiv preprint arXiv:1709.08894, 2017

by I Gulrajani · ‎2017 · ‎Cited by 4310 · ‎Related articles

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only low-quality samples or fail to converge.

Cite as‎: ‎arXiv:1704.00028

[CITATION] Improved training of wasserstein GANs (2017)

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - Available

[CITATION] Improved training of Wasserstein GANs. arXiv e-prints

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - Online

[CITATION] Improved Training of Wasserstein GANs. arXiv e-prints, art

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017

<——2017—— —2017 ——— 630—

A framework for Wasserstein-1-type metrics

[PDF] {Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - Bulletin of Mathematical Sciences, 2017 - Springer

This is an expository paper on the theory of gradient flows, and in particular of those PDEs

which can be interpreted as gradient flows for the Wasserstein metric on the space of

probability measures (a distance induced by optimal transport). The starting point is the …

B Schmitzer, B Wirth - arXiv preprint arXiv:1701.01945, 2017 - arxiv.org

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy

measure between nonnegative measures of different mass. This generalization inherits the

convexity and computational efficiency from the Wasserstein-1 metric, and it includes …

SCCS Colloquium old - Sccswiki

https://www5.in.tum.de › wiki › index.php › SCCS_Col...

June 12, Alex Melkonyan, Implementation and Evaluation of Wasserstein Generative Adversarial Networks, 10:30, 01.09.014 · Moritz August.

[CITATION] Implementation and Evaluation of Wasserstein Generative Adversarial Networks

O Melkonyan - 2017 - mediatum.ub.tum.de

mediaTUM; Universitätsbibliothek; Technische Universität München. Logo. Benutzer: Gast Login:

de; en. Erweiterte Suche. mediaTUM Gesamtbestand. Hochschulbibliographie. Elektronische

Prüfungsarbeiten. Open Access Publikationen. Forschungsdaten. TUM.University Press …

[CITATION] Implementation and Evaluation of Wasserstein Generative Adversarial Networks

O Melkonyan - 2017 - mediatum.ub.tum.de

mediaTUM; Universitätsbibliothek; Technische Universität München. Logo. Benutzer: Gast Login:

de; en. Erweiterte Suche. mediaTUM Gesamtbestand. Hochschulbibliographie. Kollektionen.

Einrichtungen. Fakultäten. Fakultät für Mathematik. TUM School of Governance. Fakultät für Physik …

[CITATION] Implementation and Evaluation of Wasserstein Generative Adversarial Networks

O Melkonyan - 2017 - mediatum.ub.tum.de

mediaTUM; Universitätsbibliothek; Technische Universität München. Logo. Benutzer: Gast Login:

de; en. Erweiterte Suche. mediaTUM Gesamtbestand. Hochschulbibliographie. Elektronische

Prüfungsarbeiten. Open Access Publikationen. Forschungsdaten. TUM.University Press …

2017

Generalised Wasserstein Dice Score for Imbalanced Multi ...

by L Fidon · ‎2017 · ‎Cited by 89 · ‎Related articles

Jul 3, 2017 — 2) We propose a holistic CNN that embeds spatial information at multiple scales with deep supervision. 3) We show that the joint use of holistic CNNs and generalised Wasserstein Dice scores achieves segmentations that are more semantically meaningful for brain tumour segmentation.

Cite as: arXiv:1707.00478

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

Low Dose CT Image Denoising Using a Generative ... - arXiv

2017

PDF

by Q Yang · 2017 · Cited by 545 — 1. Low Dose CT Image Denoising Using a Generative. Adversarial Network with Wasserstein Distance and. Perceptual Loss. Qingsong Yang, Pingkun Yan*, ...

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

[HTML] Vers un théorème de la limite centrale dans l'espace de Wasserstein?

M Agueh, G Carlier - Comptes Rendus Mathématique, 2017 - Elsevier

Résumé Les barycentres dans l'espace de Wasserstein constituent une manière naturelle

d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines

appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons …

[French Towards a central limit theorem in Wasserstein space?]

2017 [PDF] uni-heidelberg.de

MAP Image Labeling Using Wasserstein Messages and Geometric Assignment

C Schnörr - Scale Space and Variational Methods in Computer …, 2017 - books.google.com

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by

following the Riemannian gradient flow of a given objective function on the so-called

assignment manifold. The approach evaluates user-defined data term and additionally …

2017

A Stochastic gradient method to compute Wasserstein barycenters of distributions

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

2017 [PDF] asso-afig.fr

[PDF] Barycentres de Wasserstein pour les diagrammes de persistance

J Tierny - annonces.asso-afig.fr

Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui

permet en pratique d'introduire une mesure de bruit sur les structures topologiques, comme

les singularités (sphères de couleur) dans cet exemple de carte d'élévation. Cette mesure …

The cramer distance as a solution to biased wasserstein gradients

2017

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

<——2017—— —2017 ——— 640—

Wasserstein distributional robustness and regularization in statistical learning

R Gao, X Chen, AJ Kleywegt - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

A central question in statistical learning is to design algorithms that not only perform well on

training data, but also generalize to new and unseen data. In this paper, we tackle this

question by formulating a distributionally robust stochastic optimization (DRSO) problem …

Cited by 82 Related articles

Minimax statistical learning with wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017 - arxiv.org

As opposed to standard empirical risk minimization (ERM), distributionally robust

optimization aims to minimize the worst-case risk over a larger ambiguity set containing the

original empirical distribution of the training data. In this work, we describe a minimax …

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

Cited by 2 Relate

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - … of the 31st International Conference on Neural …, 2017 - dl.acm.org

We introduce a novel framework for statistical analysis of populations of non-degenerate

Gaussian processes (GPs), which are natural representations of uncertain curves. This

allows inherent variation or uncertainty in function-valued data to be properly incorporated in …

2017

Ambiguity set and learning via Bregman and Wasserstein

X Guo, J Hong, N Yang - arXiv preprint arXiv:1705.08056, 2017 - arxiv.org

Construction of ambiguity set in robust optimization relies on the choice of divergences

between probability distributions. In distribution learning, choosing appropriate probability

distributions based on observed data is critical for approximating the true distribution. To …

A Robust Learning Algorithm for Regression Models Using Distributionally Robust Optimization under the Wasserstein Metric

R Chen, IC Paschalidis - arXiv preprint arXiv:1706.02412, 2017 - arxiv.org

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified

regression plane in a linear regression setting, when the observed samples are potentially

contaminated with adversarially corrupted outliers. Our approach mitigates the impact of …

www.researchgate.net › publication › 321070354_Unsup...

Unsupervised Audio Source Separation via Spectrum Energy ...

Download Citation | Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning | Sep

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

[PDF] SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole, D Coeurjolly… - perso.liris.cnrs.fr

SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based

unsupervised non-linear dictionary learning∗ … Morgan A. Schmitz† , Matthieu Heitz‡ , Nicolas

Bonneel‡ , Fred Ngol`e§ , David Coeurjolly‡ , Marco Cuturi¶, Gabriel Peyré , and Jean-Luc …

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

<——2017—— —2017 ——— 650—

inkhorn-AutoDiff: Tractable Wasserstein Learning of ...

www.semanticscholar.org › paper › Sinkhorn-AutoDiff:-...

Sinkhorn-AutoDiff: Tractable Wasserstein Learning of Generative Models ... Peyré, Marco Cuturi; Published 2017; Computer Science; arXiv: Machine Learning.

[CITATION] Sinkhorn-autodiff: Tractable wasserstein learning of generative models

A Genevay, G Peyré, M Cuturi - arXiv preprint arXiv:1706.00292, 2017

www.researchgate.net › publication › 317062116_Minim...

Request PDF | Minimax Statistical Learning and Domain Adaptation with ... the Wasserstein distance can be found in [Bernton et al., 2017, Lee and Raginsky, ...

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

Data-driven distributed optimization using Wasserstein ambiguity sets

A Cherukuri, J Cortés - 2017 55th Annual Allerton Conference …, 2017 - ieeexplore.ieee.org

This paper considers a general class of stochastic optimization problem for multiagent

systems. We assume that the probability distribution of the uncertain parameters is unknown

to the agents and instead, each agent gathers a certain number of samples of it. The …

Wasserstein identity testing

S Deng, W Li, X Wu - arXiv preprint arXiv:1710.10457, 2017 - arxiv.org

Uniformity testing and the more general identity testing are well studied problems in

distributional property testing. Most previous work focuses on testing under $ L_1 $-

distance. However, when the support is very large or even continuous, testing under $ L_1 …

[PDF] optimization-online.org

[PDF] Distributionally robust reward–risk ratio programming with Wasserstein metric

Y Zhao, Y Liu, J Zhang, X Yang - Available on Optimization …, 2017 - optimization-online.org

Reward-risk ratio (RR) is a very important stock market definition. In order to capture the

situation that the investor does not have complete information on the distribution of the

underlying uncertainty, people extend RR model to distributionally robust reward-risk ratio …

Wasserstein Distributionally Robust Optimization and Variation Regularization

R Gao, X Chen, AJ Kleywegt - arXiv preprint arXiv:1712.06050, 2017 - arxiv.org

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical

success for various applications in operations research and machine learning, owing partly

to its regularization effect. Although connection between Wasserstein DRO and …

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu, Y Zhang - IET Generation, Transmission …, 2017 - IET

In order to address the wind power uncertainty in the security constrained economic

dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve

and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

2017

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

MG Mora, MA Peletier, L Scardia - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider systems of n parallel edge dislocations in a single slip system, represented by

points in a two-dimensional domain; the elastic medium is modeled as a continuum. We

formulate the energy of this system in terms of the empirical measure of the dislocations and …

<——2017—— —2017 ——— 660—

Data-driven distributed optimization using Wasserstein ambiguity sets

A Cherukuri, J Cortés - 2017 55th Annual Allerton Conference …, 2017 - ieeexplore.ieee.org

This paper considers a general class of stochastic optimization problem for multiagent

systems. We assume that the probability distribution of the uncertain parameters is unknown

to the agents and instead, each agent gathers a certain number of samples of it. The …

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

On interpolation and curvature via Wasserstein geodesics

M Kell - Advances in Calculus of Variations, 2017 - degruyter.com

In this article, a proof of the interpolation inequality along geodesics in p-Wasserstein

spaces is given. This interpolation inequality was the main ingredient to prove the Borel–

Brascamp–Lieb inequality for general Riemannian and Finsler manifolds and led Lott …

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

Ambiguity set and learning via Bregman and Wasserstein

X Guo, J Hong, N Yang - arXiv preprint arXiv:1705.08056, 2017 - arxiv.org

Construction of ambiguity set in robust optimization relies on the choice of divergences

between probability distributions. In distribution learning, choosing appropriate probability

distributions based on observed data is critical for approximating the true distribution. To …

2017

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost

functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017 - arxiv.org

The Wasserstein distance between two probability measures on a metric space is a

measure of closeness with applications in statistics, probability, and machine learning. In

this work, we consider the fundamental question of how quickly the empirical measure …

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Relaxed Wasserstein with applications to GANs

X Guo, J Hong, T Lin, N Yang - arXiv preprint arXiv:1705.07164, 2017 - arxiv.org

Comparing probability distributions is an integral part of many modern data-driven

applications, such as generative adversarial networks (GANs) and distributionally robust

optimization (DRO). We propose a novel class of statistical divergences called\textit …

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more

generally, semiconvex) energies has led to advances in several areas of partial differential

equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

Enhancing diffusion MRI measures by integrating grey and white matter morphometry with hyperbolic wasserstein distance

W Zhang, J Shi, J Yu, L Zhan… - 2017 IEEE 14th …, 2017 - ieeexplore.ieee.org

In order to improve the preclinical diagnose of Alzheimer's disease (AD), there is a great

deal of interest in analyzing the AD related brain structural changes with magnetic

resonance image (MRI) analyses. As the major features, variation of the structural …

<——2017—— —2017 ——— 670—

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given …

Fast discrete distribution clustering using Wasserstein barycenter with sparse support

J Ye, P Wu, JZ Wang, J Li - IEEE Transactions on Signal …, 2017 - ieeexplore.ieee.org

In a variety of research areas, the weighted bag of vectors and the histogram are widely

used descriptors for complex objects. Both can be expressed as discrete distributions. D2-

clustering pursues the minimum total within-cluster variation for a set of discrete distributions …

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging

but highly valuable in real application scenarios. In most situations, the source and the target

speakers do not repeat the same texts or they may even speak different languages. In this …

CITATION] Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks. arXiv preprint arXiv: 170400849

CC Hsu, HT Hwang, YC Wu, Y Tsao, HM Wang - 2017

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

The Dice score is widely used for binary segmentation due to its robustness to class

imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for

training convolutional neural networks (CNN). Although CNNs trained using mean-class …

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

2017

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

Data-driven distributed optimization using Wasserstein ambiguity sets

A Cherukuri, J Cortés - 2017 55th Annual Allerton Conference …, 2017 - ieeexplore.ieee.org

This paper considers a general class of stochastic optimization problem for multiagent

systems. We assume that the probability distribution of the uncertain parameters is unknown

to the agents and instead, each agent gathers a certain number of samples of it. The …

Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant Sliced-Wasserstein Distance via Laplace--Beltrami Eigenmap

R Lai, H Zhao - SIAM Journal on Imaging Sciences, 2017 - SIAM

In this work, we propose computational models and algorithms for point cloud registration

with nonrigid transformation. First, point clouds sampled from manifolds originally embedded

in some Euclidean space are transformed to new point clouds embedded in R^n by the …

Correcting nuisance variation using wasserstein distance

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - arXiv preprint arXiv …, 2017 - arxiv.org

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological

information resulting from various factors affecting the cells. One motivating application is

drug development: morphological cell features can be captured from images, from which …

[CITATION] Correcting Nuisance Variation using Wasserstein Distance. arXiv

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - 2017 - Nov

MAP image labeling using Wasserstein messages and geometric assignment

F Åström, R Hühnerbein, F Savarino… - … Conference on Scale …, 2017 - Springer

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by

following the Riemannian gradient flow of a given objective function on the so-called

assignment manifold. The approach evaluates user-defined data term and additionally …

Posterior contraction in Gaussian process regression using Wasserstein approximations

<——2017—— —2017 ——— 680—

A Bhattacharya, D Pati - Information and Inference: A Journal of …, 2017 - academic.oup.com

We study posterior rates of contraction in Gaussian process regression with potentially

unbounded covariate domain. Our argument relies on developing a Gaussian

approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of …

A Robust Learning Algorithm for Regression Models Using Distributionally Robust Optimization under the Wasserstein Metric

R Chen, IC Paschalidis - arXiv preprint arXiv:1706.02412, 2017 - arxiv.org

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified

regression plane in a linear regression setting, when the observed samples are potentially

contaminated with adversarially corrupted outliers. Our approach mitigates the impact of …

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

www.researchgate.net › publication › 342021527_Image...

In recent years, generative adversarial network (GAN) becomes a new avenue in computer vision research. The GANs are adversarial networks with generative ...

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

Correcting nuisance variation using wasserstein distance

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - arXiv preprint arXiv …, 2017 - arxiv.org

Page 1. Correcting Nuisance Variation using Wasserstein Distance … Lee et al. (2014) proposed

a multivariate batch adjustment method that can correct for the variance-covariance of data

across batches … (2017). 2.5.2 Silhouette Score on Mechanism of Action …

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Davis, G Tabak, M Fan, S Yang, S Hoyer - 2017

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Tabak, M Fan, S Yang, S Hoyer, G Davis - 2017

2017

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given

parameters and comparing summaries of these simulations with the corresponding

observed values. We propose to avoid these summaries and the ensuing loss of information

through the use of Wasserstein distances between empirical distributions of observed and …

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary -dependent sequences

J Dedecker, F Merlevede - Bernoulli, 2017 - projecteuclid.org

We study the Wasserstein distance of order 1 between the empirical distribution and the

marginal distribution of stationary $\alpha $-dependent sequences. We prove some

moments inequalities of order $ p $ for any $ p\geq1 $, and we give some conditions under …

Unsupervised Audio Source Separation via Spectrum Energy ...

deepai.org › publication › unsupervised-audio-source

Nov 11, 2017 · Algorithm 1 Source Separation GAN (SSGAN): Energy preserved Wasserstein learning of audio source separation. 2.3 Architecture of ASS Generator/Discriminator In our model, the generator aims to separate the mixed signal into n sources, while the discriminator tries to distinguish each separated source with the real ones.

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

Sharp asymptotic and finite-sample rates of convergence of ...

arxiv.org › abs › 1707

Jul 01, 2017 · The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the empirical measure obtained from independent samples from approaches in the Wasserstein distance of any order. We prove sharp asymptotic and finite-sample results for this rate of convergence for general measures on general compact metric spaces.

Author: Jonathan Weed, Francis Bach

Cited by: 107

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Separating audio mixtures into individual instrument tracks has been a long standing

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[PDF] pku.edu.cn

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by C Duan · 2017 · Cited by 75 — ... Chance-Constrained Approximate AC-OPF with Wasserstein Metric ... employed in the distributionally robust formulation is the Wasserstein ..

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arXiv [v1] Tue, 18 Apr 2017 18:38:15 UTC (141 KB)

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A kind of pedestrian detection method based on WGAN model

CN CN108009568A 周智恒华南理工大学

Priority 2017-11-14 • Filed 2017-11-14 • Published 2018-05-08

1. a kind of pedestrian detection method based on WGAN models, it is characterised in that the pedestrian detection method includes following step Suddenly： S1, construction are originally generated confrontation network model, and generating image by maker inputs to arbiter progress network

2017 zzz 36 see 2017 in Frech

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Jun 1, 2017 — Corpus ID: 125154984. Sinkhorn-AutoDiff: Tractable Wasserstein Learning of Generative Models. @article{Genevay2017SinkhornAutoDiffTW ...

[CITATION] Sinkhorn-autodiff: Tractable wasserstein learning of generative models

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the space of probability measures with a finite first moment on a complete and separable …

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - Annals of Economics and Statistics …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality

V Barbu - SIAM Journal on Control and Optimization, 2017 - SIAM

The nonlinear diffusion equation \rho_t-Δ(ρH(ρ-\rho_c))=0 in (0,∞)*R^n, ρ(0,x)=\rho_0(x),

where H is the Heaviside function, describes the sandpile model P. Bak, C. Tang, and K.

Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and IM Janosi, Phys. A, 185 (1992) …

2017

On reproduction of On the regularization of Wasserstein GANs

J Seo, T Jeon - arXiv preprint arXiv:1712.05882, 2017 - arxiv.org

This report has several purposes. First, our report is written to investigate the reproducibility

of the submitted paper On the regularization of Wasserstein GANs (2018). Second, among

the experiments performed in the submitted paper, five aspects were emphasized and …

[PDF] Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

[PDF] rwth-aachen.de

M Kampschulte, M Westdickenberg, RL Jerrard… - 2017 - publications.rwth-aachen.de

The main aim of this thesis is to explore a possible approach to gradient flows for Cartesian

(and other) currents. We will do so using the method of minimizing movements. The key

ingredient for this turns out to be the right choice of metric. For this we propose a …

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

[PDF] Hybrid Machine Learning Approaches of Weather Data with Distribution-Valued Based on Wasserstein Distance

ZQ Wang, JT Jeng, CC Chuang - maselab318.nfu.edu.tw

In this paper, we present a hybrid machine learning approaches to analyze distribution-

valued weather data with Wasserstein distance. In general, distribution-valued data are

described as multivalued data (eg, an interval, a histogram, a density, or a quantile function) …

PDF] Wasserstein Training of Deep Boltzmann Machines

C Wang, T Tong, Y Zou - cs.cmu.edu

Training various probabilistic graphical models, such as restricted Boltzmann machines

(RBMs), deep Boltzmann machines (DBMs), is usually done by maximum likelihood

estimation, or equivalently minimizing the Kullback-Leibler (KL) divergence between the …

<——2017—— —2017 ——— 770—

2017

Evolution of the Wasserstein distance between the marginals of two Markov processes

J Corbetta - 2017 - pdfs.semanticscholar.org

Page 1. Evolution of the Wasserstein distance between the marginals of two Markov

processes Jacopo Corbetta (École des Ponts - ParisTech) Joint work with: Aurélien

Alfonsi and Benjamin Jourdain January 10, 2017 …

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

In this paper we derive a formula for the sample size of a nonparametric test based on

weighted L 2-Wasserstein distance with a known alternative. As an example we apply the

formula to determine the sample size for a hypothesis testing from the Tukey's contaminated …

Sinkhorn-AutoDiff: Tractable Wasserstein Learning of ...

https://www.semanticscholar.org › paper › Sinkhorn-Auto...

This paper presents the first tractable computational method to train large scale generative models using an optimal transport loss, and tackles both these issues ...

[CITATION] Sinkhorn-autodiff: Tractable wasserstein learning of generative models

A Genevay, G Peyré, M Cuturi - arXiv preprint arXiv:1706.00292, 2017

[CITATION] Improved training of Wasserstein GANs. arXiv e-prints

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - Online

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Save Cite Cited by 17 Related articles All 5 versions

2017

2017 [HTML] sciencedirect.com

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

… The time discretization of gradient flows in metric spaces uses … In a metric space framework,

we show that the schemes are … –Planck gradient flow in the Wasserstein space, we obtain (…

by I Gulrajani · 2017 · Cited by 4544 — The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but ... Comments: NIPS camera-ready.

[CITATION] Improved training of wasserstein gans. in Advances in neural information processing systems

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - 2017

[CITATION] V. & Courville, A. Improved training of Wasserstein GANs

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin - Neural, Information Processing …, 2017

Coalescing-fragmentating Wasserstein dynamics: particle approach

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - arxiv.org

… where dW denotes the usual Wasserstein distance on the space of probability measures

P2(R) on the real line with a finite second moment. This led to a new family of measure-valued …

Cited by 9 Related articles A

Approximation of stable law in Wasserstein-1 distance by ...

Approximation of stable law in Wasserstein-1 distance by Stein's method. can be interpreted as an L^{1} Stein discrepancy. As an application, we prove a general theorem of stable law convergence rate when \zeta_{n,i} are i.i.d. and the distribution falls in the normal domain of attraction of \mu.Sep 4, 2017

[CITATION] Approximation of stable law in Wasserstein-1 distance by Stein's method. Accepted by Annals of Applied Probability

L Xu - arXiv preprint arXiv:1709.00805, 2017

Wasserstein distributional robustness and regularization in statistical learning

<——2017—— —2017 ——— 780—

[PDF] {Euclidean, metric, and Wasserstein} gradient flows: an overview

F Santambrogio - Bulletin of Mathematical Sciences, 2017 - Springer

This is an expository paper on the theory of gradient flows, and in particular of those PDEs

which can be interpreted as gradient flows for the Wasserstein metric on the space of

probability measures (a distance induced by optimal transport). The starting point is the …

R Gao, X Chen, AJ Kleywegt - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

A central question in statistical learning is to design algorithms that not only perform well on

training data, but also generalize to new and unseen data. In this paper, we tackle this

question by formulating a distributionally robust stochastic optimization (DRSO) problem …

Cited by 83 Related articles

[PDF] wiley.com

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu, Y Zhang - IET Generation, Transmission …, 2017 - IET

In order to address the wind power uncertainty in the security constrained economic

dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve

and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

The time discretization of gradient flows in metric spaces uses variants of the celebrated

implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in this Note a

different approach, which allows us to construct two second-order in time numerical …

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

2017

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more

generally, semiconvex) energies has led to advances in several areas of partial differential

equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

MAP image labeling using Wasserstein messages and geometric assignment

F Åström, R Hühnerbein, F Savarino… - … on Scale Space and …, 2017 - Springer

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by

following the Riemannian gradient flow of a given objective function on the so-called

assignment manifold. The approach evaluates user-defined data term and additionally …

Optimal ballistic transport and Hopf-Lax formulae on Wasserstein space

N Ghoussoub - arXiv preprint arXiv:1705.05951, 2017 - arxiv.org

We investigate the optimal mass transport problem associated to the following" ballistic" cost

functional on phase space $ M\times M^* $, $$ b_T (v, x):=\inf\{\langle v,\gamma

(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt,\gamma\in C^ 1 ([0, T), M),\gamma …

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite

first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices,

and consider the problem of differentiability of the corresponding Cartan barycentric …

<——2017—— —2017 ——— 790—

Strongly Polynomial 2-Approximations of ... - ResearchGate

https://www.researchgate.net › ... › Algebra › Polynomials

Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals. These arise in applications from economics to ...

[CITATION] Strongly polynomial 2-approximations of discrete Wasserstein barycenters

S Borgwardt - arXiv preprint arXiv:1704.05491, 2017

Sampling of probability measures in the convex order ... - arXiv

by A Alfonsi · 2017 · Cited by 26 — Title:Sampling of probability measures in the convex order by Wasserstein projection ; Subjects: Probability (math.PR); Computational Finance (q- ...

[CITATION] Sampling of probability measures in the convex order by Wasserstein projection. arXiv e-prints, page

A Alfonsi, J Corbetta, B Jourdain - arXiv preprint arXiv:1709.05287, 2017

Contraction in the Wasserstein metric for some Markov chains ...

z2017 see 2014 2015

https://www.researchgate.net › publication › 269116364_...

We employ techniques from optimal transport in order to prove the decay of transfer operators associated with iterated functions systems and expanding maps, ...

[CITATION] Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

A Stochastic gradient method to compute Wasserstein barycenters of distributions

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

2017 [PDF] mlr.press [cited by many!]

Wasserstein generative adversarial networks

M Arjovsky, S Chintala, L Bottou - … conference on machine …, 2017 - proceedings.mlr.press

… • In Section 3, we define a form of GAN called Wasserstein-GAN that minimizes a reasonable and efficient approximation of the EM distance, and we theoretically show that the …

Cited by 10094 Related articles All 11 versions

CITATION] Wasserstein GAN. arXiv e-prints, page

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017

Cited by 22 Related articles

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

Cited by 27 Related articles

[CITATION] Wasserstein GAN. arXiv e-prints

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017

[CITATION] Martin and L. Bottou. Wasserstein GAN

SC Arjovsky - arXiv preprint arXiv:1701.07875, 2017

[CITATION] Wasserstein GAN. ArXiv e-prints, January 2017

M Arjovsky, S Chintala, L Bottou - arXiv preprint arXiv:1701.07875, 2017

ave Cite Cited by 113 Related articles

2017

Ambiguity set and learning via Bregman and Wasserstein

X Guo, J Hong, N Yang - arXiv preprint arXiv:1705.08056, 2017 - arxiv.org

Construction of ambiguity set in robust optimization relies on the choice of divergences

between probability distributions. In distribution learning, choosing appropriate probability

distributions based on observed data is critical for approximating the true distribution. To …

Enhancing diffusion MRI measures by integrating grey and white matter morphometry with hyperbolic wasserstein distance

W Zhang, J Shi, J Yu, L Zhan… - 2017 IEEE 14th …, 2017 - ieeexplore.ieee.org

In order to improve the preclinical diagnose of Alzheimer's disease (AD), there is a great

deal of interest in analyzing the AD related brain structural changes with magnetic

resonance image (MRI) analyses. As the major features, variation of the structural …

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too

large and complex for easy computation. Because continuous transport problems are

generally solved by conversion to either discrete or semi-discrete forms, I focused on …

Aggregated Wasserstein Metric and State Registration for Hidden Markov Models

Y Chen, J Ye, J Li - arXiv preprint arXiv:1711.05792, 2017 - arxiv.org

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity

measure or distance between two Hidden Markov Models with state conditional distributions

being Gaussian. For such HMMs, the marginal distribution at any time position follows a …

Wasserstein Distributionally Robust Optimization and Variation Regularization

R Gao, X Chen, AJ Kleywegt - arXiv preprint arXiv:1712.06050, 2017 - arxiv.org

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical

success for various applications in operations research and machine learning, owing partly

to its regularization effect. Although connection between Wasserstein DRO and …

<——2017—— —2017 ——— 800—

Hyperspectral and multispectral Wasserstein barycenter for image fusion

J Mifdal, B Coll, N Courty, J Froment… - … Geoscience and …, 2017 - ieeexplore.ieee.org

The fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows

the extraction of relevant information from the fused image. Fusion consists of the

combination of the spectral information of the hypespectral image (h) and the spatial …

MAP Image Labeling Using Wasserstein Messages and Geometric Assignment

C Schnörr - Scale Space and Variational Methods in Computer …, 2017 - books.google.com

Recently, a smooth geometric approach to the image labeling problem was proposed [1] by

following the Riemannian gradient flow of a given objective function on the so-called

assignment manifold. The approach evaluates user-defined data term and additionally …

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN

method is proposed based on LBP features and entropy-regularized Wasserstein distance,

by combining the mathematical properties of Wasserstein distance in optimal mass …

On interpolation and curvature via Wasserstein geodesics in ...

https://www.degruyter.com › journals › acv › article-p125

by M Kell · 2017 · Cited by 14 — Based on Ohta's proof [25] we show how to prove an interpolation inequality via geodesics in the p-Wasserstein spaces for any p > 1 . This interpolation ...

Minimax Statistical Learning with Wasserstein Distances

[CITATION] On interpolation and curvature via Wasserstein geodesics

M Kell - Advances in Calculus of Variations, 2017 - De Gruyter

by J Lee · 2017 · Cited by 62 — As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data.

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

Wasserstein GAN and the Kantorovich-Rubinstein Duality ...

2017

https://vincentherrmann.github.io › blog › wasserstein

Feb 24, 2017 — The argument for our case of the Kantorovich-Rubinstein duality is ... For discrete probability distributions, the Wasserstein distance is also ...

[CITATION] Wasserstein gan and the kantorovich-rubinstein duality

V Herrmann - … : https://vincentherrmann. github. io/blog/wasserstein, 2017

Optimal Transport and Wasserstein Distance - CMU Statistics

2017 see 2018 2019 PDF

https://www.stat.cmu.edu › ~larry › Opt

by S Kolouri — Optimal Mass Transport: Signal processing and machine-learning applications. IEEE Signal Processing Magazine 34.4 (2017): 43-59. Villani, Cedric. Topics in ...

[CITATION] Optimal transport and wasserstein distance

L Wasserman - 2017

earning to solve inverse problems using Wasserstein loss

by J Adler · 2017 · Cited by 22 — [Submitted on 30 Oct 2017] ... We prove that training with the Wasserstein loss gives a reconstruction operator that ... mean squared error and optimal transport loss for a problem in computerized tomography. .

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

2017 see 2003

[CITATION] Optimal transport and wasserstein distance

L Wasserman - 2017

[PDF] SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

2017 [PDF] cnrs.fr

MA Schmitz, M Heitz, N Bonneel, F Ngole, D Coeurjolly… - perso.liris.cnrs.fr

SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning∗ … Morgan A. Schmitz† , Matthieu Heitz‡ , Nicolas Bonneel‡ , Fred Ngol`e§ , David Coeurjolly‡ , Marco Cuturi¶, Gabriel Peyré , and Jean-Luc …

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

<——2017—— —2017 ——— 810 —

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given …

[CITATION] Inference in generative models using the Wasserstein distance

Geodesic PCA in the Wasserstein space by convex PCA

J Bigot, R Gouet, T Klein, A López - Annales de l'Institut Henri …, 2017 - projecteuclid.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

Reversible coalescing-fragmentating Wasserstein dynamics on the real line

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1709.02839, 2017 - arxiv.org

We introduce a family of reversible fragmentating-coagulating processes of particles of

varying size-scaled diffusivity with strictly local interaction on the real line. The construction

is based on a new family of measures on the set of real increasing functions as reference …

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and

energy loads, as well as their multi-energy interactions and dependencies, have negligible

effects on the operation and analyses of integrated energy systems. Determining how to …

2017

On wasserstein reinforcement learning and the fokker-planck equation

PH Richemond, B Maginnis - arXiv preprint arXiv:1712.07185, 2017 - arxiv.org

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

[PDF] Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

A Mallasto, A Feragen - … of the 31st International Conference on …, 2017 - papers.neurips.cc

We introduce a novel framework for statistical analysis of populations of nondegenerate

Gaussian processes (GPs), which are natural representations of uncertain curves. This

allows inherent variation or uncertainty in function-valued data to be properly incorporated in …

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more

generally, semiconvex) energies has led to advances in several areas of partial differential

equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices

F Hiai, Y Lim - Linear Algebra and its Applications, 2017 - Elsevier

We introduce a class of flows on the Wasserstein space of probability measures with finite

first moment on the Cartan–Hadamard Riemannian manifold of positive definite matrices,

and consider the problem of differentiability of the corresponding Cartan barycentric …

Regularized barycenters in the Wasserstein space

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

This paper is an overview of results that have been obtain in 2 on the convex regularization

of Wasserstein barycenters for random measures supported on\mathbb R^ d. We discuss

the existence and uniqueness of such barycenters for a large class of regularizing functions …

<——2017—— —2017 ——— 820 —

Exponential convergence in the Wasserstein metric for one dimensional diffusions

L Cheng, R Li, L Wu - arXiv preprint arXiv:1703.00507, 2017 - arxiv.org

In this paper, we find some general and efficient sufficient conditions for the exponential

convergence $ W_ {1, d}(P_t (x,\cdot), P_t (y,\cdot))\le Ke^{-\delta t} d (x, y) $ for the

semigroup $(P_t) $ of one-dimensional diffusion. Moreover some sharp estimates of the …

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too

large and complex for easy computation. Because continuous transport problems are

generally solved by conversion to either discrete or semi-discrete forms, I focused on …

A partial Laplacian as an infinitesimal generator on the Wasserstein space

[PDF] The WASSERSTEIN DISTANCE AS A UNIVARIATE NEUROIMAGING BIOMARKER FOR FDG-PET ANALYSIS

L Mi, W Zhang, J Zhang, Y Fan, D Goradia, K Chen… - gsl.lab.asu.edu

We propose a univariate biomarker of the FDGPET images by using the Wasserstein

distance. We apply the biomarker to the Alzheimer's disease (AD) analysis. The

experimental results demonstrate the robustness of our biomarker in distinguishing AD from …

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

D Cheng, KA Okoudjou - Wavelets and Sparsity XVII, 2017 - spiedigitallibrary.org

It is known in the standard l 2 distance that the closest Parseval frame to a given frame {Φ i}

mi= 1⊂ ℜ d is {S-1/2 (Φ i)} mi= 1 where S is the frame operator of the original frame. We

show this is also the case for probabilistic frames in the 2-Wasserstein distance. In the …

Wasserstein GAN and the Kantorovich-Rubinstein Duality ...

2017

https://vincentherrmann.github.io › blog › wasserstein

Feb 24, 2017 — The argument for our case of the Kantorovich-Rubinstein duality is ... For discrete probability distributions, the Wasserstein distance is also ...

[CITATION] Wasserstein gan and the kantorovich-rubinstein duality

V Herrmann - … : https://vincentherrmann. github. io/blog/wasserstein, 2017

Towards a central limit theorem in the Wasserstein space?

D] Wasserstein GAN and the Kantorovich-Rubinstein Duality

ut the underlying reason for people to want to "care about WGAN" is ... Research 2022 - Outperforms the 600x larger PaLM-540B on XSum!

Reddit · Leo ·

Feb 24, 2017

https://dspace.library.uvic.ca › handle

An Informal Introduction to the Maths Behind Wasserstein GAN

byM Agueh · 2017 · Cited by 13 — Vers un théorème de la limite centrale dans l'espace de Wasserstein ?/ Towards a central limit theorem in the ... Date: 2017 ... We conjecture that such barycenters obey a central limit theorem which we prove in some (very) particular cases.

[CITATION] Towards a central limit theorem in the Wasserstein space?

M Agueh, G Carlier - COMPTES …, 2017 - ELSEVIER FRANCE-EDITIONS …

2017 PDF

by Q Bai · 2017 — An Informal Introduction to the Maths Behind. Wasserstein GAN. Qinxun Bai. February, 2017. Briefly speaking, [1] explains from a theoretical perspective why ...

6 pages

CITATION] An Informal Introduction to the Maths Behind Wasserstein GAN

Q Bai - 2017

A simulated annealing based inexact oracle for Wasserstein loss minimization

J Ye, JZ Wang, J Li - International Conference on Machine …, 2017 - proceedings.mlr.press

Learning under a Wasserstein loss, aka Wasserstein loss minimization (WLM), is an

emerging research topic for gaining insights from a large set of structured objects. Despite

being conceptually simple, WLM problems are computationally challenging because they …

[PDF] A particle model for Wasserstein type diffusion

V Konarovskyi, M von Renesse - math.uni-leipzig.de

A particle model for Wasserstein type diffusion … ∂tµt = β 2 ∆µt + ∇ · ( µt∇ δF(µt) δµt … –

Dean-Kawasaki equation The equation appears in macroscopic fluctuation theory and glass

dynamic models D. Dean '96, K. Kawasaki, E. Vanden-Eijnden, A. Donev, B. Derrida, J …

Sliced wasserstein kernel for persistence diagrams

<——2017—— —2017 ——— 830 —

2017

M Carriere, M Cuturi, S Oudot - International Conference on …, 2017 - proceedings.mlr.press

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they

are routinely used to describe succinctly complex topological properties of complicated

shapes. PDs enjoy strong stability properties and have proven their utility in various learning …

[CITATION] Sliced wasserstein kernel for persistence diagrams. arXiv preprint 548

M Carriere, M Cuturi, S Oudot - arXiv preprint arXiv:1706.03358, 2017

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

The Dice score is widely used for binary segmentation due to its robustness to class

imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for

training convolutional neural networks (CNN). Although CNNs trained using mean-class …

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

Order-preserving wasserstein distance for sequence matching

B Su, G Hua - Proceedings of the IEEE conference on …, 2017 - openaccess.thecvf.com

We present a new distance measure between sequences that can tackle local temporal

distortion and periodic sequences with arbitrary starting points. Through viewing the

instances of sequences as empirical samples of an unknown distribution, we cast the …

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

A framework for Wasserstein-1-type metrics

B Schmitzer, B Wirth - arXiv preprint arXiv:1701.01945, 2017 - arxiv.org

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy

measure between nonnegative measures of different mass. This generalization inherits the

convexity and computational efficiency from the Wasserstein-1 metric, and it includes …

2017

A Central Limit Theorem for Wasserstein type distances between two different laws

P Berthet, JC Fort, T Klein - arXiv preprint arXiv:1710.09763, 2017 - arxiv.org

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

Automatic color correction for multisource remote sensing images with Wasserstein CNN

J Guo, Z Pan, B Lei, C Ding - Remote Sensing, 2017 - mdpi.com

In this paper a non-parametric model based on Wasserstein CNN is proposed for color

correction. It is suitable for large-scale remote sensing image preprocessing from multiple

sources under various viewing conditions, including illumination variances, atmosphere …

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

[PDF] mjstaib.com

[PDF] Wasserstein k-means++ for cloud regime histogram clustering

M Staib, S Jegelka - Climate informatics, 2017 - mjstaib.com

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

k-means clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

Effective Lipschitz constraint enforcement for Wasserstein GAN training

S Cui, Y Jiang - 2017 2nd IEEE International Conference on …, 2017 - ieeexplore.ieee.org

Generative Adversarial Networks (GANs) are efficient frameworks for estimating generative

model via adversarial process. However, GAN has known for suffering from training

instability. Wasserstein GAN (WGAN) improves the training stability significantly but also …

<——2017—— —2017 ——— 840 —

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a

variational model for nonuniform illumination correction, that incorporates a penalty term that …

Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction

X CAO, Y XIN - Journal of Computer Applications, 2017 - en.cnki.com.cn

Dimensionality reduction plays an important role in big data analysis and visualization.

Many dimensionality reduction techniques with probabilistic distribution models rely on the

optimizaition of cost function between low-dimensional model distribution and high …

[PDF] AP Clustering with Wasserstein Distances for Distribution-Valued Data Analysis

YC Li, JT Jeng, CC Chuang, SH Du - maselab318.nfu.edu.tw

In general, Affinity Propagation (AP) Clustering is a new grouping method by passing

messages between data points. AP clustering can cluster without known the number of

cluster in advance. However, the Euclidean distance widely used for calculating similarity …

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

https://www.researchgate.net › publication › fulltext › Cor...

by G Tabak · 2017 · Cited by 3 — Correcting Nuisance Variation using Wasserstein Distance ... particular batch a set of experiments were conducted in constitutes the domain of the ... unknown effects) are mapped to embeddings, which are used to reveal ...

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Davis, G Tabak, M Fan, S Yang, S Hoyer - 2017

[CITATION] Correcting for Batch Effects Using Wasserstein Distance

G Tabak, M Fan, S Yang, S Hoyer, G Davis - 2017

2017

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

A framework for Wasserstein-1-type metrics

B Schmitzer, B Wirth - arXiv preprint arXiv:1701.01945, 2017 - arxiv.org

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy

measure between nonnegative measures of different mass. This generalization inherits the

convexity and computational efficiency from the Wasserstein-1 metric, and it includes …

A Central Limit Theorem for Wasserstein type distances between two different laws

P Berthet, JC Fort, T Klein - arXiv preprint arXiv:1710.09763, 2017 - arxiv.org

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

A simulated annealing based inexact oracle for Wasserstein loss minimization

J Ye, JZ Wang, J Li - International Conference on Machine …, 2017 - proceedings.mlr.press

Learning under a Wasserstein loss, aka Wasserstein loss minimization (WLM), is an

emerging research topic for gaining insights from a large set of structured objects. Despite

being conceptually simple, WLM problems are computationally challenging because they …

<——2017—— —2017 ——— 850 —

[PDF] A particle model for Wasserstein type diffusion

V Konarovskyi, M von Renesse - math.uni-leipzig.de

A particle model for Wasserstein type diffusion … ∂tµt = β 2 ∆µt + ∇ · ( µt∇ δF(µt) δµt … –

Dean-Kawasaki equation The equation appears in macroscopic fluctuation theory and glass

dynamic models D. Dean '96, K. Kawasaki, E. Vanden-Eijnden, A. Donev, B. Derrida, J …

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a

variational model for nonuniform illumination correction, that incorporates a penalty term that …

2017 zzz 37 see 2019

[CITATION] A degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

[CITATION] A degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

D Cheng, KA Okoudjou - Wavelets and Sparsity XVII, 2017 - spiedigitallibrary.org

It is known in the standard l 2 distance that the closest Parseval frame to a given frame {Φ i}

mi= 1⊂ ℜ d is {S-1/2 (Φ i)} mi= 1 where S is the frame operator of the original frame. We

show this is also the case for probabilistic frames in the 2-Wasserstein distance. In the …

2017 see 2018

by I Gulrajani · 2017 · Cited by 4589 — The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but ... Comments: NIPS camera-ready.

[CITATION] Improved training of wasserstein gans. in Advances in neural information processing systems

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - 2017

Cited by 6774 Related articles All 12 versions ßƒ

[CITATION] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - Ecole Polytechnique Fédérale de …

Approximation of stable law in Wasserstein-1 distance by ...

2017

https://ui.adsabs.harvard.edu › abs › abstract

by L Xu · 2017 · Cited by 19 — The integral term $$\sum_{i=1}^n\int_{-N}^N \left|\frac{\mathcal K_\alpha(t,N)}n -\frac{ ... Approximation of stable law in Wasserstein-1 distance by Stein's method.

[CITATION] Approximation of stable law in Wasserstein-1 distance by Stein's method. Accepted by Annals of Applied Probability

L Xu - arXiv preprint arXiv:1709.00805, 2017

Sampling of probability measures in the convex order by ...

by A Alfonsi · 2017 · Cited by 19 — Sampling of probability measures in the convex order by Wasserstein projection. ... The motivation is the design of sampling techniques preserving the convex order in order to approximate Martingale Optimal Transport problems by using linear programming solvers.

[CITATION] Sampling of probability measures in the convex order by Wasserstein projection. arXiv e-prints, page

A Alfonsi, J Corbetta, B Jourdain - arXiv preprint arXiv:1709.05287, 2017

SAMPLING OF PROBABILITY MEASURES IN THE CONVEX ORDER BY WASSERSTEIN PROJECTION

2017 see 2015 2014

Controlling the statistical properties of expanding maps

https://iopscience.iop.org › article

by S Galatolo · 2017 · Cited by 21 — Controlling the statistical properties of expanding maps. Stefano Galatolo3,1 and Mark Pollicott2. Published 26 May 2017 • © 2017 IOP Publishing Ltd ...

[CITATION] Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

[PDF] An Informal Introduction to the Maths Behind | Semantic ...

https://www.semanticscholar.org › paper › An-Informal-I...

Briefly speaking, [1] explains from a theoretical perspective why training GAN is hard, and [2] suggests a solution from the perspective of geometric foundation of ...

Missing: Wasserstein ‎| Must include: Wasserstein

[CITATION] An Informal Introduction to the Maths Behind Wasserstein GAN

Q Bai - 2017

Towards a central limit theorem in the Wasserstein space?

https://dspace.library.uvic.ca › handle

Comptes Rendus Mathematique

by M Agueh · 2017 · Cited by 13 — Vers un théorème de la limite centrale dans l'espace de Wasserstein ?/ Towards a central limit theorem in the ... Date: 2017 ... We conjecture that such barycenters obey a central limit theorem which we prove in some (very) particular cases.

[CITATION] Towards a central limit theorem in the Wasserstein space?

M Agueh, G Carlier - COMPTES …, 2017 - ELSEVIER FRANCE-EDITIONS …

[CITATION] Towards a central limit theorem in the Wasserstein space?

M ƒ, G Carlier - COMPTES …, 2017 - ELSEVIER FRANCE-EDITIONS …

Volume 355, Issue 7, July 2017, Pages 812-818

Vers un théorème de la limite centrale dans l'espace de Wasserstein ?

Vers un théorème de la limite centrale dans l'espace de Wasserstein ?

A Stochastic gradient method to compute Wasserstein barycenters of distributions

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability

distributions, in the sense of Wassertein. The objective is to devise a fast method which can

be used for instance to perform clustering for machine learning. The optimal transport [1] …

<——2017—— —2017 ——— 860 —

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

Wasserstein distributional robustness and regularization in statistical learning

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given …

R Gao, X Chen, AJ Kleywegt - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

A central question in statistical learning is to design algorithms that not only perform well on

training data, but also generalize to new and unseen data. In this paper, we tackle this

question by formulating a distributionally robust stochastic optimization (DRSO) problem …

Cited by 84 Related articles

Geodesic PCA in the Wasserstein space by convex PCA

J Bigot, R Gouet, T Klein, A López - Annales de l'Institut Henri …, 2017 - projecteuclid.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] Learning to solve inverse problems using Wasserstein loss, ArXiv, 1710.10898 (2017)

J Adler, A Ringh, O Öktem, J Karlsson - Poster in NIPS, 2017

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

2017

Relaxed Wasserstein with applications to GANs

X Guo, J Hong, T Lin, N Yang - arXiv preprint arXiv:1705.07164, 2017 - arxiv.org

Comparing probability distributions is an integral part of many modern data-driven

applications, such as generative adversarial networks (GANs) and distributionally robust

optimization (DRO). We propose a novel class of statistical divergences called\textit …

Detecting changes in forced climate attractors with Wasserstein distance

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - npg.copernicus.org

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

Extremal curves in Wasserstein space

G Conforti, M Pavon - International Conference on Geometric Science of …, 2017 - Springer

We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges

and the classic Madelung fluid can be derived from variational principles on Wasserstein

space. The second order differential equations are accordingly obtained by annihilating the …

<——2017—— —2017 ——— 870 —

The cramer distance as a solution to biased wasserstein gradients

MG Bellemare, I Danihelka, W Dabney… - arXiv preprint arXiv …, 2017 - arxiv.org

The Wasserstein probability metric has received much attention from the machine learning

community. Unlike the Kullback-Leibler divergence, which strictly measures change in

probability, the Wasserstein metric reflects the underlying geometry between outcomes. The …

Wasserstein distributional robustness and regularization in statistical learning

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given …

R Gao, X Chen, AJ Kleywegt - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

A central question in statistical learning is to design algorithms that not only perform well on

training data, but also generalize to new and unseen data. In this paper, we tackle this

question by formulating a distributionally robust stochastic optimization (DRSO) problem …

Cited by 84 Related articles

Geodesic PCA in the Wasserstein space by convex PCA

J Bigot, R Gouet, T Klein, A López - Annales de l'Institut Henri …, 2017 - projecteuclid.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

Learning to solve inverse problems using Wasserstein loss

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] Learning to solve inverse problems using Wasserstein loss, ArXiv, 1710.10898 (2017)

J Adler, A Ringh, O Öktem, J Karlsson - Poster in NIPS, 2017

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

2017

Relaxed Wasserstein with applications to GANs

X Guo, J Hong, T Lin, N Yang - arXiv preprint arXiv:1705.07164, 2017 - arxiv.org

Comparing probability distributions is an integral part of many modern data-driven

applications, such as generative adversarial networks (GANs) and distributionally robust

optimization (DRO). We propose a novel class of statistical divergences called\textit …

Detecting changes in forced climate attractors with Wasserstein distance

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - npg.copernicus.org

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations

D Kinderlehrer, L Monsaingeon, X Xu - … : Control, Optimisation and …, 2017 - esaim-cocv.org

The Poisson− Nernst− Planck system of equations used to model ionic transport is

interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of

probability measures with finite second moment. A variational scheme is then set up and is …

Extremal curves in Wasserstein space

G Conforti, M Pavon - International Conference on Geometric Science of …, 2017 - Springer

We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges

and the classic Madelung fluid can be derived from variational principles on Wasserstein

space. The second order differential equations are accordingly obtained by annihilating the …

<——2017—— —2017 ——— 880 —

Wasserstein blue noise sampling

H Qin, Y Chen, J He, B Chen - ACM Transactions on Graphics (TOG), 2017 - dl.acm.org

In this article, we present a multi-class blue noise sampling algorithm by throwing samples

as the constrained Wasserstein barycenter of multiple density distributions. Using an

entropic regularization term, a constrained transport plan in the optimal transport problem is …

[PDF] berkeley.edu

Wasserstein stability of the entropy power inequality for log-concave random vectors

TA Courtade, M Fathi… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

We establish quantitative stability results for the entropy power inequality (EPI) in arbitrary

dimension. Specifically, we show that if uniformly log-concave densities nearly saturate the

EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance …

[PDF] [PDF] arxiv.org

Face super-resolution through wasserstein gans

Z Chen, Y Tong - arXiv preprint arXiv:1705.02438, 2017 - arxiv.org

Generative adversarial networks (GANs) have received a tremendous amount of attention in

the past few years, and have inspired applications addressing a wide range of problems.

Despite its great potential, GANs are difficult to train. Recently, a series of papers (Arjovsky & …

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and

energy loads, as well as their multi-energy interactions and dependencies, have negligible

effects on the operation and analyses of integrated energy systems. Determining how to …

12 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

M Laborde - Topological Optimization and Optimal Transport: In …, 2017 - books.google.com

This chapter presents existence and uniqueness results for a class of parabolic systems with

nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular

perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic …

2017

An elementary proof for the structure of Wasserstein derivatives

C Wu, J Zhang - arXiv preprint arXiv:1705.08046, 2017 - arxiv.org

Let $ F:\mathbb {L}^ 2 (\Omega,\mathbb {R})\to\mathbb {R} $ be a law invariant and

continuously Fréchet differentiable mapping. Based on Lions\cite {Lions}, Cardaliaguet\cite

{Cardaliaguet}(Theorem 6.2 and 6.5) proved that:\bea\label {Derivative} DF (\xi)= g (\xi),\eea …

Enhancing diffusion MRI measures by integrating grey and white matter morphometry with hyperbolic wasserstein distance

W Zhang, J Shi, J Yu, L Zhan… - 2017 IEEE 14th …, 2017 - ieeexplore.ieee.org

In order to improve the preclinical diagnose of Alzheimer's disease (AD), there is a great

deal of interest in analyzing the AD related brain structural changes with magnetic

resonance image (MRI) analyses. As the major features, variation of the structural …

An intrinsic parallel transport in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact connected Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. We describe a geometric construction

of parallel transport of some tangent cones along geodesics in $ P (M) $. We show that …

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

<——2017—— —2017 ——— 890 —

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

https://euro-math-soc.eu › review › informal-introducti...

An Informal Introduction to stochastic Calculus with ...

An Informal Introduction to stochastic Calculus with Applications. By Marco Castrillon Lopez 18 / Aug / 2017 ... As a consequence, many scientists, engineerings and economists, even with a good mathematical background, oftem find ...

[CITATION] An Informal Introduction to the Maths Behind Wasserstein GAN

Q Bai - 2017

Multilevel clustering via Wasserstein means

N Ho, XL Nguyen, M Yurochkin… - International …, 2017 - proceedings.mlr.press

We propose a novel approach to the problem of multilevel clustering, which aims to

simultaneously partition data in each group and discover grouping patterns among groups

in a potentially large hierarchically structured corpus of data. Our method involves a joint …

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

[HTML] Vers un théorème de la limite centrale dans l'espace de Wasserstein?

M Agueh, G Carlier - Comptes Rendus Mathématique, 2017 - Elsevier

Résumé Les barycentres dans l'espace de Wasserstein constituent une manière naturelle

d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines

appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons …

2017

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

[CITATION] On interpolation and curvature via Wasserstein geodesics

M Kell - Advances in Calculus of Variations, 2017 - De Gruyter

see 2016

Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

T Klein, JC Fort, P Berthet - 2017 - hal.archives-ouvertes.fr

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

[PDF] Unsupervised Audio Source Separation via Spectrum ...

https://www.semanticscholar.org › paper › Unsupervised-...

Separating audio mixtures into individual tracks has been a long standing challenging task. We introduce a novel unsupervised audio source separation ...

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

Sliced wasserstein kernel for persistence diagrams

2017

M Carriere, M Cuturi, S Oudot - International Conference on …, 2017 - proceedings.mlr.press

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they

are routinely used to describe succinctly complex topological properties of complicated

shapes. PDs enjoy strong stability properties and have proven their utility in various learning …

[CITATION] Sliced wasserstein kernel for persistence diagrams. arXiv preprint 548

M Carriere, M Cuturi, S Oudot - arXiv preprint arXiv:1706.03358, 2017

<——2017—— —2017 ——— 900 —

Multilevel clustering via Wasserstein means

N Ho, XL Nguyen, M Yurochkin… - International …, 2017 - proceedings.mlr.press

We propose a novel approach to the problem of multilevel clustering, which aims to

simultaneously partition data in each group and discover grouping patterns among groups

in a potentially large hierarchically structured corpus of data. Our method involves a joint …

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

Minimax statistical learning with wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017 - arxiv.org

As opposed to standard empirical risk minimization (ERM), distributionally robust

optimization aims to minimize the worst-case risk over a larger ambiguity set containing the

original empirical distribution of the training data. In this work, we describe a minimax …

2017

Fréchet means in Wasserstein space

Y Zemel - 2017 - infoscience.epfl.ch

This work studies the problem of statistical inference for Fréchet means in the Wasserstein

space of measures on Euclidean spaces, W2 (Rd). This question arises naturally from the

problem of separating amplitude and phase variation in point processes, analogous to a …

[PDF] Fréchet means in Wasserstein space: gradient descent and Procrustes analysis

Y Zemel, VM Panaretos - 2016 - epfl.ch

Given a collection of absolutely continuous measures on Rd, we consider the

complementary problems of: determining their Fréchet mean with respect to the L2-

Wasserstein metric; and of constructing their optimal multi-coupling in the mean square …

Minimax Statistical Learning with Wasserstein Distances

https://arxiv.org › cs\

by J Lee · 2017 · Cited by 62 — [Submitted on 22 May 2017 (v1), last revised 26 Oct 2018 (this version, v2)] ... In this work, we describe a minimax framework for statistical learning with ... for transport-based domain adaptation problems where the Wasserstein distance ...

[CITATION] Minimax statistical learning and domain adaptation with Wasserstein distances

J Lee, M Raginsky - arXiv preprint arXiv:1705.07815, 2017

Fréchet means in Wasserstein space: theory and ... - Infoscience

https://infoscience.epfl.ch › files › EPFL_TH7601

PDF

by Y Zemel · 2017 — Prof. S. Morgenthaler, rapporteur. Fréchet means in Wasserstein space: theory and algorithms. THÈSE NO 7601 (2017). ÉCOLE POLYTECHNIQUE FÉDÉRALE ...

[CITATION] Fréchet means in Wasserstein space: theory and algorithms

Y Zemel - 2017 - Ecole Polytechnique Fédérale de …

Multilevel clustering via Wasserstein means

2017

N Ho, XL Nguyen, M Yurochkin… - International …, 2017 - proceedings.mlr.press

We propose a novel approach to the problem of multilevel clustering, which aims to

simultaneously partition data in each group and discover grouping patterns among groups

in a potentially large hierarchically structured corpus of data. Our method involves a joint …

Sharp asymptotic and finite-sample rates of convergence of ...

[PDF] Supplementary Material for Multilevel Clustering via Wasserstein Means

N Ho, XL Nguyen, M Yurochkin, HH Bui, V Huynh… - proceedings.mlr.press

In this appendix, we collect relevant information on the Wasserstein metric and Wasserstein

barycenter problem, which were introduced in Section 2 in the paper. For any Borel map g:

Θ→ Θ and probability measure G on Θ, the push-forward measure of G through g, denoted …

All 2 versions ∂

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

by J Weed · 2017 · Cited by 173 — Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning.

2017

Authors:Weed J., Bach F.
Article, 2017
Publication:arXiv, 2017 06 30
Publisher:2017

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

[CITATION] Bach F. Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

J Weed - arXiv preprint arXiv:1707.00087, 201

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

FB Jonathan Weed - arXiv preprint arXiv:1707.00087, 2017

Sharp asymptotic and finite-sample rates of convergence of ...

by J Weed · 2017 · Cited by 232 — The Wasserstein distance between two probability measures on a metric space is a measure of closeness with application

[CITATION] Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. arXiv e-prints, art

J Weed, F Bach - arXiv preprint arXiv:1707.00087, 2017

Dimension-free Wasserstein contraction of nonlinear filters

N Whiteley - arXiv preprint arXiv:1708.01582, 2017 - arxiv.org

For a class of partially observed diffusions, sufficient conditions are given for the map from

initial condition of the signal to filtering distribution to be contractive with respect to

Wasserstein distances, with rate which has no dependence on the dimension of the state …

year 2017

[PDF] asso-afig.fr

[PDF] Barycentres de Wasserstein pour les diagrammes de persistance

J Tierny - annonces.asso-afig.fr

Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui

permet en pratique d'introduire une mesure de bruit sur les structures topologiques, comme

les singularités (sphères de couleur) dans cet exemple de carte d'élévation. Cette mesure …

2017

[HTML] Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

We study barycenters in the space of probability measures on a Riemannian manifold,

equipped with the Wasserstein metric. Under reasonable assumptions, we establish

absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on Wasserstein …

<——2017—— —2017 ——— 910 —

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too

large and complex for easy computation. Because continuous transport problems are

generally solved by conversion to either discrete or semi-discrete forms, I focused on …

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

The Dice score is widely used for binary segmentation due to its robustness to class

imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for

training convolutional neural networks (CNN). Although CNNs trained using mean-class …

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

K Craig - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library

Over the past 15 years, the theory of Wasserstein gradient flows of convex (or, more

generally, semiconvex) energies has led to advances in several areas of partial differential

equations and analysis. In this work, we extend the well‐posedness theory for Wasserstein …

L ow Dose CT Image Denoising Using a Generative ... - arXiv

https://arxiv.org › pdfPDF

by Q Yang · 2017 · Cited by 700 — This paper introduces a new CT image denoising method based on the generative adversarial network (GAN) with Wasserstein distance and perceptual similarity. The ...

Missing: 275 ‎| Must include: 275

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary -dependent sequences

2017 [PDF] projecteuclid.org

J Dedecker, F Merlevede - Bernoulli, 2017 - projecteuclid.org

… the Wasserstein distance of order 1 between the empirical distribution and the marginal

distribution of stationary α-dependent sequences. … The moment inequalities for the Wasserstein …

2017

[HTML] Limit laws of the empirical Wasserstein distance: Gaussian distributions

T Rippl, A Munk, A Sturm - Journal of Multivariate Analysis, 2016 - Elsevier

We derive central limit theorems for the Wasserstein distance between the empirical

distributions of Gaussian samples. The cases are distinguished whether the underlying laws

are the same or different. Results are based on the (quadratic) Fréchet differentiability of the …

Uniform contractivity in Wasserstein metric for the original 1D Kac's model

M Hauray - Journal of Statistical Physics, 2016 - Springer

We study here a very popular 1D jump model introduced by Kac: it consists of N velocities

encountering random binary collisions at which they randomly exchange energy. We show

the uniform (in N) exponential contractivity of the dynamics in a non-standard Monge …

2017

Wasserstein distributional robustness and regularization in statistical learning

R Gao, X Chen, AJ Kleywegt - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

A central question in statistical learning is to design algorithms that not only perform well on

training data, but also generalize to new and unseen data. In this paper, we tackle this

question by formulating a distributionally robust stochastic optimization (DRSO) problem …

Cited by 85 Related articles

Order-preserving wasserstein distance for sequence matching

B Su, G Hua - Proceedings of the IEEE conference on …, 2017 - openaccess.thecvf.com

We present a new distance measure between sequences that can tackle local temporal

distortion and periodic sequences with arbitrary starting points. Through viewing the

instances of sequences as empirical samples of an unknown distribution, we cast the …

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

<——2017—— —2017 ——— 920 —

Face super-resolution through wasserstein gans

Z Chen, Y Tong - arXiv preprint arXiv:1705.02438, 2017 - arxiv.org

Generative adversarial networks (GANs) have received a tremendous amount of attention in

the past few years, and have inspired applications addressing a wide range of problems.

Despite its great potential, GANs are difficult to train. Recently, a series of papers (Arjovsky & …

An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric

B Berckmoes, T Hellemans, M Sioen… - Journal of Mathematical …, 2017 - Elsevier

After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in

1989, we show that this theory is intimately related to the well-known Wasserstein metric on

the space of probability measures with a finite first moment on a complete and separable …

2017

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

… Numerical analysis. Second-order in time schemes for gradient flows in Wasserstein

and geodesic metric spacesSchémas d'ordre deux en temps pour des flots de gradient

dans des espaces métriques géodésiques et de Wasserstein …

2017

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

MG Mora, MA Peletier, L Scardia - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider systems of n parallel edge dislocations in a single slip system, represented by

points in a two-dimensional domain; the elastic medium is modeled as a continuum. We

formulate the energy of this system in terms of the empirical measure of the dislocations and …

2017

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a

variational model for nonuniform illumination correction, that incorporates a penalty term that …

2017

Automatic color correction for multisource remote sensing images with Wasserstein CNN

J Guo, Z Pan, B Lei, C Ding - Remote Sensing, 2017 - mdpi.com

In this paper a non-parametric model based on Wasserstein CNN is proposed for color

correction. It is suitable for large-scale remote sensing image preprocessing from multiple

sources under various viewing conditions, including illumination variances, atmosphere …

An elementary proof for the structure of Wasserstein derivatives

C Wu, J Zhang - arXiv preprint arXiv:1705.08046, 2017 - arxiv.org

Let $ F:\mathbb {L}^ 2 (\Omega,\mathbb {R})\to\mathbb {R} $ be a law invariant and

continuously Fréchet differentiable mapping. Based on Lions\cite {Lions}, Cardaliaguet\cite

{Cardaliaguet}(Theorem 6.2 and 6.5) proved that:\bea\label {Derivative} DF (\xi)= g (\xi),\eea …

2017

A Central Limit Theorem for Wasserstein type distances between two different laws

P Berthet, JC Fort, T Klein - arXiv preprint arXiv:1710.09763, 2017 - arxiv.org

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The

estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G …

2017

[CITATION] Towards a central limit theorem in the Wasserstein space?

M Agueh, G Carlier - COMPTES …, 2017 - ELSEVIER FRANCE-EDITIONS …

焦艳艳 - 2017 - cdmd.cnki.com.cn

随着科学技术的飞速发展及3D 技术的提高, 人们在数据采集和图形建模领域取得了很大的进步.

基于数字分析的应用领域有很多, 如: 分子生物学, 人脸识别, 模式识别等.

图形匹配是计算机视觉, 计算机图形学, 机器人学等领域的基本问题之一, 也是数字分析的重要 …

[Chinese 3D pattern matching method based on Gromov-Wasserstein distance]

<——2017—— —2017 ——— 930 —

2017

[CITATION] A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information

M Benning, L Calatroni, B Düring, CB Schönlieb - 2013 - Springer, Heidelberg

[CITATION] Correcting Nuisance Variation using Wasserstein Distance. arXiv

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - 2017 - Nov

Correcting nuisance variation using wasserstein distance

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - arXiv preprint arXiv …, 2017 - arxiv.org

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological

information resulting from various factors affecting the cells. One motivating application is

drug development: morphological cell features can be captured from images, from which …

2017

An intrinsic parallel transport in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact connected Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. We describe a geometric construction

of parallel transport of some tangent cones along geodesics in $ P (M) $. We show that …

2017

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

Detecting changes in forced climate attractors with Wasserstein distance

Y Robin, P Yiou, P Naveau - Nonlinear Processes in Geophysics, 2017 - npg.copernicus.org

The climate system can been described by a dynamical system and its associated attractor.

The dynamics of this attractor depends on the external forcings that influence the climate.

Such forcings can affect the mean values or variances, but regions of the attractor that are …

Finsler structure in the p-Wasserstein space and gradient flows

https://www.sciencedirect.com › science › article › pii › pdf

by Mgueh · 2012 · Cited by 9 — This paper deals with the geometric structure of the p-Wasserstein space and its applications to partial differential equations (pde). The starting point is the ...

[CITATION] Finsler structure in the p-Wasserstein space and applications to PDEs

M Agueh - CR Math. Acad. Sci. Paris, Ser. I, 2012

2017

An elementary proof for the structure of Wasserstein derivatives

C Wu, J Zhang - arXiv preprint arXiv:1705.08046, 2017 - arxiv.org

Let $ F:\mathbb {L}^ 2 (\Omega,\mathbb {R})\to\mathbb {R} $ be a law invariant and

continuously Fréchet differentiable mapping. Based on Lions\cite {Lions}, Cardaliaguet\cite

{Cardaliaguet}(Theorem 6.2 and 6.5) proved that:\bea\label {Derivative} DF (\xi)= g (\xi),\eea …

2017

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that

involves identifying differences between two random variables without making parametric

assumptions about their underlying distributions. The literature is old and rich, with a wide …

2017

Wasserstein identity testing

S Deng, W Li, X Wu - arXiv preprint arXiv:1710.10457, 2017 - arxiv.org

Uniformity testing and the more general identity testing are well studied problems in

distributional property testing. Most previous work focuses on testing under $ L_1 $-

distance. However, when the support is very large or even continuous, testing under $ L_1 …

2017

12 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

M Laborde - Topological Optimization and Optimal Transport: In …, 2017 - books.google.com

This chapter presents existence and uniqueness results for a class of parabolic systems with

nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular

perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic …

Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

JX Xiang - Statistics & Probability Letters, 2017 - Elsevier

In this paper we derive a formula for the sample size of a nonparametric test based on

weighted L 2-Wasserstein distance with a known alternative. As an example we apply the

formula to determine the sample size for a hypothesis testing from the Tukey's contaminated …

<——2017—— —2017 ——— 940 —

year 2017

A partial Laplacian as an infinitesimal generator on the Wasserstein space

[PDF] The WASSERSTEIN DISTANCE AS A UNIVARIATE NEUROIMAGING BIOMARKER FOR FDG-PET ANALYSIS

L Mi, W Zhang, J Zhang, Y Fan, D Goradia, K Chen… - gsl.lab.asu.edu

We propose a univariate biomarker of the FDGPET images by using the Wasserstein

distance. We apply the biomarker to the Alzheimer's disease (AD) analysis. The

experimental results demonstrate the robustness of our biomarker in distinguishing AD from …

2017

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

Cited by 2 Related article

year 2017

[PDF] Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in weighted Wasserstein metrics

G Savaré - www-dimat.unipv.it

… Cahn-Hilliard and Thin film equations with nonlinear mobility as gradient flows in

weighted Wasserstein metrics Giuseppe Savaré http://www.imati.cnr.it/∼savare

Department of Mathematics, University of Pavia, Italy DIMO2013 Levico Terme …

[CITATION] Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. Preprint

S Lisini, D Matthes, G Savaré - arXiv preprint arXiv:1201.2367, 2012

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

Evolution of the Wasserstein distance between the marginals of two Markov processes

2017 see 2018

J Corbetta - 2017 - pdfs.semanticscholar.org

Page 1. Evolution of the Wasserstein distance between the marginals of two Markov

processes Jacopo Corbetta (École des Ponts - ParisTech) Joint work with: Aurélien Alfonsi

and Benjamin Jourdain January 10, 2017 … Page 2. The Wasserstein distance Definition …

2017

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

Facial Expression Recognition Based on LBP Features and Entropy-regularized Wasserstein Distance

C ZHENG, D ZHANG, K SU, X WU… - Computer & Digital …, 2017 - en.cnki.com.cn

To solve quantification of similarity measure in the K-nearest neighbor classification, a KNN

method is proposed based on LBP features and entropy-regularized Wasserstein distance,

by combining the mathematical properties of Wasserstein distance in optimal mass …

2017 PDF

Low Dose CT Image Denoising Using a Generative ... - arXiv

by Q Yang · 2017 · Cited by 592 — 1. Low Dose CT Image Denoising Using a Generative. Adversarial Network with Wasserstein Distance and. Perceptual Loss. Qingsong Yang, Pingkun Yan*, ...

[CITATION] Low Dose CT Image Denoising Using a Generative Adversarial Network with 275 Wasserstein Distance and Perceptual Loss

Q Yang, P Yan, Y Zhang - arXiv preprint arXiv:1703.01383, 2017

2017

[HTML] Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

G Legendre, G Turinici - Comptes Rendus Mathematique, 2017 - Elsevier

The time discretization of gradient flows in metric spaces uses variants of the celebrated

implicit Euler-type scheme of Jordan, Kinderlehrer, and Otto [9]. We propose in this Note a

different approach, which allows us to construct two second-order in time numerical …

2017

15. Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

F Al Reda, B Maury - Topological Optimization and Optimal Transport, 2017 - degruyter.com

This paper establishes a link between some space discretization strategies of the finite

volume type for the Fokker–Planck equation in general meshes (Voronoï tesselations) and

gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein …

Cited by 6 Related a

<——2017—— —2017 ——— 950 —

On interpolation and curvature via Wasserstein geodesics

M Kell - Advances in Calculus of Variations, 2017 - degruyter.com

In this article, a proof of the interpolation inequality along geodesics in p-Wasserstein

spaces is given. This interpolation inequality was the main ingredient to prove the Borel–

Brascamp–Lieb inequality for general Riemannian and Finsler manifolds and led Lott …

2017

Order-preserving wasserstein distance for sequence matching

B Su, G Hua - Proceedings of the IEEE conference on …, 2017 - openaccess.thecvf.com

We present a new distance measure between sequences that can tackle local temporal

distortion and periodic sequences with arbitrary starting points. Through viewing the

instances of sequences as empirical samples of an unknown distribution, we cast the …

2017

[PDF] Wasserstein k-means++ for cloud regime histogram clustering

M Staib, S Jegelka - Climate informatics, 2017 - mjstaib.com

… 5 Discussion We propose Wasserstein histogram clustering as a way to leverage prior

knowledge about similarity and geometry in learning from climate datasets … Fast Computation

of Wasserstein Barycenters … Parallel Streaming Wasser- stein Barycenters …

Log-PCA versus Geodesic PCA of histograms in the Wasserstein space

[PDF] WASSERSTEIN k-MEANS+ HISTOGRAM CLUSTERING

M Staib, S Jegelka - NCAR Technical Notes NCAR/TN536+ PROC - par.nsf.gov

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

kmeans clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

2017 [PDF] arxiv.org

E Cazelles, V Seguy, J Bigot, M Cuturi… - arXiv preprint arXiv …, 2017 - arxiv.org

This paper is concerned by the statistical analysis of data sets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the PCA of histograms with respect to the 2-Wasserstein …

2017 [PDF] mjstaib.com

[PDF] Wasserstein k-means++ for cloud regime histogram clustering

M Staib, S Jegelka - Climate informatics, 2017 - mjstaib.com

Much work has sought to discern the different types of cloud regimes, typically via Euclidean

k-means clustering of histograms. However, these methods ignore the underlying similarity

structure of cloud types. Wasserstein k-means clustering is a promising candidate for …

Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant Sliced-Wasserstein Distance via Laplace--Beltrami Eigenmap

2017

R Lai, H Zhao - SIAM Journal on Imaging Sciences, 2017 - SIAM

In this work, we propose computational models and algorithms for point cloud registration

with nonrigid transformation. First, point clouds sampled from manifolds originally embedded

in some Euclidean space are transformed to new point clouds embedded in R^n by the …

Geodesic PCA in the Wasserstein space by convex PCA

2017 [PDF] projecteuclid.org

J Bigot, R Gouet, T Klein, A López - Annales de l'Institut Henri …, 2017 - projecteuclid.org

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space

of probability measures on the line, with finite second moment, endowed with the

Wasserstein metric. We discuss the advantages of this approach, over a standard functional …

2017 [PDF] arxiv.org

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

2017

Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric

X Fu, Q Guo, H Sun, Z Pan, W Xiong, L Wang - Energy, 2017 - Elsevier

The stochastic fluctuation characteristics of intermittent renewable energy sources and

energy loads, as well as their multi-energy interactions and dependencies, have negligible

effects on the operation and analyses of integrated energy systems. Determining how to …

2017 [PDF] arxiv.org

Log-PCA versus Geodesic PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - arXiv preprint arXiv …, 2017 - arxiv.org

This paper is concerned by the statistical analysis of data sets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the PCA of histograms with respect to the 2-Wasserstein …

<——2017—— —2017 ——— 960 —

2017 [PDF] arxiv.org

Improved training of wasserstein gans

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - arxiv.org

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from

training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward

stable training of GANs, but sometimes can still generate only low-quality samples or fail to …

Cited by 5202 Related articles All 13 versions

[CITATION] Improved Training of Wasserstein GANs, CoRR, arXiv

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017

The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality

2017

V Barbu - SIAM Journal on Control and Optimization, 2017 - SIAM

The nonlinear diffusion equation \rho_t-Δ(ρH(ρ-\rho_c))=0 in (0,∞)*R^n, ρ(0,x)=\rho_0(x),

where H is the Heaviside function, describes the sandpile model P. Bak, C. Tang, and K.

Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and IM Janosi, Phys. A, 185 (1992) …

2017 [PDF] arxiv.org

A Robust Learning Algorithm for Regression Models Using Distributionally Robust Optimization under the Wasserstein Metric

R Chen, IC Paschalidis - arXiv preprint arXiv:1706.02412, 2017 - arxiv.org

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified

regression plane in a linear regression setting, when the observed samples are potentially

contaminated with adversarially corrupted outliers. Our approach mitigates the impact of …

2017 [PDF] gatech.edu

The boundary method and general auction for optimal mass transportation and Wasserstein distance computation

JD Walsh - 2017 - smartech.gatech.edu

Numerical optimal transport is an important area of research, but most problems are too

large and complex for easy computation. Because continuous transport problems are

generally solved by conversion to either discrete or semi-discrete forms, I focused on …

2017

Условие выживаемости в пространстве Васерштейна

Ю. В. Авербух

Институт математики и механики им. Н. Н. Красовского Уральского отделения РАН, г. Екатеринбург

http://www.mathnet.ru › present17891

Институт проблем передачи информации им. А.А. Харкевича Российской академии наук, г. Москва

Sep 19, 2017 — Аннотация: В докладе рассматривается управляемая система "среднего поля" т.е. динамическая система в пространстве вероятностей (пространстве ...

[Russian Survival conditions in Vaserstein space]

Tранспортная задача Монжа-Канторовича, пространство Васерштейна и его геометрия

А. Н. Соболевский

Семинары: А. Н. Соболевский, Транспортная задача ...

http://www.mathnet.ru › present16835

Absolute continuity of Wasserstein barycenters over Alexandrov spaces

Семинар Добрушинской математической лаборатории ИППИ РАН 21 марта 2017 г. 16:00, г. Москва, комн. 307 ИППИ РАН (Большой Каретный пер., 19) ...

[Russion Monte-Kantorovich transportation problem, Vaserstein space, and his geometry]

2017

Y Jiang - Canadian Journal of Mathematics, 2017 - cambridge.org

In this paper, we study the barycenters in Wasserstein space over a compact Alexan- drov

space. Let M be a compact, n-dimensional Alexandrov space with curvature at least − . Denote

by P(M) the set of Borel probability measures on M, and by Pac(M) the set of absolutely continuous …

Wasserstein Distance Guided Representation Learning for Domain Adaptation.

307 citations* for all

284 citations*

2018 NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE

Jian Shen ,Yanru Qu ,Weinan Zhang ,Yong Yu

Shanghai Jiao Tong University

Domain (software engineering)

Feature learning

View More (9+)

Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to learn domain invariant feature representations while the learne... View Full Abstract

Voice Conversion from Unaligned Corpora using Variational Autoencoding Wasserstein Generative Adversarial Networks

152 citations*

2017 ARXIV: COMPUTATION AND LANGUAGE

Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss

330 citations*

2017 ARXIV: COMPUTER VISION AND PATTERN RECOGNITION

Qingsong Yang ,Pingkun Yan ,Yanbo Zhang ,Hengyong Yu ,Yongyi Shi see all 8 authors

Image noise

Feature vector

View More (9+)

In this paper, we introduce a new CT image denoising method based on the generative adversarial network (GAN) with Wasserstein distance and perceptual similarity. The Wasserstein distance is a key concept of the optimal transform theory, and promises to improve the performance of the GAN. The percep... View Full Abstract

<——2017—— —2017 ——— 970—

Association Between Wait Time and 30-Day Mortality in Adults Undergoing Hip Fracture Surgery.

287 citations*

2017 JAMA

Daniel Pincus ^1,2,Bheeshma Ravi ^1,2,3,David Wasserstein ^1,3,Anjie Huang ¹,J. Michael Paterson ^1,2 see all 9 authors

¹ University of Toronto ,² York University ,³ Sunnybrook Health Sciences Centre

Hip fracture

Fracture fixation

View More (24+)

Importance Although wait times for hip fracture surgery have been linked to mortality and are being used as quality-of-care indicators worldwide, controversy exists about the duration of the wait that leads to complications. Objective To use population-based wait-time data to identify the optimal... View Full Abstract

Wasserstein CNN: Learning Invariant Features for NIR-VIS Face Recognition

142 citations* for all

132 citations*

2019 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE

Ran He ,Xiang Wu ,Zhenan Sun ,Tieniu Tan

Chinese Academy of Sciences

Facial recognition system

Feature extraction

View More (21+)

Heterogeneous face recognition (HFR) aims at matching facial images acquired from different sensing modalities with mission-critical applications in forensics, security and commercial sectors. However, HFR presents more challenging issues than traditional face recognition because of the large intra-... View Full Abstract

EXCERPTS (141)

On parameter estimation with the Wasserstein distance

The Cramer Distance as a Solution to Biased Wasserstein Gradients

2017 ARXIV: METHODOLOGY

237 citations*

2017 ARXIV: LEARNING

Marc G. Bellemare ,Ivo Danihelka ,Will Dabney ,Shakir Mohamed ,Balaji Lakshminarayanan see all 7 authors

Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric

View More (9+)

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The value of being sensitive to this ge... View Full Abstract

2017 ARXIV: OPTIMIZATION AND CONTROL

Statistical Aspects of Wasserstein Distances

120 citations* for all

118 citations*

2019 SOCIAL SCIENCE RESEARCH NETWORK

Victor M. Panaretos ¹,Yoav Zemel ²

¹ École Polytechnique Fédérale de Lausanne ,² University of Göttingen

Measure (mathematics)

Generalised wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks

View More (7+)

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the ...

2017 see 2013 [PDF] arxiv.org

L Fidon, W Li, LC Garcia-Peraza-Herrera… - International MICCAI …, 2017 - Springer

The Dice score is widely used for binary segmentation due to its robustness to class

imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for

training convolutional neural networks (CNN). Although CNNs trained using mean-class …

[CITATION] Garcia-peraza herrera, LC: Generalised Wasserstein Dice score for imbalanced multi-class segmentation using holistic convolutional networks

L Fidon, W Li - arXiv preprint arXiv:1707.00478, 2017

2017

Posterior contraction in Gaussian process regression using Wasserstein approximations

A Bhattacharya, D Pati - Information and Inference: A Journal of …, 2017 - academic.oup.com

We study posterior rates of contraction in Gaussian process regression with potentially

unbounded covariate domain. Our argument relies on developing a Gaussian

approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of …

2017 [HTML] sciencedirect.com

[HTML] Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

2017 [PDF] arxiv.org

Weakly supervised audio source separation via spectrum energy preserved Wasserstein learning

N Zhang, J Yan, Y Zhou - arXiv preprint arXiv:1711.04121, 2017 - arxiv.org

Separating audio mixtures into individual instrument tracks has been a long standing

challenging task. We introduce a novel weakly supervised audio source separation

approach based on deep adversarial learning. Specifically, our loss function adopts the …

2017

https://www.sciencedirect.com › science › article › pii

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates

by D Han-Kwan · 2017 · Cited by 24 — Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension. Author links open overlay panelDanielHan-Kwan ...

2017

Unsupervised Audio Source Separation via Spectrum Energy ...

https://deepai.org › publication › unsupervised-audio-s...

Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning. 11/11/2017 ∙ by Ning Zhang, et al.

[CITATION] Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

N Zhang, J Yan, YC Zhou - CoRR, abs/1711.04121, 2017

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

<——2017—— —2017 ——— 980—

2017 [PDF] arxiv.org

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging

but highly valuable in real application scenarios. In most situations, the source and the target

speakers do not repeat the same texts or they may even speak different languages. In this …

[CITATION] Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks. arXiv preprint arXiv: 170400849

CC Hsu, HT Hwang, YC Wu, Y Tsao, HM Wang - 2017

Parallel Streaming Wasserstein Barycenters

2017

Stochastic Wasserstein Barycenters

2017 ARXIV: LEARNING

39 citations* for all

2018 INTERNATIONAL CONFERENCE ON MACHINE LEARNING

Sebastian Claici ,Edward Chien ,Justin Solomon

Massachusetts Institute of Technology

Wasserstein Divergence for GANs

View More (6+)

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iter... View Full Abstract

2017 see 2016

2017 ARXIV: COMPUTER VISION AND PATTERN RECOGNITION

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

2018 SIAM JOURNAL ON IMAGING SCIENCES

82 citations*

Morgan A. Schmitz ¹,Matthieu Heitz ²,Nicolas Bonneel ²,Fred Maurice Ngolè Mboula ³,David Coeurjolly ² see all 8 authors

¹ Institut de Recherches sur les lois Fondamentales de l'Univers,² Geometry Processing and Constrained Optimization,³ Laboratoire d'analyse des données et d'intelligence des systèmes

Smoothing

Regularization (mathematics)

View More (8+)

This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so called displacement interpolations (a.k.a. Wasserstein barycenters) between di... View Full Abstract

22017

On the Bures-Wasserstein distance between positive definite matrices

2017 ARXIV: FUNCTIONAL ANALYSIS

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

61 citations*

2018 NEUROCOMPUTING

Yifan Liu ¹,Zengchang Qin ¹,Tao Wan ¹,Zhenbo Luo ²

¹ Beihang University ,² Samsung

Sketch

Artificial intelligence

View More (7+)

Abstract Recently, realistic image generation using deep neural networks has become a hot topic in machine learning and computer vision. Such an image can be generated at pixel level by learning from a large collection of images. Learning to generate colorful cartoon images from black-and-white sk... View Full Abstract

2017

Minimax Statistical Learning with Wasserstein Distances.

16 citations*

2017 ARXIV: LEARNING

Stochastic Wasserstein Barycenters

39 citations* for all

2018 INTERNATIONAL CONFERENCE ON MACHINE LEARNING

Sebastian Claici ,Edward Chien ,Justin Solomon

Massachusetts Institute of Technology

[PDF] SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

View More (6+)

2017

year 2017 [PDF] cnrs.fr

MA Schmitz, M Heitz, N Bonneel, F Ngole, D Coeurjolly… - perso.liris.cnrs.fr

SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based

unsupervised non-linear dictionary learning∗ … Morgan A. Schmitz† , Matthieu Heitz‡ , Nicolas

Bonneel‡ , Fred Ngol`e§ , David Coeurjolly‡ , Marco Cuturi¶, Gabriel Peyré , and Jean-Luc …

An inverse problem: recovery of a distribution using Wasserstein Barycenter

2017 [PDF] researchgate.net

E Del Barrio, JM Loubes, B Pelletier - … of Economics and Statistics/Annales d …, 2017 - JSTOR

We propose to study the inverse problem of estimating a distribution observed through an

image by a parametric operator. We construct first estimators for the individual parameters of

the operators and study their behaviour, then we invert the approximated operator to obtain …

Learning to solve inverse problems using Wasserstein loss

2017 [PDF] arxiv.org

J Adler, A Ringh, O Öktem, J Karlsson - arXiv preprint arXiv:1710.10898, 2017 - arxiv.org

We propose using the Wasserstein loss for training in inverse problems. In particular, we

consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using

the Wasserstein distance as loss function in the learning. This is motivated by miss …

[CITATION] Learning to solve inverse problems using Wasserstein loss, ArXiv, 1710.10898 (2017)

J Adler, A Ringh, O Öktem, J Karlsson - Poster in NIPS, 2017

12. On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

[CITATION] Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator. arXivpreprint

VA Nguyen, D Kuhn, PM Esfahani - arXiv preprint arXiv:1805.07194, 2018

[CITATION] O.\" Oktem, and J. Karlsson, Learning to Solve Inverse Problems Using Wasserstein Loss

J Adler, A Ringh - 2017

2017 [PDF] arxiv.org

M Laborde - Topological optimization and optimal transport, 2017 - degruyter.com

This chapter presents existence and uniqueness results for a class of parabolic systems with

nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular

perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic …

2017 [PDF] ams.org

An intrinsic parallel transport in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact connected Riemannian manifold, let $ P (M) $ denote the

Wasserstein space of probability measures on $ M $. We describe a geometric construction

of parallel transport of some tangent cones along geodesics in $ P (M) $. We show that …

<——2017—— —2017 ——— 990—

2017 [PDF] arxiv.org

Parallel streaming Wasserstein barycenters

M Staib, S Claici, J Solomon, S Jegelka - arXiv preprint arXiv:1705.07443, 2017 - arxiv.org

Efficiently aggregating data from different sources is a challenging problem, particularly

when samples from each source are distributed differently. These differences can be

inherent to the inference task or present for other reasons: sensors in a sensor network may …

2017

Wasserstein Learning of Deep Generative Point Process Models

23 citations*

2017 ARXIV: LEARNING

Parallel Streaming Wasserstein Barycenters

63 citations* for all

45 citations*

2017 NEURAL INFORMATION PROCESSING SYSTEMS

Matthew Staib ,Sebastian Claici ,Justin M. Solomon ,Stefanie Jegelka

Massachusetts Institute of Technology

Bayesian inference

Parallel algorithm

View More (7+)

Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons: sensors in a sensor network may be placed far apart, affecting t... View Full Abstract

2017 see 2016

{ Euclidean, Metric, and Wasserstein } Gradient Flows: an overview

113 citations* for all

111 citations*

2017 BULLETIN OF MATHEMATICAL SCIENCES

Filippo Santambrogio

Université Paris-Saclay

Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem

Intrinsic metric

View More (8+)

2017

2017 ARXIV: OPTIMIZATION AND CONTROL

Manifold-valued Image Generation with Wasserstein Generative Adversarial Nets

7 citations* for all

2019 NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE

Zhiwu Huang ¹,Jiqing Wu ²,Luc Van Gool ²

¹ Katholieke Universiteit Leuven ,² ETH Zurich

Color image

HSL and HSV

View More (9+)

Generative modeling over natural images is one of the most fundamental machine learning problems. However, few modern generative models, including Wasserstein Generative Adversarial Nets (WGANs), are studied on manifold-valued images that are frequently encountered in real-world applications. To fil... View Full Abstract

2017

On quantum versions of the classical Wasserstein distance

Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem

2017 STOCHASTICS

J. Agredo ¹,Franco Fagnola ²

¹ National University of Colombia ,² Polytechnic University of Milan

Quantum

Trace distance

View More (9+)

We investigate a definition of quantum Wasserstein distance of two states based on their couplings on the product algebra as in the classical case. A detailed analysis of the two qubit model leads to a formal definition fulfilling some minimal requirements. It also shows that a clear-cut definition,... View Full Abstract

2017

2017 ARXIV: OPTIMIZATION AND CONTROL

Wasserstein Geometry of Quantum States and Optimal Transport of Matrix-Valued Measures

12 citations*

2018

Yongxin Chen ¹,Tryphon T. Georgiou ²,Allen Tannenbaum ³

¹ Iowa State University ,² University of California ,³ Stony Brook University

Hermitian matrix

Quantum state

View More (3+)

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices and of matrix-valued distributions, as well as some extensions of the theory to vector-valued distributions and discrete spac... View Full Abstract

2017

The Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flow

2017 REVIEWS IN MATHEMATICAL PHYSICS

Mauro Carfora

Istituto Nazionale di Fisica Nucleare

Ricci flow

Ricci curvature

View More (9+)

2017

On quantum versions of the classical Wasserstein distance

J Agredo, F Fagnola - Stochastics, 2017 - Taylor & Francis

We investigate a definition of quantum Wasserstein distance of two states based on their

couplings on the product algebra as in the classical case. A detailed analysis of the two

qubit model leads to a formal definition fulfilling some minimal requirements. It also shows …

2017

[CITATION] Sinkhorn-autodiff: Tractable wasserstein learning of generative models

A Genevay, G Peyré, M Cuturi - arXiv preprint arXiv:1706.00292, 2017

Construction of non-asymptotic confidence sets in 2-Wasserstein space

2017 [PDF] arxiv.org

J Ebert, V Spokoiny, A Suvorikova - arXiv preprint arXiv:1703.03658, 2017 - arxiv.org

In this paper, we consider a probabilistic setting where the probability measures are

considered to be random objects. We propose a procedure of construction non-asymptotic

confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea …

<——2017—— —2017 ——— 1000—

Parallel streaming Wasserstein barycenters

M Staib, S Claici, J Solomon, S Jegelka - arXiv preprint arXiv:1705.07443, 2017 - arxiv.org

Efficiently aggregating data from different sources is a challenging problem, particularly

when samples from each source are distributed differently. These differences can be

inherent to the inference task or present for other reasons: sensors in a sensor network may …

Existence and consistency of Wasserstein barycenters

T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual

notion of statistical mean. We prove the existence of Wasserstein barycenters of random

probabilities defined on a geodesic space (E, d). We also prove the consistency of this …

2017

On wasserstein two-sample testing and related families of nonparametric tests

A Ramdas, NG Trillos, M Cuturi - Entropy, 2017 - mdpi.com

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that

involves identifying differences between two random variables without making parametric

assumptions about their underlying distributions. The literature is old and rich, with a wide …

2017 [PDF] mlr.press

A simulated annealing based inexact oracle for Wasserstein loss minimization

J Ye, JZ Wang, J Li - International Conference on Machine …, 2017 - proceedings.mlr.press

Learning under a Wasserstein loss, aka Wasserstein loss minimization (WLM), is an

emerging research topic for gaining insights from a large set of structured objects. Despite

being conceptually simple, WLM problems are computationally challenging because they …

2017

Manifold-valued Image Generation with Wasserstein Generative Adversarial Nets

2017 ARXIV: COMPUTER VISION AND PATTERN RECOGNITION

Gromov-Wasserstein Averaging in a Riemannian Framework

14 citations* for all

14 citations*

2020 COMPUTER VISION AND PATTERN RECOGNITION

Samir Chowdhury ¹,Tom Needham ²

¹ Stanford University ,² Florida State University

Metric space

Space (mathematics)

View More (9+)

We introduce a theoretical framework for performing statistical tasks-including, but not limited to, averaging and principal component analysis-on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is carried out under the lens of the Gromov-Wasserstein (GW) distance,... View Full Abstract

2017

Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein's method I

Progressive Wasserstein Barycenters of Persistence Diagrams

2017 ARXIV: PROBABILITY

2020 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS

Jules Vidal ,Joseph Budin ,Julien Tierny

University of Paris

Approximation algorithm

Cluster analysis

View More (8+)

This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables the computation of a persistence diagram which is representat... View Full Abstract

2017

A partial Laplacian as an infinitesimal generator on the Wasserstein space

2017 ARXIV: ANALYSIS OF PDES

2017

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Y Tin Chow, W Gangbo - arXiv e-prints, 2017 - ui.adsabs.harvard.edu

We study stochastic processes on the Wasserstein space, together with their infinitesimal

generators. One of these processes is modeled after Brownian motion and plays a central

role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel …

[CITATION] A partial Laplacian as an infinitesimal generator on the Wasserstein space

W Gangbo, YT Chow - arXiv preprint arXiv:1710.10536, 2017

Regularized barycenters in the wasserstein space

2017

E Cazelles, J Bigot, N Papadakis - International Conference on Geometric …, 2017 - Springer

This paper is an overview of results that have been obtain in 2 on the convex regularization

of Wasserstein barycenters for random measures supported on\mathbb R^ d. We discuss …

Cite Cited by 4 Related articles

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging

but highly valuable in real application scenarios. In most situations, the source and the target

speakers do not repeat the same texts or they may even speak different languages. In this

case, one possible, although indirect, solution is to build a generative model for speech.

Generative models focus on explaining the observations with latent variables instead of

learning a pairwise transformation function, thereby bypassing the requirement of speech …

[CITATION] andH.-M. Wang,“Voiceconversion from unaligned corpora using variational autoencoding Wasserstein generative adversarial networks,”

CC Hsu, HT Hwang, YC Wu, Y Tsao - arXiv, 2017

<——2017—— —2017 ——— 1010—

2017 [PDF] researchgate.net

A Variational Model for Image Artifact Correction Based on Wasserstein Distance

IN Figueiredo, L Pinto, G Gonçalves… - European Congress on …, 2017 - Springer

Uneven illumination is a recurrent problem in image processing. This is essentially due to

image acquisition sensors' malfunction or external interference. In this paper we propose a …

Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks

2017 [PDF] arxiv.org

CC Hsu, HT Hwang, YC Wu, Y Tsao… - arXiv preprint arXiv …, 2017 - arxiv.org

Building a voice conversion (VC) system from non-parallel speech corpora is challenging

but highly valuable in real application scenarios. In most situations, the source and the target …

[CITATION] Voice conversion from unaligned corpora using variational autoencoding wasserstein generative adversarial networks. arXiv preprint arXiv: 170400849

CC Hsu, HT Hwang, YC Wu, Y Tsao, HM Wang - 2017

PDF) Discrete Wasserstein Barycenters: Optimal Transport for ...

https://www.researchgate.net › publication › 280538385_...

Mar 28, 2017 — PDF | Wasserstein barycenters correspond to optimal solutions of transport problems for several

Log-PCA versus Geodesic PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - arXiv preprint arXiv …, 2017 - arxiv.org

This paper is concerned by the statistical analysis of data sets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we …

A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance

I Yang - IEEE control systems letters, 2017 - ieeexplore.ieee.org

We consider the problem of constructing control policies that are robust against distribution

errors in the model parameters of Markov decision processes. The Wasserstein metric is

used to model the ambiguity set of admissible distributions. We prove the existence and …

2017

Decomposition algorithm for distributionally robust optimization using Wasserstein metric

F Luo, S Mehrotra - arXiv preprint arXiv:1704.03920, 2017 - arxiv.org

We study distributionally robust optimization (DRO) problems where the ambiguity set is

defined using the Wasserstein metric. We show that this class of DRO problems can be

reformulated as semi-infinite programs. We give an exchange method to solve the …

Wasserstein distributionally robust optimization and variation regularization

R Gao, X Chen, AJ Kleywegt - arXiv preprint arXiv:1712.06050, 2017 - arxiv.org

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical

success for various applications in operations research and machine learning, owing partly

to its regularization effect. Although connection between Wasserstein DRO and …

[CITATION] Wasserstein Distributional Robustness and Regularization in Statistical Learning. arXiv e-prints, art

R Gao, X Chen, AJ Kleywegt - arXiv preprint arXiv:1712.06050, 2017

Matricial Wasserstein-1 Distance - NCBI

2017

https://www.ncbi.nlm.nih.gov › articles › PMC5687101

by Y Chen · 2017 · Cited by 19 — Optimal mass transport (OMT) has proven to be a powerful methodology for numerous problems in physics, probability, information theory, fluid

2017 [PDF] arxiv.org

Reversible coalescing-fragmentating Wasserstein dynamics on the real line

V Konarovskyi, M von Renesse - arXiv preprint arXiv:1709.02839, 2017 - arxiv.org

We introduce a family of reversible fragmentating-coagulating processes of particles of

varying size-scaled diffusivity with strictly local interaction on the real line. The construction

is based on a new family of measures on the set of real increasing functions as reference …

2017 [PDF] researchgate.net

[PDF] Cadlág stability and approximation of reversible coalescing-fragmentating Wasserstein dynamics

V Konarovskyi - arXiv preprint arXiv:1711.03011, 2017 - researchgate.net

We construct coalescing-fragmentating Wasserstein dynamics [27] for any initial condition

and interacting potential by a finite particle approximation. We show that such a model

admits a description by a family of continuous semimartingales, where every semimartingale …

Fuzzy clustering of distribution-valued data using an adaptive

<——2017—— —2017 ——— 1020—

Wasserstein generative adversarial networks

M Arjovsky, S Chintala, L Bottou - … conference on machine …, 2017 - proceedings.mlr.press

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In

this new model, we show that we can improve the stability of learning, get rid of problems

like mode collapse, and provide meaningful learning curves useful for debugging and …

Cited by 8435 Related articles All 9 versions

2017

Existence of weak solutions in Wasserstein space for a chemotaxis model coupled to fluid equations

K Kang, HK Kim - SIAM Journal on Mathematical Analysis, 2017 - SIAM

We consider a coupled system of Keller--Segel-type equations and the incompressible

Navier--Stokes equations in spatial dimension two and three. We first establish the existence

of a weak solution of a Fokker--Plank equation in the Wasserstein space under the …

A simulated annealing based inexact oracle for wasserstein ...

https://pennstate.pure.elsevier.com › publications › a-si...

by J Ye · 2017 · Cited by 4 — In this paper, we introduce a stochastic approach based on simulated annealing for solving WLMs. Particularly, we have developed a Gibbs sampler to approximate ...

2017

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their

likelihood functions is intractable. Approximate Bayesian computation and indirect inference

have become popular approaches to overcome this issue, simulating synthetic data given

parameters and comparing summaries of these simulations with the corresponding

observed values. We propose to avoid these summaries and the ensuing loss of information

through the use of Wasserstein distances between empirical distributions of observed and …

[CITATION] Inference in generative models using the Wasserstein distance

Wasserstein distance on finite spaces: Statistical inference and algorithms

2017 [PDF] researchgate.net

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

A growing range of generative statistical models are such the numerical evaluation of their likelihood functions is intractable. Approximate Bayesian computation and indirect inference have become popular approaches to overcome this issue, simulating synthetic data given …

2017

M Sommerfeld - 2017 - oatd.org

year 2017

A Stochastic gradient method to compute Wasserstein barycenters of distributions

A Le Rhun, F Bonnans, P Martinon, T Leroy - smai.emath.fr

We present a stochastic gradient approach to compute barycenters of probability distributions, in the sense of Wassertein. The objective is to devise a fast method which can be used for instance to perform clustering for machine learning. The optimal transport [1] …

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - arxiv.org

… (GANs) are powerful generative models, but suffer from training instability. The recently

proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, … performs

better than standard WGAN and enables stable training of a wide variety of GAN architectures …

Cited by 6073 Related a

[CITATION] Improved training of wasserstein gans. In Advances in neural information processing systems

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - 2017 - Springer

Cited by 6918 Related articles All 12 versions

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - arXiv preprint arXiv …, 2017 - arxiv.org

… (GANs) are powerful generative models, but suffer from training instability. The recently

proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, … performs

better than standard WGAN and enables stable training of a wide variety of GAN architectures …

[CITATION] Improved training of wasserstein GANs, in neural information processing systems

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - 2017

[CITATION] Improved training of wasserstein GANs-code

I Gulrajani, F Ahmed, M Arjovsky, V Dumoulin… - 2017

Order-preserving wasserstein distance for sequence matching

2017

B Su, G Hua - Proceedings of the IEEE conference on …, 2017 - openaccess.thecvf.com

We present a new distance measure between sequences that can tackle local temporal

distortion and periodic sequences with arbitrary starting points. Through viewing the

instances of sequences as empirical samples of an unknown distribution, we cast the …

<——2017—— —2017 ——— 1030—

2017 [PDF] ams.org

On tangent cones in Wasserstein space

J Lott - Proceedings of the American Mathematical Society, 2017 - ams.org

If $ M $ is a smooth compact Riemannian manifold, let $ P (M) $ denote the Wasserstein

space of probability measures on $ M $. If $ S $ is an embedded submanifold of $ M $, and

$\mu $ is an absolutely continuous measure on $ S $, then we compute the tangent cone of …

2017 [PDF] mdpi.com

A comparison between Wasserstein distance and a distance induced by Fisher-Rao metric in complex shapes clustering

AD Sanctis, SA Gattone - Multidisciplinary Digital Publishing Institute …, 2017 - mdpi.com

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a

human head in the space. The applications range from structural biology, computer vision,

medical imaging to archaeology. We focus on the selection of an appropriate measurement …

Exponential convergence in the Wasserstein metric for one dimensional diffusions

L Cheng, R Li, L Wu - arXiv preprint arXiv:1703.00507, 2017 - arxiv.org

In this paper, we find some general and efficient sufficient conditions for the exponential

convergence $ W_ {1, d}(P_t (x,\cdot), P_t (y,\cdot))\le Ke^{-\delta t} d (x, y) $ for the

semigroup $(P_t) $ of one-dimensional diffusion. Moreover some sharp estimates of the …

2017 see 2018 [PDF] researchgate.net

[PDF] Inference in generative models using the Wasserstein distance

E Bernton, PE Jacob, M Gerber… - arXiv preprint arXiv …, 2017 - researchgate.net

… We propose a new distance, termed the Hilbert distance, based on the Hilbert space-filling

curve (Sagan… distance can be computed orders of magnitude faster than the exact Wasserstein

distance, and we provide theoretical support for its use in ABC and minimum distance …

2017

[1711.01558] Wasserstein Auto-Encoders - arXiv

Data-driven distributed optimization using Wasserstein ambiguity sets

by I Tolstikhin · 2017 · Cited by 727 — We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the ...

2017

https://github.com › yenchenlin › issues

Applying Wasserstein (Earth Mover) distance to the project #21

Feb 11, 2017 — Hi... I was wondering if adding Wasserstein distance to the code would help the GAN to stabilize and give better results... from w

2017 see 2018

Conference Paper

Citation/Abstract

Data-driven distributed optimization using Wasserstein ambiguity sets

Cherukuri, Ashish; Cortes, Jorge.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2017).

Abstract/DetailsGetit!Show Abstract

Short communication
Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance
Statistics & Probability LettersApril 2017...

Jim X. Xiang

2017 7 patent
A kind of WGAN model methods based on depth convolutional neural networks

CN CN107563510A 周智恒华南理工大学

Priority 2017-08-14 • Filed 2017-08-14 • Published 2018-01-09

A kind of 3. WGAN model methods based on depth convolutional neural networks according to claim 1, it is characterised in that institute The transposition depth convolutional network number of plies of maker and the depth convolutional neural networks number of plies of arbiter are identical in the …

2017 7 patent

A kind of hyper parameter dynamic adjusting method based on WGAN

CN CN107590532A 周智恒华南理工大学

Priority 2017-08-14 • Filed 2017-08-14 • Published 2018-01-16

A kind of 3. hyper parameter dynamic adjusting method based on WGAN according to claim 1, it is characterised in that described step Rapid S2 is specific as follows： Get out image data set, random initializtion maker, arbiter convolutional neural networks in all parameter and weight, Hyper …

<—–2017———2017 ——— 1040—e

2017 7 patent

A kind of WGAN methods based on text generation

CN CN107590531A 周智恒华南理工大学

Priority 2017-08-14 • Filed 2017-08-14 • Published 2018-01-16

A kind of 3. WGAN methods based on text generation according to claim 1, it is characterised in that described text data Collection is to belong to same type of content. A kind of 4. WGAN methods based on text generation according to claim 1, it is characterised in that described step S4 tools Body …

202017 7 patent

A kind of decomposition convolution method based on WGAN models

CN CN107943750A 周智恒华南理工大学

Priority 2017-11-14 • Filed 2017-11-14 • Published 2018-04-20

1. a kind of decomposition convolution method based on WGAN models, it is characterised in that the decomposition convolution method includes following step Suddenly： S1, construction are originally generated confrontation network model, and generating image by maker inputs to arbiter progress ……

Wasserstein distance and the distributionally robust TSP

https://viterbi-web.usc.edu › ~jcarlsso › wasserstei...

https://viterbi-web.usc.edu › ~jcarlsso › wasserstei...P

by JG Carlsson · 2017 · Cited by 49 — Motivated by a districting problem in multi-vehicle routing, we consider a distributionally robust version of the Euclidean travelling salesman ...

48 pages

On the total variation Wasserstein gradient flow and the TV - IKO scheme

by G Carlier · 2017 · Cited by 8 — We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a form ...

Martin Arjovsky (WGAN) Interview - YouTube

- Uploaded by The Nutty Netter (Alex Lamb)

... AI) on the theory of generative adversarial networks, biological plausibility of deep credit assignment, and his ...

10,589 views

Jun 12, 2017

2017

Wasserstein GAN model exploration 2/2 - YouTube

- Uploaded by Sztefciu

https://github.com/martinarjovsky/WassersteinGAN.

Feb 6, 2017

Mike Tyka on Twitter: "WGAN, BE-GAN, WGAN2, LsGAN…

Never miss a Moment ... The media could not be played. ... you forgot the new queen, WGAN-GP! ... I stopped ...

Apr 4, 2017

Probability, Statistics and Machine Learning, on Monday, May 1, 2017 on the topic: Regularization of ...

May 1, 2017 - Uploaded by Banff International Research Station

Regularization of Barycenters in the Wasserstein Space

www.birs.ca › videos › watch › 201705011300-Cazelles

Elsa Cazelles speaking at BIRS workshop, Optimal Transport meets Probability, Statistics and Machine Learning, on Monday, May 1, 2017 on the ...

Banff International Research Station · Banff International Research Station ·

May 1, 2017

Video: Clarice Poon, "The total variation Wasserstein gradient flow

meets Probability, Statistics and Machine Learning, on Tuesday, May 2, 2017 on the topic: The total variation ...

- Uploaded by Banff International Research Station

The total variation Wasserstein gradient flow - Open Collections
May 2, 2017

<—–2017———2017 ———1050—

Deep adversarial learning is finally ready and will radically ...

medium.com › deep-adversarial-learning-is-finally-ready-...

Briefly introduce generative adversarial networks (GANs) and the major challenges associated with them; Summarize recent research (Wasserstein ...

Medium · Two Minute Papers ·

May 15, 2017

Video: Bertram Düring, "Lagrangian schemes for Wasserstein

54:00

... at BIRS workshop, Optimal Transportation and Differential Geometry, on Thursday, May 24, 2012 on the topic ...

May 24, 2012 · Uploaded by Banff International Research Station

Tommaso Pacini, "Differential forms and symplectic geometry on Wasserstein space

www.birs.ca › videos › watch › 201205241112-Pacini

... and Differential Geometry, on Thursday, May 24, 2012 on the topic: Differential forms and symplectic geometry on Wasserstein space.

Banff International Research Station · Banff International Research Station ·

May 24, 2012

"How to Train a GAN" at NIPS2016 workshopのメモ - 緑茶思考ブログ

- Uploaded by David Lopez-Paz

NIPS2016でのWorkshop on Adversarial Training「How to train a GAN」での ...

May 28, 2017

Cooper Union End of the Year Show 2017

cooper.edu › engineering › research › CUEOYS_2017[STUDENT POSTER] ORIGINAL FONT GENERATION USING CONDITIONAL WASSERSTEIN GAN WITH GRADIENT PENALTY -- T.K., S.P. (EE'18).

The Cooper Union · Miles Barber ·

May 30, 2017

THU AI Reading Group: Improved Training of Wasserstein ...

Improved Training of Wasserstein GANs - YouTube

https://www.slideshare.net/ckmarkohchang/nthu-ai-reading-group-improved-training-of-wasserstein-gans0:00:00 Chanwei Hu Excited !0:00:00 沅 ...

YouTube · Mark Chang ·

Jun 6, 2017

2017

- Uploaded by Mark Chang

https://www.slideshare.net/ckmarkohchang/nthu-ai-reading-group-improved-training-of-wasserstein-gans 0 ...

Jun 6, 2017

Sliced Wasserstein Generative Models | Papers With Code

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the ...

Jun 8, 2017 · Uploaded by cantabilewq

Martin Arjovsky (WGAN) Interview 4,864 views The Nutty Netter (Alex Lamb)

Streamed live on Jun 12, 2017

My interview with Martin Arjovsky (NYU PhD student studying Machine Learning and AI) on the theory of generative adversarial networks, biological plausibility of deep credit assignment, and his work on the Wasserstein GAN. 1:33 Start of Interview 15:15 Criticisms of Maximum Likelihood 27:55 Wasserstein GAN and Generative Models 54:20 Deep Learning without backprop and biological plausibility 59:54 Future of Deep Learning Research as a Professional Career Path Links to papers: https://arxiv.org/abs/1701.07875 https://arxiv.org/abs/1701.04862 https://arxiv.org/abs/1704.00028

Jun 12, 2017

Соперничающие сети (GAN) - Нейронные сети в машинном ...

- Uploaded by Технострим Mail.Ru Group

Равновесие Нэша. Генеративные конкурирующие сети (GAN). ... Wasserstein GAN. ... Семинар:Реализация архитектуры GAN для генерации лиц.

Jul 16, 2017

David Koslicki: "Using the Earth-mover's Distance to compare ...

- Uploaded by ZarlabUCLA

David Koslicki: "Using the Earth-mover's Distance to compare microbial ... The Wasserstein Metric a.k.a ...

Aug 1, 2017

<—–2017———2017 ———1060—

09. Regularized Wasserstein Distances & Minimum Kantorovich ...

Uploaded by Компьютерные науки

Deep Learning: Theory, Algorithms, and Applications. Berlin, June 2017 The workshop aims at bringing ...
Aug 3, 2017

Wasserstein GAN learns to generate MNIST digits

265 views

Aug 16, 2017

On differentiability in the Wasserstein space o... » NSF ...

mathinstitutes.org › videos › videos

- This is a video about On differentiability in the Wasserstein space of ... phase- space is the Wasserstein space of Borel probability measures ...

Aug 29, 2017

Wasserstein-geometry as a natural language for Quantum hydrodynamics

(MP4 Medium Res, MP3, PDF)

Speaker(s): Bernadette Lessel

Scientific Areas: Quantum Foundations

Collection/Series: Quantum Foundations

PIRSA Number: 16050049

Abstract In this talk I would like to put forward Wasserstein-geometry as a natural language for Quantum hydrodynamics. Wasserstein-geometry is a formal, infinite dimensional, Riemannian manifold structure on the space of probability measures on a given Riemannian manifold. The basic equations of Quantum hydrodynamics on the other hand are given by the Madelung equations. In terms of Wasserstein-geometry, Madelung equations appear in the shape of Newton's second law of motion, in which the geodesics are disturbed by the influence of a quantum potential. This was pointed out in 2008 by Max. K. von Renesse. Finally, based on the notion of Wasserstein-distance, I will will briefly introduce a natural notion of Shape Space and some of its properties.

Pirsa: 16050049 - Wasserstein-geometry as a natural language for Quantum hydrodynamics

Sep 1, 2017

Mean Field Games (Schedule) - ipam.UCLA

www.ipam.ucla.edu › programs › workshops › mean-fiel...

René Carmona (Princeton University) ... On differentiability in the Wasserstein space of probability measures. 2:50 - 3:30.

ipam.UCLA ·

Sep 1, 2017

2017

Wasserstein GAN training - YouTube

- Uploaded by M Y

Wasserstein GAN training. M Y. Loading... Unsubscribe from M Y? Cancel

Sep 8, 2017

Wasserstein Generative Adversarial Network review

YouTube · 1,000+ views

· 9/19/2017

· by Mr.JLai

Sep 19, 2017

Sliced Wasserstein Kernel for Persistence Diagrams on Vimeo

vimeo.com › TechTalksTV › Videos

This is "Sliced Wasserstein Kernel for Persistence Diagrams" by TechTalksTV on Vimeo, the home for high quality videos and the people who ...

Vimeo · TechTalksTV ·

Oct 31, 2017

WGAN和GAN直观区别和优劣- 知乎

建议开篇前前往这个链接，虽然主要是讲WGAN,前面也会讲到GAN,写得非常的棒：令人拍案叫绝的 ...

Nov 24, 2017

Wasserstein Generative adversarial Networks (WGANs) in in tensor filow

We discussed Wasserstein GANs which provide many improved functionalities over GANs. We then train a ...

Dec 23, 2017 · Uploaded by AI Journal

<—–2017———2017 ———1070—e

Wasserstein Generative adversarial Networks (WGANs) in Tensorflow

YouTube · 9,000+ views · 12/24/2017 · by AI Journal

Dec 24,2017

Архив семинаров 2017 года - Информационная система

- Uploaded by Институт Философии РАН

Выживаемость в пространстве Васерштейна также предполагается использовать при исследовании задач управления в пространстве вероятностей.

Dec 30, 2017

Jianbo Ye, James Wang, Jia Li on Vimeo

vimeo.com › TechTalksTV › Videos

This is "A Simulated Annealing Based Inexact Oracle for Wasserstein Loss Minimization --- Jianbo Ye, James Wang, Jia Li" by TechTalksTV on ...

Oct 14, 2017

2017

Lior Wolf | Papers With Code

paperswithcode.com › search

no code implementations • 16 Sep 2022 • Yoni Choukroun, Lior Wolf ... Conditional WGANs with Adaptive Gradient Balancing for Sparse MRI Reconstruction.

Papers With Code · ComputerVisionFoundation Videos ·

Nov 16, 2017

2017
Gang of GANs: Generative Adversarial Networks with Maximum Margin RankingAuthors:Juefei-Xu, Felix (Creator), Boddeti, Vishnu Naresh (Creator), Savvides, Marios (Creator)
Summary:Traditional generative adversarial networks (GAN) and many of its variants are trained by minimizing the KL or JS-divergence loss that measures how close the generated data distribution is from the true data distribution. A recent advance called the WGAN based on Wasserstein distance can improve on the KL and JS-divergence based GANs, and alleviate the gradient vanishing, instability, and mode collapse issues that are common in the GAN training. In this work, we aim at improving on the WGAN by first generalizing its discriminator loss to a margin-based one, which leads to a better discriminator, and in turn a better generator, and then carrying out a progressive training paradigm involving multiple GANs to contribute to the maximum margin ranking loss so that the GAN at later stages will improve upon early stages. We call this method Gang of GANs (GoGAN). We have shown theoretically that the proposed GoGAN can reduce the gap between the true data distribution and the generated data distribution by at least half in an optimally trained WGAN. We have also proposed a new way of measuring GAN quality which is based on image completion tasks. We have evaluated our method on four visual datasets: CelebA, LSUN Bedroom, CIFAR-10, and 50K-SSFF, and have seen both visual and quantitative improvement over baseline WGANShow more
Downloadable Archival Material, 2017-04-17
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Publis

2017

Improved Training of Wasserstein GANsAuthors:Gulrajani, Ishaan (Creator), Ahmed, Faruk (Creator), Arjovsky, Martin (Creator), Dumoulin, Vincent (Creator), Courville, Aaron (Creator)
Summary:Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only low-quality samples or fail to converge. We find that these problems are often due to the use of weight clipping in WGAN to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We propose an alternative to clipping weights: penalize the norm of gradient of the critic with respect to its input. Our proposed method performs better than standard WGAN and enables stable training of a wide variety of GAN architectures with almost no hyperparameter tuning, including 101-layer ResNets and language models over discrete data. We also achieve high quality generations on CIFAR-10 and LSUN bedroomsShow more
Downloadable Archival Material, 2017-03-31
Undefined
Publisher:2017-03-31ß

2017

Wasserstein Introspective Neural NetworksAuthors:Lee, Kwonjoon (Creator), Xu, Weijian (Creator), Fan, Fan (Creator), Tu, Zhuowen (Creator)
Summary:We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing INN's generative modeling capability. WINN has three interesting properties: (1) A mathematical connection between the formulation of the INN algorithm and that of Wasserstein generative adversarial networks (WGAN) is made. (2) The explicit adoption of the Wasserstein distance into INN results in a large enhancement to INN, achieving compelling results even with a single classifier --- e.g., providing nearly a 20 times reduction in model size over INN for unsupervised generative modeling. (3) When applied to supervised classification, WINN also gives rise to improved robustness against adversarial examples in terms of the error reduction. In the experiments, we report encouraging results on unsupervised learning problems including texture, face, and object modeling, as well as a supervised classification task against adversarial attacksShow more
Downloadable Archival Material, 2017-11-24
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Publisher:2017-11-24

2017

Face Super-Resolution Through Wasserstein GANsAuthors:Chen, Zhimin (Creator), Tong, Yuguang (Creator)
Summary:Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide range of problems. Despite its great potential, GANs are difficult to train. Recently, a series of papers (Arjovsky & Bottou, 2017a; Arjovsky et al. 2017b; and Gulrajani et al. 2017) proposed using Wasserstein distance as the training objective and promised easy, stable GAN training across architectures with minimal hyperparameter tuning. In this paper, we compare the performance of Wasserstein distance with other training objectives on a variety of GAN architectures in the context of single image super-resolution. Our results agree that Wasserstein GAN with gradient penalty (WGAN-GP) provides stable and converging GAN training and that Wasserstein distance is an effective metric to gauge training progressShow more
Downloadable Archival Material, 2017-05-05
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Publisher:2017-05-05

2017
Manifold-valued Image Generation with Wasserstein Generative Adversarial NetsAuthors:Huang, Zhiwu (Creator), Wu, Jiqing (Creator), Van Gool, Luc (Creator)
Summary:Generative modeling over natural images is one of the most fundamental machine learning problems. However, few modern generative models, including Wasserstein Generative Adversarial Nets (WGANs), are studied on manifold-valued images that are frequently encountered in real-world applications. To fill the gap, this paper first formulates the problem of generating manifold-valued images and exploits three typical instances: hue-saturation-value (HSV) color image generation, chromaticity-brightness (CB) color image generation, and diffusion-tensor (DT) image generation. For the proposed generative modeling problem, we then introduce a theorem of optimal transport to derive a new Wasserstein distance of data distributions on complete manifolds, enabling us to achieve a tractable objective under the WGAN framework. In addition, we recommend three benchmark datasets that are CIFAR-10 HSV/CB color images, ImageNet HSV/CB color images, UCL DT image datasets. On the three datasets, we experimentally demonstrate the proposed manifold-aware WGAN model can generate more plausible manifold-valued images than its competitorsShow more
Downloadable Archival Material, 2017-12-05
Undefined

Manifold-valued image generation with wasserstein generative adversarial nets

2017

Wasserstein Divergence for GANsAuthors:Wu, Jiqing (Creator), Huang, Zhiwu (Creator), Thoma, Janine (Creator), Acharya, Dinesh (Creator), Van Gool, Luc (Creator)
Summary:In many domains of computer vision, generative adversarial networks (GANs) have achieved great success, among which the family of Wasserstein GANs (WGANs) is considered to be state-of-the-art due to the theoretical contributions and competitive qualitative performance. However, it is very challenging to approximate the $k$-Lipschitz constraint required by the Wasserstein-1 metric~(W-met). In this paper, we propose a novel Wasserstein divergence~(W-div), which is a relaxed version of W-met and does not require the $k$-Lipschitz constraint. As a concrete application, we introduce a Wasserstein divergence objective for GANs~(WGAN-div), which can faithfully approximate W-div through optimization. Under various settings, including progressive growing training, we demonstrate the stability of the proposed WGAN-div owing to its theoretical and practical advantages over WGANs. Also, we study the quantitative and visual performance of WGAN-div on standard image synthesis benchmarks of computer vision, showing the superior performance of WGAN-div compared to the state-of-the-art methodsShow more
Downloadable Archival Material, 2017-12-04
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Publisher:2017-12-04

<—–2017———2017 ———1080—

2017
Visual Feature Attribution using Wasserstein GANsAuthors:Baumgartner, Christian F. (Creator), Koch, Lisa M. (Creator), Tezcan, Kerem Can (Creator), Ang, Jia Xi (Creator), Konukoglu, Ender (Creator)
Summary:Attributing the pixels of an input image to a certain category is an important and well-studied problem in computer vision, with applications ranging from weakly supervised localisation to understanding hidden effects in the data. In recent years, approaches based on interpreting a previously trained neural network classifier have become the de facto state-of-the-art and are commonly used on medical as well as natural image datasets. In this paper, we discuss a limitation of these approaches which may lead to only a subset of the category specific features being detected. To address this problem we develop a novel feature attribution technique based on Wasserstein Generative Adversarial Networks (WGAN), which does not suffer from this limitation. We show that our proposed method performs substantially better than the state-of-the-art for visual attribution on a synthetic dataset and on real 3D neuroimaging data from patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD). For AD patients the method produces compellingly realistic disease effect maps which are very close to the observed effectsShow more
Downloadable Archival Material, 2017-11-24
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Publisher:2017-11-24

2017
Wasserstein GANAuthors:Arjovsky, Martin (Creator), Chintala, Soumith (Creator), Bottou, Léon (Creator)
Summary:We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributionsShow more
Downloadable Archival Material, 2017-01-26
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Publisher:2017-01-26

2017

[R] [1701.07875] Wasserstein GAN : r/MachineLearning - Reddit

www.reddit.com › r_170107875_wasserstein_gan

www.reddit.com › r_170107875_wasserstein_gan[R] [1701.07875] Wasserstein GAN. r/MachineLearning - [R] [1701.07875] Wasserstein GAN ... ian_goodfellow Google Brain • 6 yr. ago.

Reddit ·

Jan 30, 2017

Peer-reviewed
Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $\alpha$-dependent sequences

Authors:Jérôme Dedecker, Florence Merlevède
Summary:We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order $p$ for any $p\geq1$, and we give some conditions under which the central limit theorem holds. We apply our results to unbounded functions of expanding maps of the interval with a neutral fixed point at zero. The moment inequalities for the Wasserstein distance are similar to the well-known von Bahr–Esseen or Rosenthal bounds for partial sums, and seem to be new even in the case of independent and identically distributed random variablesShow more
Downloadable Article
Publication:Bernoulli, 23, 2017-08, 2083

2017 see 2018
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

Authors:Schmitz, Morgan A. (Creator), Heitz, Matthieu (Creator), Bonneel, Nicolas (Creator), Mboula, Fred Maurice Ngolè (Creator), Coeurjolly, David (Creator), Cuturi, Marco (Creator), Peyré, Gabriel (Creator), Starck, Jean-Luc (Creator)Show more
Summary:This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in the probability simplex. Our method simultaneously estimates such atoms, and, for each datapoint, the vector of weights that can optimally reconstruct it as an optimal transport barycenter of such atoms. Our method is computationally tractable thanks to the addition of an entropic regularization to the usual optimal transportation problem, leading to an approximation scheme that is efficient, parallel and simple to differentiate. Both atoms and weights are learned using a gradient-based descent method. Gradients are obtained by automatic differentiation of the generalized Sinkhorn iterations that yield barycenters with entropic smoothing. Because of its formulation relying on Wasserstein barycenters instead of the usual matrix product between dictionary and codes, our method allows for nonlinear relationships between atoms and the reconstruction of input data. We illustrate its application in several different image processing settingsShow more
Downloadable Archival Material, 2017-08-06
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Publisher:2017-08-06

2017

2017 see 2016
Learning with a Wasserstein loss

Authors:McGovern Institute for Brain Research at MIT Center for Brains, Minds, and Machines (Contributor), Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology Department of Brain and Cognitive Sciences (Contributor), Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science (Contributor), Frogner, Charles Albert (Contributor), Zhang, Chiyuan (Contributor), Mobahi, Hossein (Contributor), Poggio, Tomaso A (Contributor), Araya-Polo, Mauricio (Creator)Show more
Summary:Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions.In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well as a novel extension of the Wasserstein distance from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, outperforming a baseline that doesn't use the metricShow more
Downloadable Archival Material, 2017-11-28T20:02:00Z
Undefined
Publisher:MIT Press, 2017-11-28T20:02:00Z

2017

Markov type constants of Wasserstein spaces

https://www.mpim-bonn.mpg.de › node

Sep 14, 2017 — In the talk I'm going to present an idea which allows to compute Markov type constants for Wasserstein spaces. Let P p ( R d ) \mathcal{P}_p(\ ...

Wasserstein Distributionally Robust Optimization and Variation Regularization

Authors:Gao, Rui (Creator), Chen, Xi (Creator), Kleywegt, Anton J. (Creator)
Summary:Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existing results often require restrictive assumptions, such as smoothness or convexity, that are not satisfied for many problems. In this paper, we develop a general theory on the variation regularization effect of the Wasserstein DRO - a new form of regularization that generalizes total-variation regularization, Lipschitz regularization and gradient regularization. Our results cover possibly non-convex and non-smooth losses and losses on non-Euclidean spaces. Examples include multi-item newsvendor, portfolio selection, linear prediction, neural networks, manifold learning, and intensity estimation for Poisson processes, etc. As an application of our theory of variation regularization, we derive new generalization guarantees for adversarial robust learningShow more
Downloadable Archival Material, 2017-12-16
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Publisher:2017-12-16

Peer-reviewed
The Steepest Descent Algorithm in Wasserstein Metric for the Sandpile Model of Self-Organized Criticality

Author:Viorel Barbu
Summary:The nonlinear diffusion equation $\rho_t-\Delta(\rhoH(\rho-\rho_c))=0$ in $(0,\infty)\times \mathbb{R}^n$,$\rho(0,x)=\rho_0(x)$, where $H$ is the Heaviside function,describes the sandpile model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A (3), pp. 364--374;P. Bantay and I. M. Janosi, Phys. A , 185 (1992), pp. 11--18; R. Cafiero et al., Europhys. Lett. , 29 (1995), pp. 111--116]withcritical state $\rho_c\in L^\infty(\mathbb{R}^n)\cap L^1(\mathbb{R}^n)$. Here, oneproves that a solution $\rho=\rho(t,x)$ can be obtained as the limitof the time-stepping approximation scheme associated with thevariational problem $\rho_k={\rmarg}\,\min_{\rho\in\mathcal{P}}\{\frac1h\d^2(\rho_{k-1},\rho)+\mathbb{E}(\rho)\}$, where $d$ is the$2$-Wasserstein distance and $\mathbb{E}$ is the energy functionalcorresponding to the above nonlinear diffusion process. Thisresult is on the line of that previously obtained for the linearFokker--Planck andporous media equations by Jordan, Kinderlehrer, and Otto [ SIAM J. Math. Anal. , 29 (1998), pp. 1--17] and Otto [ Arch. Ration. Mech. Anal. , 141 (1998), pp. 63--103; Comm. Partial Differential Equations , 26 (2001), pp. 101--174]Show more
Downloadable Article
Publication:SIAM Journal on Control and Optimization, 55, 2017, 413

Peer-reviewed
Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to FluidEquations

Authors:Kyungkeun Kang, Hwa Kil Kim
Summary:We consider a coupled system of Keller--Segel-type equations and theincompressible Navier--Stokes equations in spatial dimension two andthree. We first establish the existence of a weak solution of a Fokker--Plankequation in the Wasserstein space under the assumption that initial massis integrable and has finite entropy. As a result, we construct solutionsof Keller--Segel--Navier--Stokes equations such that the density of biologicalorganism belongs to the absolutely continuous curves in the Wasserstein space,in the case that its initial mass is assumed to be bounded and integrableShow more
Downloadable Article
Publication:SIAM Journal on Mathematical Analysis, 49, 2017, 2965

<—–2017———2017 ———1090—

Peer-reviewed
The Wasserstein geometry of nonlinear σ models and the Hamilton-Perelman Ricci flow

Author:Mauro Carfora
Summary:Nonlinear sigma models are quantum field theories describing, in the large deviation sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci flow. By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between nonlinear sigma models and Ricci flow theory. In particular, we analyze the embedding of Ricci flow into a heat kernel renormalization group flow for dilatonic nonlinear sigma models, and characterize a non-trivial generalization of the Hamilton-Perelman version of the Ricci flow. We discuss in detail the monotonicity and gradient flow properties of this extended flowShow more
Article, 2017
Publication:Reviews in Mathematical Physics, 29, February 2017
Publisher:2017

MAP image labeling using Wasserstein messages and geometric assignment

Authors:Astrom F., Huhnerbein R., Savarino F., Recknagel J., Schnorr C., 6th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2017
Article, 2017
Publication:Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10302 LNCS, 2017, 373
Publisher:2017

A Convex Optimization Approach to Distributionally Robust Markov Decision Processes With Wasserstein Distance

Author:Insoon Yang
Summary:We consider the problem of constructing control policies that are robust against distribution errors in the model parameters of Markov decision processes. The Wasserstein metric is used to model the ambiguity set of admissible distributions. We prove the existence and optimality of Markov policies and develop convex optimization-based tools to compute and analyze the policies. Our methods, which are based on the Kantorovich convex relaxation and duality principle, have the following advantages. First, the proposed dual formulation of an associated Bellman equation resolves the infinite dimensionality issue that is inherent in its original formulation when the nominal distribution has a finite support. Second, our duality analysis identifies the structure of a worst-case distribution and provides a simple decentralized method for its construction. Third, a sensitivity analysis tool is developed to quantify the effect of ambiguity set parameters on the performance of distributionally robust policies. The effectiveness of our proposed tools is demonstrated through a human-centered air conditioning problemShow more
Article, 2017
Publication:IEEE Control Systems Letters, 1, 201707, 164
Publisher:2017

Peer-reviewed
Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

Author:Xiang J.X.
Article, 2017
Publication:Statistics and Probability Letters, 123, 2017 04 01, 160
Publisher:2017

Peer-reviewed
Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary a-dependent sequences

Authors:Dedecker J., MerlevEDe F.
Article, 2017
Publication:Bernoulli, 23, 2017 08 01, 2083
Publisher:2017
.;/Author:Zinsl J.
Article, 2017
Publication:Discrete and Continuous Dynamical Systems - Series S, 10, 2017 08 01, 919
Publisher:2017

2017

Peer-reviewed
Bayes and maximum likelihood for L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document}-Wasserstein deconvolution of Laplace mixturesShow more

Author:Catia Scricciolo
Article, 2017
Publication:Statistical methods & applications, 27, 2017, 333
Publisher:2017

2017 see 2016
Gromov-wasserstein averaging of kernel and distance matrices

Authors:Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science (Contributor), Solomon, Justin (Contributor), Peyre, Gabriel (Creator), Cuturi, Marco (Creator)Show more
Summary:This paper presents a new technique for computing the barycenter of a set of distance or kernel matrices. These matrices, which define the interrelationships between points sampled from individual domains, are not required to have the same size or to be in row-by-row correspondence. We compare these matrices using the softassign criterion, which measures the minimum distortion induced by a probabilistic map from the rows of one similarity matrix to the rows of another; this criterion amounts to a regularized version of the Gromov-Wasserstein (GW) distance between metric-measure spaces. The barycenter is then defined as a Fréchet mean of the input matrices with respect to this criterion, minimizing a weighted sum of softassign values. We provide a fast iterative algorithm for the resulting nonconvex optimization problem, built upon state-of-the-art tools for regularized optimal transportation. We demonstrate its application to the computation of shape barycenters and to the prediction of energy levels from molecular configurations in quantum chemistryShow more
Downloadable Archival Material, 2017-12-21T14:48:51Z
Undefined
Publisher:Association for Computing Machinery, 2017-12-21T14:48:51Z

Peer-reviewed
The quasineutral limit of the Vlasov—Poisson equation in Wasserstein metric

Authors:Daniel Han-Kwan, Mikaela Iacobelli
Article, 2017
Publication:Communications in mathematical sciences, 15, 2017, 481
Publisher:2017

2017 thesis
Fréchet means in Wasserstein space : theory and algorithms

Authors:Yoav Zemel, Victor M. Panaretos
Summary:Mots-clés de l'auteur: Fréchet mean ; functional data analysis ; geodesic variation ; optimal transportation ; phase variation ; point process ; random measure ; registration ; warping ; Wasserstein distanceShow more
Thesis, Dissertation, 2017

2017 see 2014
Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

Authors:Peletier, M.A. (Contributor), Scardia, L. (Contributor), Mora, M.G. (Creator)
Summary:We consider systems of $n$ parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modeled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations and prove several convergence results in the limit $n\to\infty$. The main aim of the paper is to study the convergence of the evolution of the empirical measure as $n\to\infty$. We consider rate-independent, quasi-static evolutions, in which the motion of the dislocations is restricted to the same slip plane. This leads to a formulation of the quasi-static evolution problem in terms of a modified Wasserstein distance, which is only finite when the transport plan is slip-plane-confined. Since the focus is on interaction between dislocations, we renormalize the elastic energy to remove the potentially large self- or core energy. We prove Gamma-convergence of this renormalized energy, and we construct joint recovery sequences for which both the energies and the modified distances converge. With this augmented Gamma-convergence we prove the convergence of the quasi-static evolutions as $n\to\infty$.Show more
Downloadable Archival Material, 2017
English
Publisher:2017

<—–2017———2017 ———1100—

Accelerated discrete distribution clustering under wasserstein distance

by Li, Jia; Ye, Jianbo; Wang, James Z 07/2018

Computationally efficient accelerated D2-clustering algorithms are disclosed for clustering discrete distributions under the Wasserstein distance with improved...

Patent: Citation Online

Accelerated Discrete Distribution Clustering under Wasserstein Distance

Aug 1, 2018 - Request PDF on ResearchGate | Accelerated Discrete Distribution Clustering under Wasserstein Distance | In a variety of research areas, the ...

The Penn State Research Foundation Submits United States Patent Application for Accelerated Discrete Distribution Clustering Under Wasserstein Distance

Global IP News. Software Patent News, Mar 23, 2017

Newspaper Article: Citation Online

Accelerated Discrete Distribution Clustering under Wasserstein Distance slides

O We have developed and compared three rst-order methods for optimizing the Wasserstein centroids in. D -clustering. We refer to the modi ed Bregman ADMM as the main algorithm. O The new methods, collectively called AD -clustering, improve scalability signi cantly. We have also developed a parallel algorithm for the ...

Peer-reviewed
Schémas d'ordre deux en temps pour des flots de gradient dans des espaces métriques géodésiques et de Wasserstein

Authors:Legendre G., Turinici G.
Article, 2017
Publication:Comptes Rendus Mathematique, 355, 2017 03 01, 345
Publisher:2017

Peer-reviewed
Bayes and maximum likelihood for $$L^1$$ L 1 -Wasserstein deconvolution of Laplace mixtures

Authors:Catia Scricciolo, SpringerLink (Online service)
Downloadable Article, 2017
English
Publication:Statistical methods & applications.
Publisher:2017

Decomposition algorithms for distributionally robust optimization using Wasserstein metric

Authors:Luo F., Mehrotra S.
Article, 2017
Publication:arXiv, 2017 04 12
Publisher:2017

2917

2017

Wasserstein auto-encoders

I Tolstikhin, O Bousquet, S Gelly… - arXiv preprint arXiv …, 2017 - arxiv.org

… Wasserstein Auto-Encoder (WAE)—a new algorithm for building a generative model of

the data distribution. WAE minimizes a penalized form of the Wasserstein … a novel auto-encoder …

Enhancing Underwater Imagery using GANs

irvlab.cs.umn.edu › underwater-image-restoration

"Improved training of wasserstein gans." arXiv preprint arXiv:1704.00028 (2017). [9] Arjovsky, Martin, Soumith Chintala, and Léon Bottou. "Wasserstein gan." ...

Minnesota Interactive Robotics and Vision Laboratory · Cam Fabbri ·

Oct 1, 2017

SAMPLING OF PROBABILITY MEASURES IN THE CONVEX ORDER BY WASSERSTEIN PROJECTION

Authors:Alfonsi A., Corbetta J., Jourdain B.
Article, 2017
Publication:arXiv, 2017 09 15
Publisher:2017

Peer-reviewed
Fast discrete distribution clustering using wasserstein barycenter with sparse support

Authors:Ye J., Wang J.Z., Wu P., Li J.
Article, 2017
Publication:IEEE Transactions on Signal Processing, 65, 2017 05 01, 2317
Publisher:2017

2017 see 2018
W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

Authors:Li S., Li X.-D.
Article, 2017
Publication:arXiv, 2017 10 12
Publisher:2017

<—–2017———2017 ———1110—

2017 see 2018
Convergence to equilibrium in wasserstein distance for damped euler equations with interaction forces

Authors:Carrillo J.A., Choi Y.-P., Tse O.
Article, 2017
Publication:arXiv, 2017 12 16
Publisher:2017

2017 see 2018
Image labeling based on graphical models using wasserstein messages and geometric assignment

Authors:Huhnerbein R., Savarino F., Schnorr C., Astrom F.
Article, 2017
Publication:arXiv, 2017 10 04
Publisher:2017

Exponential convergence in the Wasserstein metric W1 for one dimensional diffusions

Authors:Cheng L., Ruinan L.I., Wu L.
Article, 2017
Publication:arXiv, 2017 03 01
Publisher:2017

2017 see 2918
Weakly supervised audio source separation via spectrum energy preserved wasserstein learning

Authors:Zhang N., Zhou Y., Yan J.
Article, 2017
Publication:arXiv, 2017 11 11
Publisher:2017

2017 see 2918
Wasserstein and total variation distance between marginals of Lévy processes

Authors:Mariucci E., Reiss M.
Article, 2017
Publication:arXiv, 2017 10 07
Publisher:2017

2017

Fréchet means and procrustes analysis in Wasserstein space

Authors:Zemel Y., Panaretos V.M.
Article, 2017
Publication:arXiv, 2017 01 24
Publisher:2017

Relaxed wasserstein, with applications to GANs and distributionally robust optimization

Authors:Guo X., Lin T., Yang N., Hong J.
Article, 2017
Publication:arXiv, 2017 05 19
Publisher:2017

2017 see 2018
Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

Authors:Schmitz M.A., Starck J.-L., Heitz M., Bonneel N., Ngolez F., Coeurjolly D., Cuturi M., Peyre G.
Article, 2017
Publication:arXiv, 2017 08 06
Publisher:2017

2017 zzz

[CITATION] Upper bounds for the Wasserstein and Kolmogorov distances between random sums and their weak limits via Stein's method

P Porkert - 2017 - repositum.tuwien.at

reposiTUm: Upper bounds for the Wasserstein and Kolmogorov distances between random

sums and their weak limits via Stein's method … Upper bounds for the Wasserstein and …

Read-through: Wasserstein GAN

Feb 22, 2017

<—–2017———2017 ———1120—end 2017 Wasserstein

Includes 3 Vaserstein

start 2018 Wasserstein Vaserstein

асерштейна вассерштейна

Wasserstein is all you need | Sidak Pal Singh

sidakpal.com/publication/wasserstein-all-you-need

This approach can be used for any unsupervised or supervised8problem (on text or other modalities) with a co-occurrence structure, such as any sequence data. The key tools underlying

the framework are Wasserstein distances and Wasserstein barycenters (and, hence the title!).

arXiv version 1 29 Aug 2018 arXiv:1808.09663v1

SP Singh, A Hug, A Dieuleveut, M Jaggi - arXiv preprint arXiv:1808.09663, 2018 - arxiv.org

We propose a unified framework for building unsupervised representations of individual

objects or entities (and their compositions), by associating with each object both a

distributional as well as a point estimate (vector embedding). This is made possible by the …

IS WASSERSTEIN ALL YOU NEED - arxiv.org

Hence, this naturally allows for the use of optimal transport (or Wasserstein metric) in the space containing the contexts, and leads to an interpretation (Figure 1) not available in the above approaches.

version 2 29 Aug 2018

[v3] Thu, 20 Dec 2018 21:18:56 UTC (479 KB)

[R] Wasserstein is all you need : MachineLearning reddit

Title: Wasserstein is all you need Authors: Sidak Pal Singh , Andreas Hug , Aymeric Dieuleveut , Martin Jaggi Abstract: We propose a unified framework for building unsupervised representations of individual objects or entities (and their compositions),

by associating with each object both a distributional as well as a point estimate (vector embedding).

Wasserstein is all you need - openreview.net Anonymous pdf

https://openreview.net/pdf?id=Bkx2jd4Nx7

Wasserstein is all you need Anonymous EMNLP submission Abstract We propose a uniﬁed framework for building unsupervised representations of individual ob-jects or entities (and their compositions), by associating with each object both

a distribu-tional as well as a point estimate (vector em-

On the rate of convergence of empirical measure in $\infty-$Wasserstein distance for unbounded density...

by Liu, Anning; Liu, Jian-Guo; Lu, Yulong 07/2018

We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with...

Journal Article: Full Text Online

On the rate of convergence of empirical measure in $\infty ...

by A Liu - ‎2018

Jul 22, 2018 - We establish a new rate of convergence of the Wasserstein distance between ... to the case that the true distribution has an unbounded density.

One-dimensional data augmentation using a wasserstein generative adversarial network with supervised signal

2018

One-dimensional data augmentation using a wasserstein generative adversarial network with supervised signal

by Lou, Huan; Qi, Zongfeng; Li, Jianxun

2018 Chinese Control And Decision Conference (CCDC), 06/2018

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains; however, there is still some difficulties in training the network,...

Conference Proceeding: Full Text Online

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains;

however, there is still some difficulties in training the network, which are mainly caused by

mode collapse, vanishing gradient of generator and indirect assessment criteria of …

Precise simulation of electromagnetic calorimeter showers using a Wasserstein Generative Adversarial Network

by Erdmann, Martin; Glombitza, Jonas; Quast, Thorben 07/2018

Simulations of particle showers in calorimeters are computationally time-consuming, as they have to reproduce both energy depositions and their considerable...

Journal Article: Full Text Online

Precise simulation of electromagnetic calorimeter showers using a Wasserstein Generative Adversarial Network

M Erdmann, J Glombitza, T Quast - arXiv preprint arXiv:1807.01954, 2018 - arxiv.org

Simulations of particle showers in calorimeters are computationally time-consuming, as they

have to reproduce both energy depositions and their considerable fluctuations. A new

approach to ultra-fast simulations are generative models where all calorimeter energy …

Accelerated First-order Methods on the Wasserstein Space for Bayesian Inference

Accelerated First-order Methods on the Wasserstein Space for Bayesian Inference

by Liu, Chang; Zhuo, Jingwei; Cheng, Pengyu; More... 07/2018

We consider doing Bayesian inference by minimizing the KL divergence on the 2-Wasserstein space $\mathcal{P}_2$. By exploring the Riemannian structure of...

Journal Article: Full Text Online

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu… - arXiv preprint arXiv …, 2018 - arxiv.org

We consider doing Bayesian inference by minimizing the KL divergence on the 2-

Wasserstein space $\mathcal {P} _2 $. By exploring the Riemannian structure of $\mathcal

{P} _2 $, we develop two inference methods by simulating the gradient flow on $\mathcal {P} …

Cited by 1 All 3 versions

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

by Zhang, Min; Ma, Qianli; Wen, Chengfeng; More...

06/2018

Lung nodules are commonly detected in screening for patients with a risk for lung cancer. Though the status of large nodules can be easily diagnosed by fine...

Journal Article: Full Text Online

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

by Şimşekli, Umut; Liutkus, Antoine; Majewski, Szymon; More... 06/2018

By building up on the recent theory that established the connection between implicit generative modeling and optimal transport, in this study, we propose a...

Journal Article: Full Text Online

Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

U Şimşekli, A Liutkus, S Majewski, A Durmus - arXiv preprint arXiv …, 2018 - arxiv.org

By building up on the recent theory that established the connection between implicit

generative modeling and optimal transport, in this study, we propose a novel parameter-free

algorithm for learning the underlying distributions of complicated datasets and sampling …

$ L^{2} $-Wasserstein distances of tracial $ W^{*} $-algebras and their ...

<-—2018——————— 2018 ——10—-

$L^{2}$-Wasserstein distances of tracial $W^{}$-algebras and their disintegration problem

by Hornshaw, David F 06/2018

We introduce $L^{2}$-Wasserstein distances on densities of tracial $W^{*}$-algebras based on a Benamou-Brenier formulation, replacing multiplication by...

Journal Article: Full Text Online

by DF Hornshaw - ‎2018 - ‎Cited by 3 - ‎Related articles

Jun 4, 2018 - Mathematics > Operator Algebras. Title: -Wasserstein distances of tracial -algebras and their disintegration problem. Authors:David F.

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

by Asadi, Kavosh; Cater, Evan; Misra, Dipendra; More... 06/2018

Learning a generative model is a key component of model-based reinforcement learning. Though learning a good model in the tabular setting is a simple task,...

Journal Article: Full Text Online

[PDF] reinforcement-learning.ml

[PDF] Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - 2018 - reinforcement-learning.ml

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. In this context, an important question is the …

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

Computing Kantorovich-Wasserstein Distances on $d$-dimensional histograms using $(d+1)$-partite graphs

by Auricchio, Gennaro; Bassetti, Federico; Gualandi, Stefano; More... 05/2018

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of $d$-dimensional histograms having $n$ bins each. We...

Journal Article: Full Text Online

Computing Kantorovich-Wasserstein Distances on $d$-dimensional ...

by G Auricchio - ‎2018 - ‎Related articles

d-dimensional histograms using (d + 1)-partite graphs ... very large, and hence the computation of Kantorovich-Wasserstein distances implies an important.

Computing Kantorovich-Wasserstein Distances on $ d $-dimensional ...

by G Auricchio - ‎2018 - ‎Related articles

May 18, 2018 - ... Distances on -dimensional histograms using -partite graphs ... to compute the exact Kantorovich-Wasserstein distance between a pair of ...

Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces

Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces

by Lei, Jing 04/2018

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite...

Journal Article: Full Text Online

J Lei - arXiv preprint arXiv:1804.10556, 2018 - arxiv.org

We provide upper bounds of the expected Wasserstein distance between a probability

measure and its empirical version, generalizing recent results for finite dimensional

Euclidean spaces and bounded functional spaces. Such a generalization can cover …

Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration

by Bigot, Jérémie; Cazelles, Elsa; Papadakis, Nicolas 04/2018

We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a...

Journal Article: Full Text Online

Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration

J Bigot, E Cazelles, N Papadakis - arXiv preprint arXiv:1804.08962, 2018 - arxiv.org

We present a framework to simultaneously align and smooth data in the form of multiple

point clouds sampled from unknown densities with support in a d-dimensional Euclidean

space. This work is motivated by applications in bio-informatics where researchers aim to …

2018

Bounds for the Wasserstein mean with applications to the Lie-Trotter mean

by Hwang, Jinmi; Kim, Sejong 04/2018

As the least squares mean for the Riemannian trace metric on the cone of positive definite matrices, the Riemannian mean with its computational and theoretical...

Journal Article: Full Text Online

Bounds for the Wasserstein mean with applications to the Lie-Trotter mean

J Hwang, S Kim - arXiv preprint arXiv:1804.04323, 2018 - arxiv.org

As the least squares mean for the Riemannian trace metric on the cone of positive definite

matrices, the Riemannian mean with its computational and theoretical approaches has been

widely studied. Recently the new metric and the least squares mean on the cone of positive …

On the Computation of Kantorovich-Wasserstein Distances between ...

On the Computation of Kantorovich-Wasserstein Distances between 2D-Histograms by Uncapacitated Minimum Cost...

by Bassetti, Federico; Gualandi, Stefano; Veneroni, Marco 04/2018

In this work, we present a method to compute the Kantorovich distance, that is, the Wasserstein distance of order one, between a pair of two-dimensional...

Journal Article: Full Text Online

by F Bassetti - ‎2018 - ‎Cited by 2 - ‎Related articles

Apr 2, 2018 - ... Distances between 2D-Histograms by Uncapacitated Minimum Cost ... to compute the Kantorovich distance, that is, the Wasserstein distance ...

On the Computation of Kantorovich-Wasserstein Distances between ...

Apr 4, 2018 - tion problem by an uncapacitated min cost ﬂow problem on a reduced ﬂow .... Distances between 2D-Histograms by Minimum Cost Flows 3.

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein...

by Han, Yanjun; Jiao, Jiantao; Weissman, Tsach 02/2018

We present \emph{Local Moment Matching (LMM)}, a unified methodology for symmetric functional estimation and distribution estimation under Wasserstein...

Journal Article: Full Text Online

About 17,300 results (0.54 seconds)

Local moment matching: A unified methodology for symmetric ...

by Y Han - ‎2018 - ‎Cited by 2 - ‎Related articles

Feb 23, 2018 - Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance. We present \emph{Local Moment Matching (LMM)}, a unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance.

Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula

by Fang, Xiao; Shao, Qi-Man; Xu, Lihu 01/2018

Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal...

Journal Article: Full Text Online

Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula

X Fang, QM Shao, L Xu - Probability Theory and Related Fields, 2018 - Springer

Stein's method has been widely used for probability approximations. However, in the multi-

dimensional setting, most of the results are for multivariate normal approximation or for test

functions with bounded second-or higher-order derivatives. For a class of multivariate …

Characterization of probability distribution convergence in ...

Characterization of probability distribution convergence in Wasserstein distance by $L^{p}$-quantization error function

by Liu, Yating; Pagès, Gilles 01/2018

We establish the condition for probability measure characterization by $L^{p}$-quantization error function in $\mathbb{R}^{d}$. There are two types of...

Journal Article: Full Text Online

by Y Liu - ‎2018 - ‎Related articles

Jan 18, 2018 - Mathematics > Probability. Title: Characterization of probability distribution convergence in Wasserstein distance by -quantization error function.

(PDF) Characterization of probability distribution convergence in ...

Jan 18, 2018 - Characterization of probability distribution convergence in Wasserstein distance by $L^{p}$-quantization error function. Article (PDF Available) ...

Characterization of probability distribution convergence in Wasserstein distance by Lp-quantization error function
Authors:Liu Y., Pages G.
Article, 2018
Publication:arXiv, 2018 01 18
Publisher:2018
<-—2018——————— 2018 ——20—-

Unsupervised and semi-supervised learning with Categorical Generative Adversarial Networks assisted by Wasserstein...

by Yi, Xin; Walia, Ekta; Babyn, Paul 04/2018

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis involves initial screening with subsequent biopsy and...

Journal Article: Full Text Online

Unsupervised and semi-supervised learning with Categorical Generative Adversarial Networks assisted by Wasserstein distance for dermoscopy image Classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

necessary. Computer aided diagnosis offers an objective score that is independent of …

Wasserstein GAN and Waveform Loss-based Acoustic Model Training for Multi-speaker Text-to-Speech Synthesis...

by Zhao, Yi; Takaki, Shinji; Luong, Hieu-Thi; More... 07/2018

Recent neural networks such as WaveNet and sampleRNN that learn directly from speech waveform samples have achieved very high-quality synthetic speech in terms...

Journal Article: Full Text Online

Wasserstein GAN and Waveform Loss-based Acoustic Model Training for Multi-speaker Text-to-Speech Synthesis Systems Using a WaveNet Vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

Researchers at Tsinghua University Have Reported New Data on Computational Physics

(The quadratic Wasserstein metric for earthquake location)

Journal of Technology & Science, 10/2018

Newsletter: Full Text Online

The quadratic Wasserstein metric for earthquake location ...

by J Chen - ‎2018 - ‎Cited by 12 - ‎Related articles

Nov 15, 2018 - (2016) [8], the Wasserstein metric was successfully introduced to the full waveform inversion. We apply this method to the earthquake location problem. For this problem, the seismic stations are far from each other. Thus, the trace by trace comparison (Yang et al.

Investigators at University of Liverpool Describe Findings in Power Systems

.(Distributionally Robust Chance-Constrained Approximate AC-OPF With Wasserstein Metric)

From:Energy Weekly NewsEnergy Weekly News, 09/2018

Newsletter: Full Text Online

From:Energy Weekly News

Weak convergence of empirical Wasserstein type distances

P Berthet, J Fort - 2018 - hal.archives-ouvertes.fr

We estimate the Wasserstein type distance between two continuous distributions F and G on

R such that the set {F= G} is a finite union of intervals, possibly empty or R. The positive cost

function ρ is not necessarily symmetric and the sample may come from any joint distribution …

Defrmable convolution kernel method based on WGAN (Wasserstein-Generative

2018

Deformable convolution kernel method based on WGAN (Wasserstein-Generative Adversarial Network) model

by XU JING; LI LIPING; LI LIJUN; More... 04/2018

The invention discloses a deformable convolution kernel method based on a WGAN (Wasserstein-Generative Adversarial Network) model, and belongs to the field of...

Patent:

CN Application CN107886162A 周智恒华南理工大学

Priority 2017-11-14 • Filing 2017-11-14 • Publication 2018-04-06

The invention discloses a deformable convolution kernel method based on a WGAN (Wasserstein-Generative Adversarial Network) model, and belongs to the field of the deep learning neural network. The method comprises the following steps that: S1: constructing an original genera

DF] upmc.fr

[PDF] Barycentres de Wasserstein pour les abstractions topologiques

J Tierny - edb.upmc.fr

Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui

permet en pratique d'introduire une mesure de bruit sur les structures topologiques, comme

les singularités (sphères de couleur) dans cet exemple de carte d'élévation. Cette mesure …

Distance de Wasserstein d'une imagea une mesure quelconque

F de GOURNAY, L LEBRAT, J KHAN, P WEISS - smai.emath.fr

Mots-clés : Transport optimal, distance de Wasserstein, cellules de Laguerre Le calcul du transport

optimal entre deux mesures de probabilités i et ν a connu un spectaculaire développement durant

les derni`eres années. Il existe principalement 3 méthodes, les méthodes semi- discretes [1 …

[PDF] upatras.gr

Συσταδοποίηση κειμένων με χρήση της μετρικής Wasserstein και τεχνικές βέλτιστης μεταφοράς

Δ Καλογερόπουλος - 2018 - nemertes.lis.upatras.gr

Για τη διερεύνηση ομοιότητας ανάμεσα σε κείμενα υπάρχουν πολλές τεχνικές που

χρησιμοποιούν τις συχνότητες εμφάνισης λέξεων και άλλες στατιστικές πληροφορίες που

παράγονται από τα μητρώα όρων-κειμένων. Τι γίνεται όμως όταν οι λέξεις εκλαμβάνονται ως …

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[Greek Text formatting using the Wasserstein metric and optimal transfer techniques

]

Wasserstein Generative Adversarial Networks

[edit]Martin Arjovsky, Soumith Chintala, Léon Bottou ;

Proceedings of the 34th International Conference on Machine Learning, PMLR 70:214-223, 2017.

Abstract We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability

of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore,

we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to different distances between distributions.

Related Material Download PDF Supplementary PDF

Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein GAN. arXiv preprint arXiv:1701.07875 (2017)

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Unsupervised Alignment of Embeddings with Wasserstein Procrustes

by Grave, Edouard; Joulin, Armand; Berthet, Quentin 05/2018

We consider the task of aligning two sets of points in high dimension, which has many applications in natural language processing and computer vision. As an...

Journal Article: Full Text Online

Unsupervised Alignment of Embeddings with Wasserstein Procrustes

E Grave, A Joulin, Q Berthet - arXiv preprint arXiv:1805.11222, 2018 - arxiv.org

We consider the task of aligning two sets of points in high dimension, which has many

applications in natural language processing and computer vision. As an example, it was

recently shown that it is possible to infer a bilingual lexicon, without supervised data, by …

Unsupervised Alignment of Embeddings with Wasserstein Procrustes

Robust Hypothesis Testing Using Wasserstein Uncertainty Sets

by Gao, Rui; Xie, Liyan; Xie, Yao; More... 05/2018

We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty...

JJournal Article: Full Text Online

Robust Hypothesis Testing Using Wasserstein Uncertainty Sets

R Gao, L Xie, Y Xie, H Xu - arXiv preprint arXiv:1805.10611, 2018 - arxiv.org

We develop a novel computationally efficient and general framework for robust hypothesis

testing. The new framework features a new way to construct uncertainty sets under the null

and the alternative distributions, which are sets centered around the empirical distribution …

Natural gradient in Wasserstein statistical manifold

by Chen, Yifan; Li, Wuchen 05/2018

We study the Wasserstein natural gradient in parametric statistical models with continuous sample space. Our approach is to pull back the $L^2$-Wasserstein...

Journal Article: Full Text Online

Natural gradient in Wasserstein statistical manifold

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - arxiv.org

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample space. Our approach is to pull back the $ L^ 2$-Wasserstein metric tensor in

probability density space to parameter space, under which the parameter space become a …

[HTML] nature.com

Wasserstein regularization for sparse multi-task regression

by Janati, Hicham; Cuturi, Marco; Gramfort, Alexandre05/2018

Two important elements have driven recent innovation in the field of regression: sparsity-inducing regularization, to cope with high-dimensional problems;...

Journal Arle: Full Text Online

Wasserstein regularization for sparse multi-task regression

H Janati, M Cuturi, A Gramfort - arXiv preprint arXiv:1805.07833, 2018 - arxiv.org

Two important elements have driven recent innovation in the field of regression: sparsity-

inducing regularization, to cope with high-dimensional problems; multi-task learning through

joint parameter estimation, to augment the number of training samples. Both approaches …

Wasserstein regularization for sparse multi-task regression

Semantic Image Inpainting Through Improved Wasserstein Generative Adversarial Networks

by Vitoria, Patricia; Sintes, Joan; Ballester, Coloma12/2018

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image. In this work we tackle this problem not only by using the...

Journal Article: Full Text Online

Semantic Image Inpainting Through Improved Wasserstein Generative Adversarial Networks

P Vitoria, J Sintes, C Ballester - arXiv preprint arXiv:1812.01071, 2018 - arxiv.org

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image.

In this work we tackle this problem not only by using the available visual data but also by

incorporating image semantics through the use of generative models. Our contribution is …

2018

A Wasserstein GAN model with the total variational regularization

by Zhang, Lijun; Zhang, Yujin; Gao, Yongbin 12/2018

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train. The recently proposed Wasserstein GAN (WGAN) creates principled...

Journal Article: Full Text Online

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer

Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer

by Berwald, Jesse J; Gottlieb, Joel M; Munch, Elizabeth 09/2018

Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What...

Journal Article: Full Text Online

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to

provide a concise description of a filtered topological space. What makes them even more

useful in practice is that they come with a notion of a metric, the Wasserstein distance …

as the … In this paper, we show that the Wasserstein distance for persistence diagrams can be …

Gaussian Word Embedding with a Wasserstein Distance Loss

by Sun, Chi; Yan, Hang; Qiu, Xipeng; More... 08/2018

Compared with word embedding based on point representation, distribution-based word embedding shows more flexibility in expressing uncertainty and therefore...

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Gaussian Word Embedding with a Wasserstein Distance Loss

C Sun, H Yan, X Qiu, X Huang, Z Chen - arXiv preprint arXiv:1808.07016, 2018 - arxiv.org

Comparing with word embedding that based on the point representation, distribution-based

word embedding shows more flexibility on expressing uncertainty and therefore, embeds a

richer semantic information when representing words. While the Wasserstein distance …

MR3805843 Hühnerbein, Ruben; Savarino, Fabrizio; Åström, Freddie; Schnörr, Christoph Image labeling based on graphical models using Wasserstein messages and geometric assignment. SIAM J. Imaging Sci. 11 (2018), no. 2, 1317–1362. (Reviewer: Marian Mureşan) 94A08 (62H35 62M40 65K10 68U10)

Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment

by Hühnerbein, Ruben; Savarino, Fabrizio; Åström, Freddie; More...

SIAM Journal on Imaging Sciences, 01/2018, Volume 11, Issue 2

We introduce a novel approach to Maximum A Posteriori inference based on discrete graphical models. By utilizing local Wasserstein distances for coupling...

Newspaper Article: Full Text Online

Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete

graphical models. By utilizing local Wasserstein distances for coupling assignment

measures across edges of the underlying graph, a given discrete objective function is …

Расстояние Вассерштейна: WGAN и 2 кучи земли | OTUS

Lifted Wasserstein matcher for fast and robust topology tracking

Jun 20, 2018 - Теги: python, генеративные состязательные сети, машинное обучение, machine learning, нейронные сети, gan, deep learning,

[Russian Wasserstein distance: WGAN and and 2 piles of earth]

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Lifted Wasserstein Matcher for Fast and Robust Topology Tracking

by Soler, Maxime; Plainchault, Mélanie; Conche, Bruno; More... 08/2018

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal...

Journal Article: Full Text Online

M Soler, M Plainchault, B Conche, J Tierny - arXiv preprint arXiv …, 2018 - arxiv.org

This paper presents a robust and efficient method for tracking topological features in time-

varying scalar data. Structures are tracked based on the optimal matching between

persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on …

The Gromov-Wasserstein distance between networks and stable network invariants

by Chowdhury, Samir; Mémoli, Facundo 08/2018

We define a metric---the Network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers. In addition to...

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The Gromov-Wasserstein distance between networks and stable ...

by S Chowdhury - ‎2018 - ‎Cited by 1

Aug 13, 2018 - The Gromov-Wasserstein distance between networks and stable network invariants. We define a metric---the Network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers.

pdf The Gromov-Wasserstein distance between networks and stable ...

Wasserstein Generative Recurrent Adversarial Networks for Image Generating

by Zhang, Chunping; Feng, Yong; Qiang, Baohua; More...

2018 24th International Conference on Pattern Recognition (ICPR), 08/2018

Most generative models are generating images at a time, but in fact, painting is usually done iteratively and repeatedly. Generative Adversarial Networks (GAN)...

Conference Proceeding: Full Text Online

Wasserstein Generative Recurrent Adversarial Networks for Image Generating

C Zhang, Y Feng, B Qiang… - 2018 24th International …, 2018 - ieeexplore.ieee.org

Most generative models are generating images at a time, but in fact, painting is usually done

iteratively and repeatedly. Generative Adversarial Networks (GAN) are well known for

generating images, however, it is hard to train stably. To tackle this problem, we propose a …

Wasserstein metric-driven Bayesian inversion with applications to signal processing

by Motamed, Mohammad; Appelo, Daniel 07/2018

We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstien metric. Compared to conventional Bayesian...

Journal Article: Full Text Online published 2019

Wasserstein metric-driven Bayesian inversion with applications to signal processing

Wasserstein metric-driven Bayesian inversion with applications to signal processing

[Submitted on 21 Jul 2018 (v1), last revised 26 Dec 2018 (this version, v3)] ... We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstien metric. ... Cite as: arXiv:180

On Distributionally Robust Chance Constrained Program with Wasserstein Distance

by Xie, Weijun06/2018

This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should satisfy...

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Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters

by Dvurechensky, Pavel; Dvinskikh, Darina; Gasnikov, Alexander; More... 06/2018

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous...

Journal Article: Full Text Online

On Distributionally Robust Chance Constrained Program with Wasserstein Distance

W Xie - arXiv preprint arXiv:1806.07418, 2018 - arxiv.org

This paper studies a distributionally robust chance constrained program (DRCCP) with

Wasserstein ambiguity set, where the uncertain constraints should satisfy with a probability

at least a given threshold for all the probability distributions of the uncertain parameters …

2018

DialogWAE: Multimodal Response Generation with Conditional Wasserstein Auto-Encoder

by Gu, Xiaodong; Cho, Kyunghyun; Ha, Jungwoo; More... 05/2018

Variational autoencoders (VAEs) have shown a promise in data-driven conversation modeling. However, most VAE conversation models match the approximate...

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DialogWAE: Multimodal Response Generation with Conditional Wasserstein Auto-Encoder

X Gu, K Cho, J Ha, S Kim - arXiv preprint arXiv:1805.12352, 2018 - arxiv.org

Variational autoencoders (VAEs) have shown a promise in data-driven conversation

modeling. However, most VAE conversation models match the approximate posterior

distribution over the latent variables to a simple prior such as standard normal distribution …

[PDF] cvut.cz

Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance

by Luise, Giulia; Rudi, Alessandro; Pontil, Massimiliano; More... 05/2018

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most...

Journal Article: Full Text Online x

Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance

G Luise, A Rudi, M Pontil, C Ciliberto - arXiv preprint arXiv:1805.11897, 2018 - arxiv.org

Applications of optimal transport have recently gained remarkable attention thanks to the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version …

Learning to Optimize via Wasserstein Deep Inverse Optimal Control

by Wang, Yichen; Song, Le; Zha, Hongyuan 05/2018

We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In...

Journal Article: Full Text Online

Learning to Optimize via Wasserstein Deep Inverse Optimal Control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's

true cost function from the observed temporal behavior. In contrast to traditional

phenomenological works that aim to learn a generative model to fit the behavioral data, we …

Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions

by Muzellec, Boris; Cuturi, Marco 05/2018

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that...

Journal Article: Full Text Online

Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions

B Muzellec, M Cuturi - arXiv preprint arXiv:1805.07594, 2018 - arxiv.org

Embedding complex objects as vectors in low dimensional spaces is a longstanding

problem in machine learning. We propose in this work an extension of that approach, which

consists in mbedding objects as elliptical probability distributions, namely distributions …

Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions

DF] arxiv.org

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

Y Chen, HG Müller - arXiv preprint arXiv:1809.03498, 2018 - arxiv.org

Many studies have been conducted on flows of probability measures, often in terms of

gradient flows. We introduce here a novel approach for the modeling of the instantaneous

evolution of empirically observed distribution flows over time with a data-analytic focus that …

GAN — Wasserstein GAN & WGAN-GP. Training GAN is hard ...

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medium.com › gan-wasserstein-gan-wgan-gp-6a1a2aa1...

Jun 13, 2018 - This article is part of the GAN series which looks into the Wasserstein GAN ( WGAN) and the WGAN-Gradient penalty in details. The equations for ...

[CITATION] GAN–Wasserstein GAN & WGAN-GP

Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets

by Hota, Ashish R; Cherukuri, Ashish; Lygeros, John 05/2018

We present a data-driven approach for distributionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker...

Journal Article: Full Text Online

Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets

AR Hota, A Cherukuri, J Lygeros - arXiv preprint arXiv:1805.06729, 2018 - arxiv.org

In this note, we present a data-driven approach for ambiguous or distributionally robust

chance constrained optimization problems. We consider the case where the decision-maker

has access to a finite number of samples or realizations of the uncertainty. The chance …

基于 WGAN 的图像修复应用

哈文全 - 电子技术与软件工程, 2018 - dzru.chinajournal.net.cn

近年来深度学习在图像处理, 音频处理以及NLP 领域取得了令人瞩目的成绩,

特别在图像处理领域, 深度学习已然成为主流方法. 本文介绍深度学习方法在图像修复领域的

应用, 通过使用WGAN 来生成破损图像中缺失的部分. 通过从可用的大批量的数据集中生成对应 …

WGAN-based image restoration application

Ha Wenquan - Electronic Technology and Software Engineering, 2018 -

Chinese

WGAN-based image restoration application

Ha Wenquan - Electronic Technology and Software Engineering, 2018 - dzru.chinajournal.net.cn

In recent years, deep learning has achieved remarkable results in image processing, audio processing, and NLP.

Especially in the field of image processing, deep learning has become the mainstream method. This paper introduces the deep learning method in the field of image restoration.

Application, by using WGAN to generate missing parts of the broken image. By generating a corresponding

A Fast Proximal Point Method for Computing Wasserstein Distance

by Xie, Yujia; Wang, Xiangfeng; Wang, Ruijia; More... 02/2018

Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to...

Journal Article: Full Text Online

A Fast Proximal Point Method for Computing Wasserstein Distance

by Y Xie - ‎2018 - ‎Cited by 3 - ‎Related articles

Feb 12, 2018 - A Fast Proximal Point Method for Computing Wasserstein Distance. Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing.

Data-driven distributed optimization using Wasserstein ambiguity sets

by Cherukuri, Ashish; Cortes, Jorge

2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 10/2017

This paper considers a general class of stochastic optimization problem for multiagent systems. We assume that the probability distribution of the uncertain...

Conference Proceeding: Full Text Online

Data-driven distributed optimization using Wasserstein ambiguity sets ...

https://ieeexplore.ieee.org/document/8262716/

Data-driven distributed optimization using Wasserstein ambiguity sets. Abstract: This paper considers a general class of stochastic optimization problem for ...

Date Added to IEEE Xplore: 18 January 2018

2018

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

by Cazelles, Elsa 2018

Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de probabilité sur R^d. L'objectif est alors de fournir une meilleure...

Dissertation/Thesis: Full Text Online

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

by Zhou, D. T; Chen, J; Wu, H; More... 12/2018

In our previous work [Chen el al., J. Comput. Phys., 373(2018)], the quadratic Wasserstein metric is successfully applied to the earthquake location problem....

Journal Article: Full Text Online

DT Zhou, J Chen, H Wu, DH Yang, LY Qiu - arXiv preprint arXiv …, 2018 - arxiv.org

In our previous work [Chen el al., J. Comput. Phys., 373 (2018)], the quadratic Wasserstein

metric is successfully applied to the earthquake location problem. The actual earthquake

hypocenter can be accurately recovered starting from initial values very far from the true …

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

by Perchet, Vianney; Quincampoix, Marc 11/2018

Studying continuous time counterpart of some discrete time dynamics is now a standard and fruitful technique, as some properties hold in both setups. In game...

Journal Article: Full Text Online

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and fruitful technique, as some properties hold in both setups. In game theory, this is usually done by considering differential games on Euclidean spaces. This allows to infer properties on the convergence of values of a repeated game, to deal with the various concepts of approachability, etc. In this paper, we introduce a specific but quite abstract differential game defined on the Wasserstein space of probability distributions and we prove the existence of …

Wasserstein Variational Gradient Descent: From Semi-Discrete Optimal Transport to Ensemble Variational Inference

by Ambrogioni, Luca; Guclu, Umut; Gucluturk, Yagmur; More... 11/2018

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce...

Journal Article: Full Text Online

Wasserstein Variational Gradient Descent: From Semi-Discrete Optimal Transport to Ensemble Variational Inference

L Ambrogioni, U Guclu, Y Gucluturk… - arXiv preprint arXiv …, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

distributions with a set of particles. In this paper we introduce a new particle-based

variational inference method based on the theory of semi-discrete optimal transport. Instead …

Wasserstein and Kolmogorov Error Bounds for Variance-Gamma Approximation via Stein’s Method I

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference
<——2018——— 2018 ————-60—

Gaunt, Robert E

Journal of Theoretical Probability

2018 FullText OnlineJournal Article

Wasserstein and Kolmogorov Error Bounds for Variance-Gamma ç via Stein’s Method I

by Gaunt, Robert E

Journal of Theoretical Probability, 11/2018

Newspaper Article: Full Text Online

[v2] Thu, 18 Oct 2018 09:54:24 UTC (34 KB) rXiv pdf

Wasserstein and Kolmogorov Error Bounds for Variance ...

Nov 1, 2018 - We apply this theory to obtain Wasserstein or Kolmogorov error bounds for SVG approximation in four settings: comparison of VG and SVG ...

Zbl 07169692

MR4064309 Prelim Gaunt, Robert E.; Wasserstein and Kolmogorov Error Bounds for Variance-Gamma Approximation via Stein's Method I. J. Theoret. Probab. 33 (2020), no. 1, 465–505. 60F05 (62E17)

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

by Bigot, Jérémie; Klein, Thierry

ESAIM: Probability and Statistics, 2018, Volume 22

Journal Article: Full Text Online

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org

This paper is concerned by the study of barycenters for random probability measures in the

Wasserstein space. Using a duality argument, we give a precise characterization of the

population barycenter for various parametric classes of random probability measures with …

Bathymetric data processing based on denoising autoencoder Wasserstein generative adversarial network

Bathymetric data processing based on denoising autoencoder Wasserstein generative adversarial network

by Zhang, Ruichen; Chen, Yongbing; Bian, Shaofeng; More... 08/2018

In view of the complexity and variability of bathymetric data, the paper introduces a new algorithm named DAE-WGAN to construct sea bottom trend surface. This...

Conference Proceeding: Full Text Online

R Zhang, Y Chen, S Bian, D Gao - Global Intelligence Industry …, 2018 - spiedigitallibrary.org

In view of the complexity and variability of bathymetric data, the paper introduces a new

algorithm named DAE-WGAN to construct sea bottom trend surface. This new model is an

alternative to traditional GAN training method, combined with the advantages of Denoising …

Application of Auxiliary Classifier Wasserstein Generative Adversarial Networks in Wireless Signal Classification of...

by Zhao, Caidan; Chen, Caiyun; He, Zeping; More...

Applied Sciences, 12/2018, Volume 8, Issue 12

Journal Article: Full Text Online

Application of Auxiliary Classifier Wasserstein Generative Adversarial Networks in Wireless Signal Classification of Illegal Unmanned Aerial Vehicles

C Zhao, C Chen, Z He, Z Wu - Applied Sciences, 2018 - mdpi.com

Recently, many studies have reported on image synthesis based on Generative Adversarial

Networks (GAN). However, the use of GAN does not provide much attention on the signal

classification problem. In the context of using wireless signals to classify illegal Unmanned …

MR3830834 Pending Bigot, Jérémie; Gouet, Raúl; Klein, Thierry; López, Alfredo Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line. Electron. J. Stat. 12 (2018), no. 2, 2253–2289. 62G05 (60G57 62G07 62G20)

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

by Bigot, Jérémie; Gouet, Raúl; Klein, Thierry; More...

Electronic Journal of Statistics, 2018, Volume 12, Issue 2

Journal Article: Full Text Online

Upper and lower risk bounds for estimating the Wasserstein ...

by J Bigot - ‎2018

. Jérémie Bigot, Raúl Gouet, Thierry Klein, and ...

MR3769700 Schmitz, Morgan A.; Heitz, Matthieu; Bonneel, Nicolas; Ngolè, Fred; Coeurjolly, David; Cuturi, Marco; Peyré, Gabriel; Starck, Jean-Luc Wasserstein dictionary learning: optimal transport-based unsupervised nonlinear dictionary learning. SIAM J. Imaging Sci. 11 (2018), no. 1, 643–678. 94A08 (49M99 90C08)

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

by Schmitz, Morgan A; Heitz, Matthieu; Bonneel, Nicolas; More...

SIAM Journal on Imaging Sciences, 2018

This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory,...

Journal Article: Full Text Online

[PDF] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

Abstract. This article introduces a new non-linear dictionary learning method for histograms

in the probability simplex. The method leverages optimal transport theory, in the sense that

our aim is to reconstruct histograms using so called displacement interpolations (aka

HashGAN: Deep Learning to Hash with Pair Conditional Wasserstein GAN

2018

Image inpainting using Wasserstein Generative Adversarial Network

by Hua, Peng; Liu, Ming; Liu, Xiaohua; More... 09/2018

Recent advances in convolution neural networks have shown promising results for the challenging task of filling large missing regions in an image with...

Conference Proceeding: Full Text Online

Image inpainting using Wasserstein Generative Adversarial Network

by P Hua - ‎2018

Sep 7, 2018 - More recently, rapid progress in deep convolutional neural networks (CNN) and generative adversarial networks (GAN) [9] inspired recent works to formulate inpainting as a conditional image generation problem where high-level recognition and low-level pixel synthesis are formulated into a convolutional encoder-decoder ...

On the Bures–Wasserstein distance between positive definite matrices

by Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo

Expositiones Mathematicae, 01/2018

Journal Article: Full Text Online

On the Bures–Wasserstein distance between positive definite matrices

R Bhatia, T Jain, Y Lim - Expositiones Mathematicae, 2018 - Elsevier

The metric d (A, B)= tr A+ tr B− 2 tr (A 1∕ 2 BA 1∕ 2) 1∕ 2 1∕ 2 on the manifold of n× n

positive definite matrices arises in various optimisation problems, in quantum information

and in the theory of optimal transport. It is also related to Riemannian geometry. In the first …

Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

by Ishiwata, Ryosuke; Kinukawa, Ryota; Sugiyama, Yuki

Scientific reports, 04/2018, Volume 8, Issue 1

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with asymmetric interactions, thus being suitable to reproduce behaviours...

Journal Article: Full Text Online

Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

by Ryosuke Ishiwata; Ryota Kinukawa; Yuki Sugiyama

Scientific Reports (Nature Publisher Group), 04/2018, Volume 8

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with asymmetric interactions, thus being suitable to reproduce behaviours...

HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with

asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian

dynamics and the collective motion of living organisms. In this study, we found that particles

in the 2d-OV model form optimal patterns in a maze-like corridor. Then, we estimated the

stability of such patterns using the Wasserstein metric. Furthermore, we mapped these

patterns into the Wasserstein metric space and represented them as points in a plane. As a …

José A. Carrillo, Young-Pil Choi, Oliver Tse

Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces

by Carrillo, José A; Choi, Young-Pil; Tse, Oliver

Communications in Mathematical Physics, 10/2018

Journal Article: Full Text Online

arXiv:1712.05923 [pdf, ps, other]

Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

Subjects: Analysis of

Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

by Liu, Yifan; Qin, Zengchang; Wan, Tao; More...

Neurocomputing, 10/2018, Volume 311

Journal Article: Full Text Online

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

machine learning and computer vision. Such an image can be generated at pixel level by

learning from a large collection of images. Learning to generate colorful cartoon images …

Cited by 4 Related articles
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Non-local Texture Optimization with Wasserstein Regularization under Convolutional Neural Network

by Li, Jie; Xiang, Yong; Hou, Jingyu; More...

IEEE Transactions on Multimedia, 11/2018

Example-based texture synthesis aims to generate a new texture from an exemplar texture and has long been drawing attention in the fields of computer graphics,...

Journal Article: Full Text Online

Non-local Texture Optimization with Wasserstein Regularization under Convolutional Neural Network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

Conic Programming Reformulations of Two-Stage Distributionally ...

2018

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein...

by Grani A Hanasusanto; Daniel Kuhn

Operations Research, 06/2018, Volume 66, Issue 3

Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the...

Journal Article: Full Text Online

by GA Hanasusanto - ‎2018 - ‎Cited by 24 - ‎Related articles

May 25, 2018 - Conic Programming Reformulations of Two-Stage Distributionally. Robust Linear Programs over Wasserstein Balls. Grani A. Hanasusanto,a ...

Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

2018

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

… we continue the study of the quadratic Wasserstein metric with more focus on its applications to FWI … Finally, after introducing the adjoint source formulas, we show the application of FWI using the W 2 … the synthetic data f and observed data g . There are two ways to apply this idea …

Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning

by Schmitz, Morgan A; Heitz, Matthieu; Bonneel, Nicolas; More...

SIAM Journal on Imaging Sciences, 01/2018, Volume 11, Issue 1

This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory,...

Journal Article: Full Text Online

Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein …

Inequalities for the Wasserstein mean of positive definite matrices

by Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo

Linear Algebra and its Applications, 03/2018

Journal Article: Full Text Online

Inequalities for the Wasserstein mean of positive definite matrices

by R Bhatia - ‎2018 - ‎Cited by 1 - ‎Related articles

Mar 9, 2018 - Inequalities for the Wasserstein mean of positive definite matrices. We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

Inequalities for the Wasserstein mean of positive definite matrices ...

Mar 13, 2018 - We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

Jun 5, 2018 - PDF | We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), ...

2018

MR3771309 Zhao, Chaoyue; Guan, Yongpei Data-driven risk-averse stochastic optimization with Wasserstein metric. Oper. Res. Lett. 46 (2018), no. 2, 262–267. (Reviewer: Meng Wu) 90C15 (60B10)

Review PDF Clipboard Journal Article 1 Citation

Data-driven risk-averse stochastic optimization with Wasserstein metric

by Zhao, Chaoyue; Guan, Yongpei

Operations Research Letters, 03/2018, Volume 46, Issue 2

Journal Article: Full Text Online

Data-driven risk-averse stochastic optimization with Wasserstein metric

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

Abstract In this paper, we study a data-driven risk-averse stochastic optimization approach

with Wasserstein Metric for the general distribution case. By using the Wasserstein Metric,

we can successfully reformulate the risk-averse two-stage stochastic optimization problem

[PDF] nonlin-processes-geophys.net

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

by Vissio, Gabriele; Lucarini, Valerio

Nonlinear Processes in Geophysics, 06/2018, Volume 25, Issue 2

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modeling of geophysical fluids. We consider...

Journal Article: Full Text Online

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in …, 2018 - nonlin-processes-geophys.net

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modeling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

Scene Classification by Coupling Convolutional Neural Networks With ...

Scene Classification by Coupling Convolutional Neural Networks With Wasserstein Distance

by Liu, Yishu; Liu, Yingbin; Ding, Liwang

IEEE Geoscience and Remote Sensing Letters, 2018

Journal Article: Full Text Online

Dec 20, 2018 - Request PDF on ResearchGate | Scene Classification by Coupling Convolutional Neural Networks With Wasserstein Distance | The traditional ...

MR3779696 Rudolf, Daniel; Schweizer, Nikolaus Perturbation theory for Markov chains via Wasserstein distance. Bernoulli 24 (2018), no. 4A, 2610–2639. 60J05 (60B10 60J22 60J35)

Perturbation theory for Markov chains via Wasserstein distance

by Rudolf, Daniel; Schweizer, Nikolaus

Bernoulli, 11/2018, Volume 24, Issue 4A

Journal Article: Full Text Online

2015arXiv150304123R

Rudolf, Daniel; Schweizer, Nikolaus

Perturbation theory for Markov chains via Wasserstein distance

Abstract: Perturbation theory for Markov chains addresses the question how small

differences in the transitions of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step ...

Unsupervised Feature Extraction in Hyperspectral Images Based on Wasserstein Generative Adversarial Network

by Zhang, Mingyang; Gong, Maoguo; Mao, Yishun; More...

IEEE Transactions on Geoscience and Remote Sensing, 11/2018

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing. Recently, due to the powerful ability of deep learning (DL) to...

Journal Article: Full Text Online

Unsupervised Feature Extraction in Hyperspectral Images Based on Wasserstein Generative Adversarial Network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

<——2018———— 2018 —————120—

Wasserstein distance for generalized persistence modules and abelian categories

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018 - arxiv.org

In persistence theory and practice, measuring distances between modules is central. The

Wasserstein distances are the standard family of L^ p distances for persistence modules.

They are defined in a combinatorial way for discrete invariants called persistence diagrams …

[HTML] Improved Wasserstein conditional generative adversarial network speech enhancement

Improved Wasserstein conditional generative adversarial network speech enhancement

by Qin, Shan; Jiang, Ting

EURASIP Journal on Wireless Communications and Networking, 12/2018, Volume 2018, Issue 1

The speech enhancement based on the generative adversarial network has achieved excellent results with large quantities of data, but performance in the...

Journal Article: Full Text Online

S Qin, T Jiang - EURASIP Journal on Wireless Communications and …, 2018 - Springer

The speech enhancement based on the generative adversarial network has achieved

excellent results with large quantities of data, but performance in the low-data regime and

tasks like unseen data learning still lag behind. In this work, we model Wasserstein …

Improved Wasserstein conditional generative adversarial network speech enhancement

Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities

by Courtade, Thomas A; Fathi, Max; Pananjady, Ashwin

IEEE Transactions on Information Theory, 2018

We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly...

Journal Article: Full Text Online

Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities arXiv

by TA Courtade - ‎2016 - ‎Cited by 5 - ‎Related articles

Oct 25, 2016 - Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities. ... As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein distance when densities are uniformly log-concave on sets of measure arbitrarily close to one.

MR3854142 Pending Chen, Jing; Chen, Yifan; Wu, Hao; Yang, Dinghui The quadratic Wasserstein metric for earthquake location. J. Comput. Phys. 373 (2018), 188–209. 86A15

The quadratic Wasserstein metric for earthquake location

by Chen, Jing; Chen, Yifan; Wu, Hao; More...

Journal of Computational Physics, 11/2018, Volume 373

In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric was successfully introduced to the full waveform inversion. We apply this method to...

Journal Article: Full Text Online

The quadratic Wasserstein metric for earthquake location

J Chen, Y Chen, H Wu, D Yang - Journal of Computational Physics, 2018 - Elsevier

Abstract In Engquist et al.(2016)[8], the Wasserstein metric was successfully introduced to

the full waveform inversion. We apply this method to the earthquake location problem. For

this problem, the seismic stations are far from each other. Thus, the trace by trace …

A Canonical Barycenter via Wasserstein Regularization

by Kim, Young-Heon; Pass, Brendan

SIAM Journal on Mathematical Analysis, 01/2018, Volume 50, Issue 2

Journal Article:

Full Text Online Preview

A canonical barycenter via Wasserstein regularization

YH Kim, B Pass - SIAM Journal on Mathematical Analysis, 2018 - SIAM

We introduce a weak notion of barycenter of a probability measure μ on a metric measure

space (X,d,\bfm), with the metric d and reference measure \bfm. Under the assumption that

all optimal transport plans transporting \bfm to any probability measure ν on X are induced …

Saliency detection based on aggregated Wasserstein distance

by Sun, Fengdong; Li, Wenhui

Journal of Electronic Imaging, 07/2018, Volume 27, Issue 4

This paper proposes a saliency detection method based on the aggregated Wasserstein distance. A multidimensional Gaussian mixture model is used to model the...

Journal Article: Full Text Online

Saliency detection based on aggregated Wasserstein distance

F Sun, W Li - Journal of Electronic Imaging, 2018 - spiedigitallibrary.org

This paper proposes a saliency detection method based on the aggregated Wasserstein

distance. A multidimensional Gaussian mixture model is used to model the superpixels,

whereby the color information of different color spaces is combined. To overcome the lack of …

aliency detection based on aggregated Wasserstein distance

Distributionally Robust Chance-Constrained Approximate AC-OPF With Wasserstein Metric

by Duan, Chao; Fang, Wanliang; Jiang, Lin; More...

IEEE Transactions on Power Systems, 09/2018, Volume 33, Issue 5

Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the...

Journal Article: Full Text Online Preview

Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In presence of VRE

uncertainties, this paper discusses a distributionally robust chance constrained approximate …

Wasserstein CNN: Learning Invariant Features for NIR-VIS Face Recognition

by He, Ran; Wu, Xiang; Sun, Zhenan; More...

IEEE Transactions on Pattern Analysis and Machine Intelligence, 05/2018

Heterogeneous face recognition (HFR) aims at matching facial images acquired from different sensing modalities with mission-critical applications in forensics,...

Journal Article: Full Text Online

Wasserstein CNN: Learning Invariant Features for NIR-VIS Face Recognition

R He, X Wu, Z Sun, T Tan - IEEE Transactions on Pattern …, 2018 - ieeexplore.ieee.org

Heterogeneous face recognition (HFR) aims at matching facial images acquired from

different sensing modalities with mission-critical applications in forensics, security and

commercial sectors. However, HFR presents more challenging issues than traditional face …

2018 cited by many [HTML] nih.gov

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

… Wasserstein distance as the discrepancy measure between distributions and a perceptual

loss that computes the difference between images … color images as input while CT images are …

Cited by 1039 Related articles All 8 versions

Low-Dose CT Image Denoising Using a Generative Adversarial ...

by Q Yang - ‎2018 - ‎Cited by 48 - ‎Related articles

Apr 17, 2018 - The continuous development and extensive use of computed tomography (CT) in medical practice has raised a public concern over the ...

Low-Dose CT Image Denoising Using a Generative Adversarial Network With Wasserstein Distance and Perceptual Loss

by Qingsong Yang; Pingkun Yan; Yanbo Zhang; More...

IEEE Transactions on Medical Imaging, 06/2018, Volume 37, Issue 6

The continuous development and extensive use of computed tomography (CT) in medical practice has raised a public concern over the associated radiation dose to...

Journal Article: Full Text Online

2018 IEEE Transactions o

F) Extremal flows in Wasserstein space - ResearchGate

Jul 15, 2018 - may be thought of as a curve in Wasserstein space [79]1. One example is the ... as extremal curves in Wasserstein space of a suitable action.

<——2018———— 2018 ——130—

MR3803713 Pending Berman, Robert J.; Önnheim, Magnus Propagation of chaos, Wasserstein gradient flows and toric Kähler-Einstein metrics. Anal. PDE 11 (2018), no. 6, 1343–1380. 53D25 (53C55 82C22)

Review PDF Clipboard Journal Article 3 Citations

Propagation of chaos, Wasserstein gradient flows and toric Kähler–Einstein metrics

by Berman, Robert J; Önnheim, Magnus

Analysis & PDE, 05/2018, Volume 11, Issue 6

Journal Article: Full Text Online

Propagation of chaos, Wasserstein gradient flows and toric Kähler–Einstein metrics

RJ Berman, M Önnheim - Analysis & PDE, 2018 - msp.org

Motivated by a probabilistic approach to Kähler–Einstein metrics we consider a general

nonequilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasiconvex N-particle interaction energy. We …

R Cited by 18 Related articles All 5 versions

MR3808205 Conforti, Giovanni; Pavon, Michele Extremal flows in Wasserstein space. J. Math. Phys. 59 (2018), no. 6, 063502, 15 pp. 49Q20 (60J60 76Y05 94A17)

Extremal flows in Wasserstein space

by Conforti, Giovanni; Pavon, Michele

Journal of Mathematical Physics, 06/2018, Volume 59, Issue 6

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein space. We show that the flows associated with the Schrödinger...

Journal Article: Full Text Online Preview

Extremal flows in Wasserstein space

G Conforti, M Pavon - Journal of Mathematical Physics, 2018 - aip.scitation.org

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein

space. We show that the flows associated with the Schrödinger bridge with general prior,

with optimal mass transport, and with the Madelung fluid can all be characterized as …

Scene Classification Using Hierarchical Wasserstein CNN

by Liu, Yishu; Suen, Ching Y; Liu, Yingbin; More...

IEEE Transactions on Geoscience and Remote Sensing, 10/2018

In multiclass classification, convolutional neural network (CNN) is generally coupled with the cross-entropy (CE) loss, which only penalizes the predicted...

Journal Article:Full Text Online Preview

Scene Classification Using Hierarchical Wasserstein CNN

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

In multiclass classification, convolutional neural network (CNN) is generally coupled with the

cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a

ground truth class and ignores the interclass relationship. We argue that CNN can be …

MR3898849 Carlsson, John Gunnar; Behroozi, Mehdi; Mihic, Kresimir

Wasserstein distance and the distributionally robust TSP. Oper. Res. 66 (2018), no. 6, 1603–1624. 90C10 (90C47)

Wasserstein Distance and the Distributionally Robust TSP

by Carlsson, John Gunnar; Behroozi, Mehdi; Mihic, Kresimir

Operations Research, 12/2018

Journal Article: Full Text Online Preview

Wasserstein distance and the distributionally robust TSP

JG Carlsson, M Behroozi, K Mihic - Operations Research, 2018 - pubsonline.informs.org

Recent research on the robust and stochastic traveling salesman problem and the vehicle

routing problem has used many different approaches for describing the region of ambiguity

Save Cite Cited by 49 Related articles All 7 versions

Wasserstein Distance and the Distributionally Robust TSP

John Gunnar Carlsson speaking at BIRS workshop, Distributionally Robust Optimization, on Tuesday, March 6, 2018 on the topic: Wasserstein ...

Banff International Research Station · Banff International Research Station ·

Mar 6, 2018

Wasserstein-Distance-Based Gaussian Mixture Reduction

by Assa, Akbar; Plataniotis, Konstantinos N

IEEE Signal Processing Letters, 10/2018, Volume 25, Issue 10

Gaussian mixtures (GMs) are widely used in signal processing applications to capture the multimodal behavior of dynamic systems. Due to an exponential increase...

Journal Article: Full Text Online

Wasserstein-Distance-Based Gaussian Mixture Reduction

A Assa, KN Plataniotis - IEEE Signal Processing Letters, 2018 - ieeexplore.ieee.org

Gaussian mixtures (GMs) are widely used in signal processing applications to capture the

multimodal behavior of dynamic systems. Due to an exponential increase in the number of

GM components in such applications, Gaussian mixture reduction (GMR) approaches are …

Snowflake universality of Wasserstein spaces - ResearchGate

MR3831034 Pending Andoni, Alexandr; Naor, Assaf; Neiman, Ofer Snowflake universality of Wasserstein spaces. Ann. Sci. Éc. Norm. Supér. (4) 51 (2018), no. 3, 657–700. 28A33 (30L05 51F99 53C23)

Snowflake universality of Wasserstein spaces

by Alexandr Andoni; Assaf Naor; Ofer Neiman

Annales scientifiques de l'École normale supérieure, 2018, Volume 51, Issue 3

Journal Article: Full Text Online

Aug 1, 2018 - Download Citation on ResearchGate | Snowflake universality of Wasserstein spaces | For $p\in (1,\infty)$ let $\mathscr{P}_p(\mathbb{R}^3)$ ...

Modified Massive Arratia Flow and Wasserstein Diffusion

by Konarovskyi, Vitalii; von Renesse, Max-K

Communications on Pure and Applied Mathematics, 07/2018

Journal Article: Full Text Online

Modified Massive Arratia Flow and Wasserstein Diffusion

V Konarovskyi, MK von Renesse - Communications on Pure …, 2018 - Wiley Online Library

Extending previous work by the first author we present a variant of the Arratia flow, which

consists of a collection of coalescing Brownian motions starting from every point of the unit

interval. The important new feature of the model is that individual particles carry mass that …

Cited by 4

MR3854402 Flamary, Rémi; Cuturi, Marco; Courty, Nicolas; Rakotomamonjy, Alain Wasserstein discriminant analysis. Mach. Learn. 107 (2018), no. 12, 1923–1945. 62H30 (60A10)

Wasserstein discriminant analysis

by Flamary, Rémi; Cuturi, Marco; Courty, Nicolas; More...

Machine Learning, 12/2018, Volume 107, Issue 12

Wasserstein discriminant analysis (WDA) is a new supervised linear dimensionality reduction algorithm. Following the blueprint of classical Fisher Discriminant...

Journal Article: Full Text Online Preview

Wasserstein discriminant analysis

R Flamary, M Cuturi, N Courty, A Rakotomamonjy - Machine Learning, 2018 - Springer

Wasserstein discriminant analysis (WDA) is a new supervised linear dimensionality

reduction algorithm. Following the blueprint of classical Fisher Discriminant Analysis, WDA

selects the projection matrix that maximizes the ratio of the dispersion of projected points …

(\… Using the definition (2) of regularized Wasserstein distance, we can write the Wasserstein …

Wasserstein Stationary Subspace Analysis

by Kaltenstadler, Stephan; Nakajima, Shinichi; Muller, Klaus-Robert; More...

IEEE Journal of Selected Topics in Signal Processing, 10/2018

Learning under non-stationarity can be achieved by decomposing the data into a subspace that is stationary and a non-stationary one (stationary subspace...

Journal Article: Full Text Online

Wasserstein Stationary Subspace Analysis

S Kaltenstadler, S Nakajima, KR Muller… - IEEE Journal of …, 2018 - ieeexplore.ieee.org

Learning under non-stationarity can be achieved by decomposing the data into a subspace

that is stationary and a non-stationary one (stationary subspace analysis (SSA)). While SSA

has been used in various applications, its robustness and computational efficiency has limits …

(PDF) Statistical Aspects of Wasserstein Distances

https://www.researchgate.net/publication/325778412_Statistical...

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the

minimal effort required to reconfigure the probability mass of one distribution in order to recover the other distribution

Statistical aspects of wasserstein distances

VM Panaretos, Y Zemel - Annual Review of Statistics and Its …, 2018 - annualreviews.org

Wasserstein distances are metrics on probability distributions inspired by the problem of

optimal mass transportation. Roughly speaking, they measure the minimal effort required to

reconfigure the probability mass of one distribution in order to recover the other distribution …

[PDF] ijcai.org Victor Panaretos arXiv June 2018 École Polytechnique

Statistical Aspects of Wasserstein Distances - Annual Reviews

https://www.annualreviews.org/doi/pdf/10.1146/annurev-statistics-030718-104938

Nov 2, 2018 - In statistics, Wasserstein distances play a prominent role in theory and ...... Bachoc F, Suvorikova A, Loubes JM, Spokoiny V. 2018. Gaussian ...

Anual Review of Statistics and Its ApplicationVol. 6:- (Volume publication date March 2019

Cited by 230 Related articles All 8 versions
<——2018——— 2018 ——140—

Sliced Wasserstein Kernel for Persistence …

2017 conference. pdf updated 2018

Sliced Wasserstein Kernel for Persistence Diagrams R X p q s (a) R X p0 q0 s0 (b) - 1 +1 f(p) + f(s) (c) Figure 1. Sketch of persistent homology: (a) the horizontal lines are the boundaries of sublevel sets f((1 ;t]), which are colored in

wasserstein: Wasserstein distance between two persistence ...

statistics 2018

The function wasserstein computes the Wasserstein distance between two persistence diagrams.

MR3782397 Kim, Young-Heon; Pass, Brendan A canonical barycenter via Wasserstein regularization. SIAM J. Math. Anal. 50 (2018), no. 2, 1817–1828. 60B05 (31E05 49Q20 94A17)

A canonical barycenter via Wasserstein regularization

YH Kim, B Pass - SIAM Journal on Mathematical Analysis, 2018 - SIAM

We introduce a weak notion of barycenter of a probability measure μ on a metric measure space (X,d,\bfm), with the metric d and reference measure \bfm. Under the assumption that all optimal transport plans transporting \bfm to any probability measure ν on X are induced by mappings, we prove that our barycenter B(μ) is well defined; it is a probability measure on X supported on the set of the usual metric barycenter points of the given measure μ. The definition uses the canonical embedding of the metric space X into its Wasserstein space …

Generative Modeling using the Sliced Wasserstein Distance

by Deshpande, Ishan; Zhang, Ziyu; Schwing, Alexander , 03/2018

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their...

Journal Article: Full Text Online

Generative Modeling using the Sliced Wasserstein Distance

I Deshpande, Z Zhang, A Schwing - arXiv preprint arXiv:1803.11188, 2018 - arxiv.org

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given

samples, even in the high-dimensional case. However, their formulation is also known to be

hard to optimize and often not stable. While this is particularly true for early GAN

formulations, there has been significant empirically motivated and theoretically founded

progress to improve stability, for instance, by using the Wasserstein distance rather than the

Jenson-Shannon divergence. Here, we consider an alternative formulation for generative …

Wasserstein distance and the distributionally robust TSP

JG Carlsson, M Behroozi, K Mihic - Operations Research, 2018 - pubsonline.informs.org

… Wasserstein distance is a particularly appropriate choice for our problem of interest: First, the Wasserstein … We will embed f in the Banach space L1(5), which consists of all functions that …

2018

Distributed Computation of Wasserstein Barycenters over Networks

by Uribe, César A; Dvinskikh, Darina; Dvurechensky, Pavel; More... , 03/2018

We propose a new class-optimal algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a...

Journal Article: Full Text Online

Distributed Computation of Wasserstein Barycenters over Networks

CA Uribe, D Dvinskikh, P Dvurechensky… - arXiv preprint arXiv …, 2018 - arxiv.org

We propose a new class-optimal algorithm for the distributed computation of Wasserstein

Barycenters over networks. Assuming that each node in a graph has a probability

distribution, we prove that every node is able to reach the barycenter of all distributions held

in the network by using local interactions compliant with the topology of the graph. We show

the minimum number of communication rounds required for the proposed method to achieve

arbitrary relative precision both in the optimality of the solution and the consensus among all …

Wasserstein Riemannian Geometry of Positive Definite Matrices

by Malagò, Luigi; Montrucchio, Luigi; Pistone, Giovanni , 01/2018

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the...

Journal Article: Full Text Online

Wasserstein-Riemannian Geometry of Positive-definite Matrices

L Malago, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we derive an explicit form of the Riemannian metrics on positive-definite matrices and

compute its tensor form with respect to the trace scalar product. The tensor is a matrix, which

is the solution of a Lyapunov equation. We compute explicit form for the Riemannian

exponential, the normal coordinates charts, the Riemannian gradient, and discuss the …

Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

by Kolouri, Soheil; Pope, Phillip E; Martin, Charles E; More... 04/2018

In this paper we study generative modeling via autoencoders while using the elegant geometric properties of the optimal transport (OT) problem and the...

Journal Article: Full Text Online

Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

ESG Model - openreview.net

In this paper we study generative modeling via autoencoders while using the elegant

geometric properties of the optimal transport (OT) problem and the Wasserstein distances.

We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that …

Effective Lipschitz constraint enforcement for Wasserstein GAN training

S Cui, Y Jiang - … and Applications (ICCIA), 2017 2nd IEEE …, 2017 - ieeexplore.ieee.org

Generative Adversarial Networks (GANs) are efficient frameworks for estimating generative

model via adversarial process. However, GAN has known for suffering from training

instability. Wasserstein GAN (WGAN) improves the training stability significantly but also …

[PDF] ENTROPIC INTERPOLATION AND GRADIENT FLOWS ON WASSERSTEIN PRODUCT SPACES

Y CHEN, T GEORGIOU, M PAVON - people.ece.umn.edu

We show that the entropic interpolation between two given marginals provided by the

Schrödinger bridge may be characterized as the curve in the Wasserstein space W2 which

minimizes a suitable action. We also study the relative entropy evolution between an …

[PDF] Numerical Schemes for Calculating the Discrete Wasserstein Distance

<——2018——— 2018 ————150—

B Cabrera - 2016 - ti.inf.uni-due.de

The goal of this thesis is to derive a feasible numerical scheme for computing time-

discretized geodesics of a recently proposed new type of “Wasserstein” metric acting on

discrete rather than on continuous spaces. Using an actual implementation of this scheme …

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

We present upper bounds for the Wasserstein distance of order $ p $ between the marginals

of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the

convolution structure, we further derive upper bounds for the total variation distance …

MR2361303 (2009b:37101) Ambrosio, Luigi; Gangbo, Wilfred Hamiltonian ODEs in the Wasserstein space of probability measures. Comm. Pure Appl. Math. 61 (2008), no. 1, 18--53. (Reviewer: Cédric Villani) 37J05 (28A33 34F05 49J52 60B10)

Hamiltonian ODEs in the Wasserstein space of probability measures

L Ambrosio, W Gangbo - Communications on Pure and Applied …, 2008 - Wiley Online Library

In this paper we consider a Hamiltonian H on 2 (ℝ 2d), the set of probability measures

with finite quadratic moments on the phase space ℝ 2d= ℝ d× ℝ d, which is a metric space

when endowed with the Wasserstein distance W 2. We study the initial value problem dμ …

Hamiltonian ODEs in the Wasserstein space of probability ...

www.researchgate.net › publication › 227653858_Hamilt...

Wilfrid Gangbo at University of California, Los Angeles ... An Optimal Transport Approach for the Kinetic Bohmian Equation. Preprint ... The dynamics is given by an Hamiltonian system in the space of measures, similar to what studied in [4] .

[CITATION] Infinite dimensional Hamiltonian systems in terms of the Wasserstein distance

W Gangbo, T Pacini - Work in progress

A Lack of Ricci Bounds for the Entropic Measure on Wasserstein ...

Aug 21, 2018 - Request PDF on ResearchGate | A Lack of Ricci Bounds for the Entropic Measure on Wasserstein space over the Interval | We examine the ...

MR2801182 Agueh, Martial; Carlier, Guillaume Barycenters in the Wasserstein space. SIAM J. Math. Anal. 43 (2011), no. 2, 904–924, 49Q20 (28A33 49K10 60D99). Zbl 1223.49045

Citations (149)

Barycenters in the Wasserstein space

M Agueh, G Carlier - SIAM Journal on Mathematical Analysis, 2011 - SIAM

In this paper, we introduce a notion of barycenter in the Wasserstein space which

generalizes McCann's interpolation to the case of more than two measures. We provide

existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the …

2018 see 2013

[PDF] Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

F Bassetti, E Perversi - Electronic Journal of Probability, 2013 - emis.ams.org

This work deals with a class of one-dimensional measure-valued kinetic equations, which

constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the

domain of normal attraction of an α-stable law, the solution of the equation converges …

[PDF] On gradient structures for Markov chains and the passage to Wasserstein gradient flows.

K Disser, M Liero - NHM, 2015 - opus4.kobv.de

We study the approximation of Wasserstein gradient structures by their finitedimensional

analog. We show that simple finite-volume discretizations of the linear Fokker-Planck

equation exhibit the recently established entropic gradient-flow structure for reversible …

Single Image Haze Removal | Papers With Code

paperswithcode.com › single-image-haze-removal › latest

paperswithcode.com › single-image-haze-removal › latest15 Feb 2022 ... IEEE Transaction on Image Processing 2020 ... Single Image Haze Removal Using Conditional Wasserstein Generative Adversarial Networks.

Papers With Code · Bharath Raj ·

Mar 9, 2018

MR3385156 Kuwada, Kazumasa; Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates. Calc. Var. Partial Differential Equations 54 (2015), no. 1, 127–161.

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

K Kuwada - Calculus of Variations and Partial Differential …, 2015 - Springer

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat

distributions is extended to that in refined estimates in a high generality. As a result, we find

an equivalent condition to Bakry–Ledoux's refined gradient estimate involving an upper …

The Wasserstein distances

C Villani - Optimal Transport, 2009 - Springer

Assume, as before, that you are in charge of the transport of goods be- tween producers and

consumers, whose respective spatial distributions are modeled by probability measures. The

farther producers and con- sumers are from each other, the more difficult will be your job, and …

<——2018————— 2018 ———160—

Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

In a non-relativistic setting the dynamics of electrons in a plasma with heavy ions uniformly distributed

in space is described by the Vlasov–Poisson system. Throughout this paper, we will focus on

the 2 and 3 dimensional periodic (in space) case. We introduce the distribution function of the …

[PDF]

wasserstein barycenter model ensembling - OpenReview

by P Dognin - ‎2018

tilabel learning setting using Wasserstein (W.) barycenters. Optimal transport metrics ... algorithms that rely on iterative Bregman projections (Benamou et al., 2015). Many applications ...... Multi-lingual fusion and Translation. µl ∈ ∆Nl, l = 1 ...m.

A new approach for the construction of a Wasserstein diffusion

18th International Workshop on Algorithms in Bioinformatics

WABI 2018, August 20–22, 2018, Helsinki, Finland

MR3896861 Marx, Victor A new approach for the construction of a Wasserstein diffusion. Electron. J. Probab. 23 (2018), Paper No. 124, 54 pp. 60K35 (60B12 60G44 60J60)

Electron. J. Probab. Volume 23 (2018), paper no. 124, 54 pp.

Victor Marx

Learning and Inference with Wasserstein Metrics | Brain and Cognitive ...

Jan 10, 2018 - This thesis develops new approaches for three problems in machine learning, using tools from the study of optimal transport (or Wasserstein) distances between probability distributions. Optimal transport distances capture an intuitive notion of similarity between distributions, by incorporating the underlying ...

MR3744719 Sommerfeld, Max; Munk, Axel Inference for empirical Wasserstein distances on finite spaces. J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 (2018), no. 1, 219–238. 60B10 (62E20 62G09)

Inference for empirical Wasserstein distances on finite spaces

By: Sommerfeld, Max; Munk, Axel

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY Volume: 80 Issue: 1 Pages: 219-238 Published: JAN

Summary The Wasserstein distance is an attractive tool for data analysis but statistical

inference is hindered by the lack of distributional limits. To overcome this obstacle, for

probability measures supported on finitely many points, we derive the asymptotic distribution

[pdf] Inference for Empirical Wasserstein Distances on Finite ... arXiv

Cited by 55 Related articles

Inference for empirical Wasserstein distances on finite spaces

50 citations* for all

40 citations*

2018 Journal of The Royal Statistical Society Series B-statistical Methodology

Max Sommerfeld ¹, Axel Munk ^{1, 2}

¹ University of Göttingen ,

² Max Planck Society

2018

Type spaces and Wasserstein spaces

S Song - Journal of the Korean Mathematical Society, 2018 - koreascience.or.kr

Abstract Types (over parameters) in the theory of atomless random variable structures

correspond precisely to (conditional) distributions in probability theory. Moreover, the logic

(resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) …

On the Bures-Wasserstein distance between positive definite matrices

R Bhatia, T Jain, Y Lim - Expositiones Mathematicae, 2018 - Elsevier

d (A, B)= tr A+ tr B− 2 tr (A 1∕ 2 BA 1∕ 2) 1∕ 2 1∕ 2 on the manifold of n× nn× n positive

definite matrices arises in various optimisation problems, in quantum information and in the

theory of optimal transport. It is also related to Riemannian geometry. In the first part of this

published 2019

Second order models for optimal transport and cubic splines on the Wasserstein space

by Benamou, Jean-David; Gallouët, Thomas; Vialard, François-Xavier 01/2018

On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After...

Journal Article: Full Text Online

Second order models for optimal transport and cubic splines on the Wasserstein space

JD Benamou, T Gallouët, FX Vialard - arXiv preprint arXiv:1801.04144, 2018 - arxiv.org

Abstract: On the space of probability densities, we extend the Wasserstein geodesics to the

case of higher-order interpolation such as cubic spline interpolation. After presenting the

natural extension of cubic splines to the Wasserstein space, we propose simpler approach,

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative...

by Wu, Hao; Ma, Peter C; Lv, Yu; More... 01/2018

In this work, methods for the evaluation of LES-quality and LES-accuracy are presented, which include the Lyapunov exponent for the analysis of short-time...

Journal Article: Full Text Online

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation

H Wu, PC Ma, Y Lv, M Ihme - 2018 AIAA Aerospace Sciences Meeting, 2018 - arc.aiaa.org

The objective of this work is to address the need for assessing the quality of large-eddy

simulations with particular application to turbulent reacting flows. Such assessments include

the consideration of resolution requirements and the quantitative evaluation of the accuracy

A Two-Step Computation of the Exact GAN Wasserstein Distance

H Liu, GU Xianfeng, D Samaras - … Conference on Machine …, 2018 - proceedings.mlr.press

In this paper, we propose a two-step method to compute the Wasserstein distance in

Wasserstein Generative Adversarial Networks (WGANs): 1) The convex part of our objective

can be solved by linear programming; 2) The non-convex residual can be approximated by …

Cited by 2 All 4 versions

A Two-Step Computation of the Exact GAN Wasserstein ...

· Uploaded by TechTalksTV

This is "A Two-Step Computation of the Exact GAN Wasserstein Distance" by TechTalksTV on Vimeo, the home ...

Oct 2, 2018
<——2018—————— 2018 ————170—

A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - arXiv preprint arXiv:1801.07815, 2018 - arxiv.org

Abstract: Stein's method has been widely used for probability approximations. However, in

the multi-dimensional setting, most of the results are for multivariate normal approximation or

for test functions with bounded second-or higher-order derivatives. For a class of multivariate

Wasserstein Coresets for Lipschitz Costs

S Claici, J Solomon - arXiv preprint arXiv:1805.07412, 2018 - arxiv.org

Sparsification is becoming more and more relevant with the proliferation of huge data sets.

Coresets are a principled way to construct representative weighted subsets of a data set that

have matching performance with the full data set for specific problems. However, coreset …

Wasserstein coresets for lipschitz costs

2018 see 2017

[PDF] Sliced Wasserstein Kernel for Persistence Diagrams M. CARRIÈRE M. CUTURI 2

S OUDOT - crest.science

Abstract Persistence diagrams play a key role in topological data analysis (TDA), in which

they are routinely used to describe topological properties of complicated shapes.

persistence diagrams enjoy strong stability properties and have proven their utility in various

[CITATION] Sliced Wasserstein Kernel for Persistence Diagrams M. CARRIÈRE M. CUTURI 2

S OUDOT

Sliced Wasserstein Kernel for Persistence Diagrams | Request ...

https://www.researchgate.net › ... › Persistence

Request PDF | Sliced Wasserstein Kernel for Persistence Diagrams | Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which ...

[CITATION] Sliced Wasserstein Kernel for Persistence Diagrams M. CARRIÈRE M. CUTURI 2

S OUDOT
liced Wasserstein kernel for persistence diagrams

[PDF] Semi-supervised Biomedical Translation with Cycle Wasserstein Regression GANs

MBA McDermott, T Yan, T Naumann, N Hunt, H Suresh… - 2018 - marzyehghassemi.com

Abstract The biomedical field offers many learning tasks that share unique challenges: large

amounts of unpaired data, and a high cost to generate labels. In this work, we develop a

method to address these issues with semi-supervised learning in regression tasks (eg,

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

by Erdmann, Martin; Geiger, Lukas; Glombitza, Jonas; More... 02/2018

We use adversarial network architectures together with the Wasserstein distance to generate or refine simulated detector data. The data reflect two-dimensional...

Journal Article: Full Text Online

M Erdmann, L Geiger, J Glombitza… - arXiv preprint arXiv …, 2018 - arxiv.org

Abstract: We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example,

Solving Approximate Wasserstein GANs to Stationarity

M Sanjabi, J Ba, M Razaviyayn, JD Lee - arXiv preprint arXiv:1802.08249, 2018 - arxiv.org

Abstract: Generative Adversarial Networks (GANs) are one of the most practical strategies to

learn data distributions. A popular GAN formulation is based on the use of Wasserstein

distance as a metric between probability distributions. Unfortunately, minimizing the

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance

Y Han, J Jiao, T Weissman - arXiv preprint arXiv:1802.08405, 2018 - arxiv.org

Abstract: We present\emph {Local Moment Matching (LMM)}, a unified methodology for

symmetric functional estimation and distribution estimation under Wasserstein distance. We

construct an efficiently computable estimator that achieves the minimax rates in estimating

All 2 versions [PDF] arxiv.org

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under

[PDF] Learning Disentangled Representations with Wasserstein Auto-Encoders

PK Rubenstein, B Schoelkopf, I Tolstikhin - 2018 - openreview.net

Page 1. Workshop track - ICLR 2018 LEARNING DISENTANGLED REPRESENTATIONS WITH

WASSERSTEIN AUTO-ENCODERS Paul Rubenstein∗, Bernhard Schölkopf, Ilya Tolstikhin

Empirical Inference Max Planck Institute for Intelligent Systems, Tübingen 1paul.rubenstein,bs,

A Fast Proximal Point Method for Wasserstein Distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018 - arxiv.org

Abstract: Wasserstein distance plays increasingly important roles in machine learning,

stochastic programming and image processing. Major efforts have been under way to

address its high computational complexity, some leading to approximate or regularized

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

by Wei, Xiang; Gong, Boqing; Liu, Zixia; More... 03/2018

Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is...

Journal Article: Full Text Online

X Wei, B Gong, Z Liu, W Lu, L Wang - 2018 - openreview.net

Abstract: Despite being impactful on a variety of problems and applications, the generative

adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed

by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the

Cited by 3931 Related articles All 10 versions

Cited by 2632 Related articles

CCited by 203 Related articles All 5 versions

<——2018————— 2018 ——————180—

Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

by Blanchet, Jose; Chen, Lin; Zhou, Xun Yu 02/2018

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty...

Journal Article: Full Text Online

Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

Abstract: We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so-

[CITATION] Distributionally robust mean–variance portfolio selection with Wasserstein distances. arXiv

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018

The existence of geodesics in Wasserstein spaces over path groups and loop groups

The existence of geodesics in Wasserstein spaces over path groups and loop groups

by Shao, Jinghai 02/2018

In this work we prove the existence and uniqueness of the optimal transport map for $L^p$-Wasserstein distance with $p>1$, and particularly present an explicit...

Journal Article: Full Text Online

J Shao - arXiv preprint arXiv:1802.10226, 2018 - arxiv.org

Abstract: In this work we prove the existence and uniqueness of the optimal transport map

for $ L^ p $-Wasserstein distance with $ p> 1$, and particularly present an explicit

expression of the optimal transport map for the case $ p= 2$. As an application, we show the

Minimax Distribution Estimation in Wasserstein Distance

Minimax Distribution Estimation in Wasserstein Distance

by Singh, Shashank; Póczos, Barnabás 02/2018

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability...

Journal Article: Full Text Online

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

Abstract: The Wasserstein metric is an important measure of distance between probability

distributions, with several applications in machine learning, statistics, probability theory, and

data analysis. In this paper, we upper and lower bound minimax rates for the problem of

C Cited by 47 Related articles All 4 versions

MR3753331 Chen, Yongxin; Georgiou, Tryphon T.; Tannenbaum, Allen Wasserstein geometry of quantum states and optimal transport of matrix-valued measures. Emerging applications of control and systems theory, 139–150, Lect. Notes Control Inf. Sci. Proc., Springer, Cham, 2018. (Reviewer: Mathieu Lewin) 81P50 (49Q20 81P15 81P45 81Q12)

Wasserstein Geometry of Quantum States and Optimal Transport of Matrix-Valued Measures

Y Chen, TT Georgiou, A Tannenbaum - Emerging Applications of Control …, 2018 - Springer

Abstract We overview recent results on generalizations of the Wasserstein 2-metric,

originally defined on the space of scalar probability densities, to the space of Hermitian

matrices and of matrix-valued distributions, as well as some extensions of the theory to

Wasserstein Distance Measure Machines

A Rakotomamonjy, A Traore, M Berar… - arXiv preprint arXiv …, 2018 - arxiv.org

Abstract: This paper presents a distance-based discriminative framework for learning with

probability distributions. Instead of using kernel mean embeddings or generalized radial

basis kernels, we introduce embeddings based on dissimilarity of distributions to some

All 5 versions [PDF] openreview.net

Comparison between W2 distance and Ḣ− 1 norm, and Localization of Wasserstein distance

<—— 2018 ———2018———190—

R Peyre - ESAIM: Control, Optimisation and Calculus of …, 2018 - esaim-cocv.org

It is well known that the quadratic Wasserstein distance W 2 (⋅,⋅) is formally equivalent, for

infinitesimally small perturbations, to some weighted H− 1 homogeneous Sobolev norm. In

this article I show that this equivalence can be integrated to get non-asymptotic comparison …

MR3922440 Peyre, Rémi Comparison between W₂ distance and H˙⁻¹ norm, and localization of Wasserstein distance. ESAIM Control Optim. Calc. Var. 24 (2018), no. 4, 1489–1501. (Reviewer: Luca Granieri) 49Q20 (28A75 46E35)

Comparison between W2 distance and Ḣ− 1 norm, and Localization of Wasserstein distance

R Peyre - ESAIM: Control, Optimisation and Calculus of …, 2018 - esaim-cocv.org

… a natural question is the following: are there non-asymptotic comparisons between the W2 … COMPARISON BETWEEN W2 DISTANCE AND ˙H−1 NORM, AND LOCALIZATION OF WASSERSTEIN DISTANCE 1493 … ν have the same mass (for otherwise the distance between …

[PDF] Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - jmlr.org

Divide-and-conquer based methods for Bayesian inference provide a general approach for

tractable posterior inference when the sample size is large. These methods divide the data

into smaller subsets, sample from the posterior distribution of parameters in parallel on all …

2018

Low dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of CT in medical practice has raised a

public concern over the associated radiation dose to the patient. Reducing the radiation

dose may lead to increased noise and artifacts, which can adversely affect the radiologists …

2018

Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

We provide an exact deterministic reformulation for data-driven chance constrained

programs over Wasserstein balls. For individual chance constraints as well as joint chance

constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer …

2018

[CITATION] Data-driven chance constrained programs over wasserstein balls.-, 2018

Z Chen, D Kuhn, W Wiesemann - Available from Optimization Online

Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises

D Luo, J Wang - Stochastic Processes and their Applications, 2018 - Elsevier

We establish the exponential convergence with respect to the L 1-Wasserstein distance and

the total variation for the semigroup corresponding to the stochastic differential equation d X

t= d Z t+ b (X t) dt, where (Z t) t≥ 0 is a pure jump Lévy process whose Lévy measure ν fulfills …

[PDF] Wasserstein introspective neural networks

K Lee, W Xu, F Fan, Z Tu - The IEEE Conference on …, 2018 - openaccess.thecvf.com

We present Wasserstein introspective neural networks (WINN) that are both a generator and

a discriminator within a single model. WINN provides a significant improvement over the

recent introspectve neural networks (INN) method by enhancing INN's generative modeling …

Wasserstein Introspective Neural Networks

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

B Arras, E Azmoodeh, G Poly, Y Swan - Stochastic processes and their …, 2018 - Elsevier

We provide a bound on a distance between finitely supported elements and general

elements of the unit sphere of ℓ 2 (N∗). We use this bound to estimate the Wasserstein-2

distance between random variables represented by linear combinations of independent …

Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem

E Bandini, A Cosso, M Fuhrman, H Pham - Stochastic Processes and their …, 2018 - Elsevier

We study a stochastic optimal control problem for a partially observed diffusion. By using the

control randomization method in Bandini et al.(2018), we prove a corresponding

randomized dynamic programming principle (DPP) for the value function, which is obtained …

MR3833742 Pending Li, Songzi; Li, Xiang-Dong

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds. Sci. China Math. 61 (2018), no. 8, 1385–1406. 58J65 (58J35 60H30 60J60)

Review PDF Clipboard Journal Article 2 Citations

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

by Li, Songzi; Li, Xiang-Dong

Science China Mathematics, 08/2018, Volume 61, Issue 8

In this survey paper, we give an overview of our recent works on the study of the W-entropy for the heat equation associated with the Witten Laplacian on...

Newspaper Article: Full Text OnlineW-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

by Li, Songzi; Li, Xiang-Dong

Science China Mathematics, 08/2018, Volume 61, Issue 8

In this survey paper, we give an overview of our recent works on the study of the W-entropy for the heat equation associated with the Witten Laplacian on...

Newspaper Article: Full Text OnlineW-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

by Li, Songzi; Li, Xiang-Dong

Science China Mathematics, 08/2018, Volume 61, Issue 8

In this survey paper, we give an overview of our recent works on the study of the W-entropy for the heat equation associated with the Witten Laplacian on...

Newspaper Article: Full Text Online

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

Probabilistic natural language generation with wasserstein autoencoders

H Bahuleyan, L Mou, K Vamaraju, H Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

Probabilistic generation of natural language sentences is an important task in NLP. Existing

models such as variational autoencoders (VAE) for sequence generation are extremely

difficult to train due to the issues associated with the Kullback-Leibler (KL) loss collapsing to …

Cited by 3 All 2 versions

[PDF] arxiv.org
<—— 2018————2018—————— -200—

Deep variational network embedding in wasserstein space

D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

Network embedding, aiming to embed a network into a low dimensional vector space while

preserving the inherent structural properties of the network, has attracted considerable

attentions recently. Most of the existing embedding methods embed nodes as point vectors …

Distributionally robust games: Wasserstein metric

J Gao, H Tembine - 2018 International Joint Conference on …, 2018 - ieeexplore.ieee.org

Deep generative models are powerful but difficult to train due to its instability, saturation

problem and high dimensional data distribution. This paper introduces a game theory

framework with Wasserstein metric to train generative models, in which the unknown data …

Distributionally Robust Games: Wasserstein Metric

Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018 - arxiv.org

We present a Bayesian framework based on a new exponential likelihood function driven by

the quadratic Wasserstien metric. Compared to conventional Bayesian models based on

Gaussian likelihood functions driven by the least-squares norm ($ L_2 $ norm), the new …

Cited by 1 All 3 versions

[CITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018

[PDF] Weakly Supervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning.

N Zhang, J Yan, Y Zhou - IJCAI, 2018 - ijcai.org

Separating audio mixtures into individual instrument tracks has been a standing challenge.

We introduce a novel weakly supervised audio source separation approach based on deep

adversarial learning. Specifically, our loss function adopts the Wasserstein distance which …

Gromov-Wasserstein Alignment of Word Embedding Spaces

D Alvarez-Melis, TS Jaakkola - arXiv preprint arXiv:1809.00013, 2018 - arxiv.org

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from

machine translation to transfer learning. Recently, purely unsupervised methods operating

on monolingual embeddings have become effective alignment tools. Current state-of-the-art …

Cited by 1 All 3 versions

Gromov-Wasserstein Alignment of Word Embedding Spaces

This is "Gromov-Wasserstein Alignment of Word Embedding Spaces" by ACL on Vimeo, the home for high ...

Dec 11, 2018 · Uploaded by ACL

2018

Uncoupled isotonic regression via minimum Wasserstein deconvolution

P Rigollet, J Weed - arXiv preprint arXiv:1806.10648, 2018 - arxiv.org

Isotonic regression is a standard problem in shape-constrained estimation where the goal is

to estimate an unknown nondecreasing regression function $ f $ from independent pairs

$(x_i, y_i) $ where $\mathbb {E}[y_i]= f (x_i), i= 1,\ldots n $. While this problem is well …

Uncoupled isotonic regression via minimum Wasserstein deconvolution

Second order models for optimal transport and cubic splines on the Wasserstein space

JD Benamou, T Gallouët, FX Vialard - arXiv preprint arXiv:1801.04144, 2018 - arxiv.org

On the space of probability densities, we extend the Wasserstein geodesics to the case of

higher-order interpolation such as cubic spline interpolation. After presenting the natural

extension of cubic splines to the Wasserstein space, we propose simpler approach, similarly …

Towards High Resolution Video Generation with Progressive Growing of Sliced Wasserstein GANs

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

since the temporal dimension of videos introduces an extra challenge during the generation

process. Besides, due to the limitation of memory and training stability, the generation …

On the Computation of Kantorovich-Wasserstein Distances between 2D-Histograms by Uncapacitated Minimum Cost Flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich distance, that is, the

Wasserstein distance of order one, between a pair of two-dimensional histograms. Recent

works in Computer Vision and Machine Learning have shown the benefits of measuring …

published 2020

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters

L Yang, J Li, D Sun, KC Toh - arXiv preprint arXiv:1809.04249, 2018 - arxiv.org

In this paper, we consider the problem of computing a Wasserstein barycenter for a set of

discrete probability distributions with finite supports, which finds many applications in

different areas such as statistics, machine learning and image processing. When the support …

A fast globally linearly convergent algorithm for the computation of wasserstein barycenters
<-- 2018———2018—————— -210—

Propriétés statistiques du barycentre dans l'espace de Wasserstein

E Cazelles - 2018 - tel.archives-ouvertes.fr

Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de

probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension des outils

statistiques usuels sur cet espace muni de la distance de Wasserstein. Une première notion …

https://www.ieice.org › ken › paper

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Wasserstein GANによるスタイル制御可能なフォント生成

https://www.ieice.org › ken › paper · Translate this page

by 阿部耕太郎 · 2018 — 本研究では，Wasserstein GANを用いてスタイル制御可能なフォント生成を試みる．Wasserstein GANは，学習パターンと生成パターンの確率分布間の距離を定義 ...

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[CITATION] Wasserstein GAN によるスタイル制御可能なフォント生成 (メディアエクスペリエンス·バーチャル環境基礎)

阿部耕太郎，早志英朗，内田誠一 - 電子情報通信学会技術研究報告= IEICE …, 2018 - ci.nii.ac.jp

… Wasserstein GANによるスタイル制御可能なフォント生成 (メディアエクスペリエンス·バーチャル環境基礎) …

All 2 versions Japanese

[CITATION] Wasserstein GAN Generates Style Controllable Fonts (Media Experience - Virtual Environmental Fundamentals)

Abe Kotaro, Hayashi Hideo, Uchida Seiichi - IEICE ..., 2018 - ci.nii.ac.jp

... Style controllable font generation by Wasserstein GAN (Media Experience · Virtual Environment Basic) ...

Model risk measurement under Wasserstein distance

Y Feng, E Schlogl - FIRN Research Paper, 2018 - papers.ssrn.com

The paper proposes a new approach to model risk measurement based on the Wasserstein

distance between two probability measures. It formulates the theoretical motivation resulting

from the interpretation of fictitious adversary of robust risk management. The proposed …

Model Risk Measurement Under Wasserstein Distance
Authors:Yu Feng (
Author), Erik Schlögl (Other)
Summary:The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for all alternative models and incorporates the economic reality of the fictitious adversary. It provides practically feasible results that overcome the restriction and the integrability issue imposed by the nominal model. The Wasserstein approach suits for all types of model risk problems, ranging from the single-asset hedging risk problem to the multi-asset allocation problem. The robust capital allocation line, accounting for the correlation risk, is not achievable with other non-parametric approachesShow more
eBook, 2018
English
Publisher:SSRN, [S.l.], 2018

A Rademacher-type Theorem on Wasserstein Spaces over Closed Riemannian Manifolds

L Schiavo - arXiv preprint arXiv:1810.10227, 2018 - arxiv.org

Let $\mathbb P $ be any Borel probability measure on the $ L^ 2$-Wasserstein space

$(\mathscr {P} _2 (X), W_2) $ over a closed Riemannian manifold $ X $. We consider the

Dirichlet energy integral $\mathcal E $ induced by $\mathbb P $ and by the Wasserstein …

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space

of Wasserstein in the framework of mean field control problems. The main motivation for this

study is given by the control of multi-agent systems, where the number of the agents is so …

[PDF] mohammedaminabdullah.org

2018

[PDF] Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - mohammedaminabdullah.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

基于 Wasserstein 距离多状态建模的冷热电联供系统优化配置

曹芷健，刘继春，武云霞，刘俊勇，李斌，卢天琪 - 电气应用, 2018 - cqvip.com

考虑冷热电联供系统中可再生能源供热供电出力和负荷的不确定性对优化配置的影响,

采用基于Wasserstein 概率距离指标的改进多状态方法对风光出力和冷热电负荷不确定性进行

建模. 在考虑经济性, 环保性基础上引入自平衡能力为目标建立优化配置模型 …

[PDF] inria.fr Chinese

Optimal Configuration of Cogeneration System Based on Wasserstein Distance Multi-State Modeling

Cao Yujian, Liu Jichun, Wu Yunxia, Liu Junyong, Li Bin, Lu Tianqi - Electrical Applications, 2018 - cqvip.com

Considering the impact of the uncertainty of the output and load of the renewable energy supply in the cogeneration system on the optimal configuration,

The improved multi-state method based on Wasserstein probability distance index is used to determine the wind power output and the thermal power load uncertainty.

Modeling. On the basis of considering economics and environmental protection, we introduce self-balancing ability to establish an optimal configuration model for the goal...

On a Wasserstein-type distance between solutions to stochastic differential equations

J Bion-Nadal, D Talay - 2018 - hal.inria.fr

In this paper we introduce a Wasserstein-type distance on the set of the probability

distributions of strong solutions to stochastic differential equations. This new distance is

defined by restricting the set of possible coupling measures. We prove that it may also be …

Wasserstein GAN によるスタイル制御可能なフオント生成

阿部耕太郎，早志英朗，内田誠一 - 研究報告コンピュータビジョンと …, 2018 - ipsj.ixsq.nii.ac.jp

本研究では, Wasserstein GAN を用いてスタイル制御可能なフォント生成を試みる. Wasserstein

GAN は, 学習パターンと生成パターンの確率分布間の距離を定義し, それを最小化するように学習

される構成の GAN である. ランダムノイズに文字情報付与を付与したものを Generator の入力とし …

All 2 versions Japanese

Stylable font generation by Wasserstein GAN

Ko Taro Abe, Hayasi Hideo, Uchida Seiichi - Research report With computer vision ..., 2018 - ipsj.ixsq.nii.ac.jp

In this research, we try to generate style controllable fonts using Wasserstein GAN Wasserstein

The GAN defines the distance between the learning pattern and the probability distribution of the generated pattern and learns to minimize it

It is a GAN with a configuration that is given a character information imparted to random noise as an input of Generator ...

Wasserstein Loss 를 이용한 모델 파라미터 학습

지종호， 신현정 - 한국정보과학회 학술발표논문집, 2018 - dbpia.co.kr

요 약그래프기반 준지도학습 (graph based semi-supervised learning) 은 그래프를 어떻게

만드냐에 따라 성능이 달라진다. 특히, 그래프의 엣지는 레코드 간 유사도로 생성되는데

유사도가 어떻게 정의되는가는 준지도학습의 성능에 상당한 영향을 미친다. 일반적으로 가장 …

All 2 versions Korean

Model parameter learning using Wasserstein Loss

Jong Jho, Shin Hyun Jung - Proceedings of the Korean Information Science Society Conference, 2018 - dbpia.co.kr

Summary Graph based semi-supervised learning is a method of

Performance varies depending on the type. In particular, the edge of the graph is generated by the similarity between records

How the similarity is defined has a significant impact on the performance of semi-tutoring. Generally the most ...

<-- 2018 ————2018—————220-

[PDF] EE-559–Deep learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

Page 1. EE-559 – Deep learning 10.2. Wasserstein GAN François Fleuret https://fleuret.org/

ee559/ Wed Aug 29 14:57:14 UTC 2018 ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

Page 2. Arjovsky et al. (2017) point out that DJS does not account [much] for the metric structure …

Wasserstein Soft Label Propagation on Hypergraphs: Algorithm and Generalization Error Bounds

T Gao, S Asoodeh, Y Huang, J Evans - arXiv preprint arXiv:1809.01833, 2018 - arxiv.org

Inspired by recent interests of developing machine learning and data mining algorithms on

hypergraphs, we investigate in this paper the semi-supervised learning algorithm of

propagating" soft labels"(eg probability distributions, class membership scores) over …

[PDF] Poincaré Wasserstein Autoencoder

I Ovinnikov - bayesiandeeplearning.org Dec 7, 2018

This work presents a reformulation of the recently proposed Wasserstein autoencoder

framework on a non-Euclidean manifold, the Poincaré ball model of the hyperbolic space

Hn. By assuming the latent space to be hyperbolic, we can use its intrinsic hierarchy to …

The optimal convergence rate of monotone schemes for conservation laws in the Wasserstein distance

AM Ruf, E Sande, S Solem - arXiv preprint arXiv:1808.04661, 2018 - arxiv.org

Abstract We prove that the first-order convergence rate for monotone finite volume approximations

of one-dimensioal scalar conservation laws in the Wasserstein distance, proved by

Nessyahu, Tadmor and Tassa in 1994, is optimal … In their 1994 paper, Nessyahu, Tadmor …

All 3 versios

Wasserstein Adversarial Mixture Clustering

T Pinetz, D Soukup, T Pock - cmp.felk.cvut.cz

Wasserstein Generative Adversarial Networks (GANs) work by approximating the

Wasserstein distance using large Neural Networks (NNs) with specific architectures,

hyperparameter and regularization techniques. We show that those networks severely …

W Harchaoui, PA Mattei, A Alamansa, C Bouveyron - 2018 - hal.archives-ouvertes.fr

Clustering complex data is a key element of unsupervised learning which is still a

challenging problem. In this work, we introduce a deep approach for unsupervised

clustering based on a latent mixture living in a low-dimensional space. We achieve this …

CONTRACTION IN THE WASSERSTEIN METRIC FOR THE KINETIC FOKKER-PLANCK EQUATION ON THE TORUS.

MR3815150 Dietert, Helge; Evans, Josephine; Holding, Thomas Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus. Kinet. Relat. Models 11 (2018), no. 6, 1427–1441. 60J60 (35Q84 60B10 60H30 82C31)

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - search.ebscohost.com

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

MR3778062 Song, Shichang Type spaces and Wasserstein spaces. J. Korean Math. Soc. 55 (2018), no. 2, 447–469. 03C90 (60B10)

TYPE SPACES AND WASSERSTEIN SPACES 1. Introduction ...

S Song -

Journal of the Korean Mathematical Society

Type spaces and Wasserstein spaces. J. Korean Math. Soc. 2018 Vol. 55, No. 2, 447-469. Published online 2018 Mar 01. Shichang Song Beijing Jiaotong ...

YPE SPACES AND WASSERSTEIN SPACES

Wasserstein Proximal of GANs

A Tong Lin, W Li, S Osher, G Montúfar - 2018 - mis.mpg.de

We introduce a new method for training GANs by applying the Wasserstein-2 metric

proximal on the generators. This approach is based on the gradient operator induced by

optimal transport theory, which connects the geometry of the sample space and the …

Graph Signal Representation with Wasserstein Barycenters

E Simou, P Frossard - arXiv preprint arXiv:1812.05517, 2018 - arxiv.org

In many applications signals reside on the vertices of weighted graphs. Thus, there is the

need to learn low dimensional representations for graph signals that will allow for data

analysis and interpretation. Existing unsupervised dimensionality reduction methods for …

Graph signal representation with Wasserstein barycenters

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Wasserstein-2 bounds in normal approximation under local dependence

X Fang - arXiv preprint arXiv:1807.05741, 2018 - arxiv.org

We obtain a general bound for the Wasserstein-2 distance in normal approximation for sums

of locally dependent random variables. The proof is based on an asymptotic expansion for

expectations of second-order differentiable functions of the sum. Applied to subgraph counts …

All 2 version

Wasserstein-2 bounds in normal approximation under local dependence

Lifted and geometric differentiability of the squared quadratic wasserstein distance
Authors:Alfonsi A., Jourdain B.
Article, 2018
Publication:arXiv, 2018 11 19
Publisher:2018

[CITATION] Lifted and geometric differentiability of the squared quadratic Wasserstein distance

A Aurélien, B Jourdain - 2018

Lifted and geometric differentiability of the squared quadratic ...

Nov 19, 2018 - Title:Lifted and geometric differentiability of the squared quadratic Wasserstein distance. Authors:Aurélien Alfonsi, Benjamin Jourdain.

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

Page 1. AMMI – Introduction to Deep Learning 10.2. Wasserstein GAN François Fleuret

https://fleuret.org/ammi-2018/ Wed Aug 29 16:57:14 CAT 2018 ÉCOLE POLYTECHNIQUE

FÉDÉRALE DE LAUSANNE Page 2. Arjovsky et al. (2017) point out that DJS does not …

Wasserstein Covariance for Multiple Random Densities

A Petersen, HG Müller - arXiv preprint arXiv:1812.07694, 2018 - arxiv.org

A common feature of methods for analyzing samples of probability density functions is that

they respect the geometry inherent to the space of densities. Once a metric is specified for

this space, the Fréchet mean is typically used to quantify and visualize the average density …

Wasserstein Covariance for Multiple Random Densities

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

Diagnosis of Schizophrenia Disorder Using Wasserstein Based Active Contour and Texture Features

M Latha, G Kavitha - Computational Signal Processing and Analysis, 2018 - Springer

Magnetic resonance (MR) brain images have a significant role in diagnosis of many

neuropsychiatric disorders such as Schizophrenia (SZ). In this work, Wasserstein-based

active contour and the texture features such as Hu moments and gray-level co-occurrence …

Diagnosis of schizophrenia disorder using wasserstein based active contour and texture features

MR3864245 Prelim Arbenz, Philipp; Guevara-Alarcón, William; Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint. J. Stat. Comput. Simul. 88 (2018), no. 16, 3193–3216. 62E17 (60B10)

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - Journal of Statistical Computation …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

sets in the size of millions of entries. We consider the situation when the information on a

large univariate data set or sample needs to be preserved, stored or transferred. We suggest …

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

Minimax statistical learning with Wasserstein distances

J Lee, M Raginsky - Advances in Neural Information Processing …, 2018 - papers.nips.cc

As opposed to standard empirical risk minimization (ERM), distributionally robust

optimization aims to minimize the worst-case risk over a larger ambiguity set containing the

original empirical distribution of the training data. In this work, we describe a minimax …

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a

data distribution and sample distribution. Recent studies have proposed stabilizing the

training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

pages 5769–5779, 2017. [5] B. Heidergott and FJ Vázquez-Abad …

Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

H Farooq, Y Chen, T Georgiou, C Lenglet - Computational Diffusion MRI, 2018 - Springer

Several studies have used structural connectivity information to parcellate brain areas like

the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult

to achieve using conventinal MRI techniques. They typically employ diffusion MRI (dMRI) …

[PDF] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

<—— 2018————2018—————— -240—

[PDF] u-psud.fr

T GOLVET, JD BENAMOU, G CARLIER… - 2018 - math.u-psud.fr

We study the numerical implementation of a minimizing movement scheme using the 1-

Wasserstein distance introduced in [1]. We implement this scheme using two different primal

dual algorithm: a Augmented Lagrangian technique with the ADMM algorithm and the …

CITATION] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018

Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

[CITATION] Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018

Gaometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

By: Li, Jia; Zhang, Fuqing

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS Volume: 27 Issue: 4 Pages: 785-797 Published: 2018

Data-driven affinely adjustable distributionally robust framework for unit commitment based on Wasserstein metric

W Hou, R Zhu, H Wei, H TranHoang - IET Generation, Transmission & …, 2018 - IET

This study proposes a data-driven distributionally robust framework for unit commitment

based on Wasserstein metric considering the wind power generation forecasting errors. The

objective of the constructed model is to minimise the expected operating cost, including the …

[CITATION] A Data-driven Affinely Adjustable Distributionally Robust Framework for Unit Commitment Based on Wasserstein Metric

R Zhu, W Hou, H Wei, H TranHoang - IET Generation, Transmission & …, 2018 - IET

… A Data-driven Affinely Adjustable Distributionally Robust Framework for Unit Commitment Based

on Wasserstein Metric. Access Full Text. A Data-driven Affinely Adjustable Distributionally Robust

Framework for Unit Commitment Based on Wasserstein Metric …

Unsupervised Feature Learning for Outlier Detection with Stacked Convolutional Autoencoders, Siamese Networks and Wasserstein Autoencoders:

Application to Epilepsy Detection

Z Alaverdyan, J Chai, C Lartizien - Deep Learning in Medical Image …, 2018 - Springer

In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric

(T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist

(MRI negative). We cast this problem as an outlier detection problem and adapt the …

[PDF] cnrs.fr

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network

L Ruan, B Chen, ML Lam - 2018 - projet.liris.cnrs.fr

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

Behavior of the empirical Wasserstein distance in R^ d under moment conditions

J Dedecker, F Merlevède - arXiv preprint arXiv:1807.09031, 2018 - arxiv.org

We establish some deviation inequalities, moment bounds and almost sure results for the

Wasserstein distance of order p $\in $[1, $\infty $) between the empirical measure of

independent and identically distributed R d-valued random variables and the common …

All 7 versions

MR3807373 Scricciolo, Catia Bayes and maximum likelihood for

L1-Wasserstein deconvolution of Laplace mixtures. Stat. Methods Appl. 27 (2018), no. 2, 333–362. 62F15 (60B10 62G07)

Bayes and maximum likelihood for L^1 -Wasserstein deconvolution of Laplace mixtures

C Scricciolo - Statistical Methods & Applications, 2018 - Springer

We consider the problem of recovering a distribution function on the real line from

observations additively contaminated with errors following the standard Laplace distribution.

Assuming that the latent distribution is completely unknown leads to a nonparametric …

[PDF] Learning Disentangled Representations with Wasserstein Auto-Encoders

PK Rubenstein, B Schoelkopf, I Tolstikhin - 2018 - openreview.net

Page 1. Workshop track - ICLR 2018 LEARNING DISENTANGLED REPRESENTATIONS WITH

WASSERSTEIN AUTO-ENCODERS Paul Rubenstein∗, Bernhard Schölkopf, Ilya Tolstikhin

Empirical Inference Max Planck Institute for Intelligent Systems, Tübingen 1paul.rubenstein,bs …

<—— 2018————2018—————— -250—

Potential Analysis; Findings in the Area of Potential Analysis Reported from Donghua University (Exponential Ergodicity for SDEs Driven by -Stable Processes with Markovian Switching in Wasserstein...

Journal of Technology & Science, Oct 28, 2018, 309

Newspaper Article: Full Text Online

[PDF] dagstuhl.de

Wasserstein Autoencoders for Collaborative Filtering

J Zhong, X Zhang - arXiv preprint arXiv:1809.05662, 2018 - arxiv.org

The recommender systems have long been investigated in the literature. Recently, users'

implicit feedback likeclick'orbrowse'are considered to be able to enhance the

recommendation performance. Therefore, a number of attempts have been made to resolve …

All 2 versions Cited by 6 Related articles All 3 versions

Wasserstein autoencoders for collaborative filtering

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

VA Nguyen, D Kuhn, PM Esfahani - arXiv preprint arXiv:1805.07194, 2018 - arxiv.org

We introduce a distributionally robust maximum likelihood estimation model with a

Wasserstein ambiguity set to infer the inverse covariance matrix of a $ p $-dimensional

Gaussian random vector from $ n $ independent samples. The proposed model minimizes …

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

by Nguyen, Viet Anh; Kuhn, Daniel; Esfahani, Peyman Mohajerin

05/2018 We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a...

Journal Article: Full Text Online

Sparse-View CT Reconstruction Using Wasserstein GANs

F Thaler, K Hammernik, C Payer, M Urschler… - … Workshop on Machine …, 2018 - Springer

We propose a 2D computed tomography (CT) slice image reconstruction method from a

limited number of projection images using Wasserstein generative adversarial networks

(wGAN). Our wGAN optimizes the 2D CT image reconstruction by utilizing an adversarial …

Sparse-View CT Reconstruction Using Wasserstein GANs

Distilled Wasserstein Learning for Word Embedding and Topic Modeling

H Xu, W Wang, W Liu, L Carin - Advances in Neural Information …, 2018 - papers.nips.cc

We propose a novel Wasserstein method with a distillation mechanism, yielding joint

learning of word embeddings and topics. The proposed method is based on the fact that the

Euclidean distance between word embeddings may be employed as the underlying …

Diffusing Policies: Towards Wasserstein Policy Gradient Flows

PH Richemond, B Maginnis - 2018 - openreview.net

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

MR3844536 Pending Mohajerin Esfahani, Peyman; Kuhn, Daniel Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations. Math. Program. 171 (2018), no. 1-2, Ser. A, 115–166. 90C15 (90C25 90C47)

Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable...

by Mohajerin Esfahani, Peyman; Kuhn, Daniel

Mathematical Programming, 09/2018, Volume 171, Issue 1

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein...

Journal Article: Full Text Online

Data-driven distributionally robust optimization using the Wasserstein ...

Mathematical Programming September 2018, Volume 171, Issue 1–2, pp 115–166 | Cite as

[HTML] Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - Mathematical Programming, 2018 - Springer

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

Data-driven distributionally robust optimization using the ...

Jul 7, 2017 - Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations. Peyman ...

by PM Esfahani - ‎2018 - ‎Cited by 432 - ‎Related articles

Image inpainting using Wasserstein Generative Adversarial Network

P Hua, X Liu, M Liu, L Dong, M Hui… - Optics and Photonics …, 2018 - spiedigitallibrary.org

Recent advances in convolution neural networks have shown promising results for the

challenging task of filling large missing regions in an image with semantically plausible and

context aware details. These learning-based methods are significantly more effective in …

<——2018————2018 ———————————260 ——

Approximate inference with Wasserstein gradient flows

C Frogner, T Poggio - arXiv preprint arXiv:1806.04542, 2018 - arxiv.org

We present a novel approximate inference method for diffusion processes, based on the

Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent

density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients …

[CITATION] Approximate inference with Wasserstein gradient flows. 2018

C Frogner, T Poggio - URL http://arxiv. org/abs, 1806

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

Regularizing feature distribution using sliced wasserstein distance for semi-supervised learning

Constructing Misfit Function for Full Waveform Inversion Based on Sliced Wasserstein Distance

F Chen, D Peter - 80th EAGE Conference and Exhibition 2018, 2018 - earthdoc.org

It has been proven that full waveform inversion (FWI) based on optimal transport (OT) is

robust against noise and contains less local minima. The accurate solution to OT problem on

the real line (1D) is analytical with the selected distance function which can be effectively …

On the computation of Wasserstein barycenters

G Puccetti, L Rüschendorf… - Available at SSRN …, 2018 - papers.ssrn.com

In recent years, the Wasserstein barycenter has become an important notion in the analysis

of high dimensional data with a broad range of applications in applied probability,

economics, statistics and in particular to clustering and image processing. We give a new …

[PDF] Wasserstein Divergence for GANs

J Wu, Z Huang, J Thoma, D Acharya… - Lecture Notes in …, 2018 - openaccess.thecvf.com

In many domains of computer vision, generative adversarial networks (GANs) have

achieved great success, among which the family of Wasserstein GANs (WGANs) is

considered to be state-of-the-art due to the theoretical contributions and competitive …

Sparsemax and Relaxed Wasserstein for Topic Sparsity

T Lin, Z Hu, X Guo - arXiv preprint arXiv:1810.09079, 2018 - arxiv.org

Topic sparsity refers to the observation that individual documents usually focus on several

salient topics instead of covering a wide variety of topics, and a real topic adopts a narrow

range of terms instead of a wide coverage of the vocabulary. Understanding this topic …

Sparsemax and Relaxed Wasserstein for Topic Sparsity

Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances

J Liu, W Yin, W Li, YT Chow - arXiv preprint arXiv:1810.00118, 2018 - arxiv.org

We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a

particular type of optimal transport distance with homogeneous of degree one ground metric.

Our algorithm is built on multilevel primal-dual algorithms. Several numerical examples and …

Sparsemax and relaxed wasserstein for topic sparsity

Denoising of 3-D Magnetic Resonance Images Using a Residual Encoder-Decoder Wasserstein Generative Adversarial Network

M Ran, J Hu, Y Chen, H Chen, H Sun, J Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

Structure-preserved denoising of 3-D magnetic resonance images (MRI) is a critical step in

the medical image analysis. Over the past years, many algorithms have been proposed with

impressive performances. Inspired by the idea of deep learning, in this paper, we introduce …

A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems

[PDF] arxiv.org pontrygin

B Bonnet, F Rossi - arXiv preprint arXiv:1810.13117, 2018 - arxiv.org Nov 28, 2018

In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control

problems in the Wasserstein space of probability measures. The dynamics, is described by a

transport equation with non-local velocities and is subject to end-point and running state …

A pontryagin maximum principle in wasserstein spaces for constrained optimal control problems

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

<——2018 -——————— 2018 -270—

[PDF] Semi-Supervised Pairing via Basis-Sharing Wasserstein Matching Auto-Encoder

Z Liu, YHH Tsai, M Yamada, R Salakhutdinov - bayesiandeeplearning.org

Semi-supervised pairing, learning explicit pairing relation between unlabeled input and

target distribution in an otherwise semisupervised setting, has recently attracted lots of

attention [16, 12], since data labeling is often time-consuming and requires lots of human …

MR3993926 Pending Malagò, Luigi; Montrucchio, Luigi; Pistone, Giovanni

Wasserstein Riemannian geometry of Gaussian densities. Inf. Geom. 1 (2018), no. 2, 137–179. 62B99 (15B48 53B05 60D05)

Wasserstein Riemannian geometry of Gaussian densities

L Malagò, L Montrucchio, G Pistone - Information Geometry, 2018 - Springer

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and

compute its tensor form with respect to the trace inner product. The tensor is a matrix which

is the solution to a Lyapunov equation. We compute the explicit formula for the Riemannian

exponential, the normal coordinates charts and the Riemannian gradient. Finally, the Levi …

Using Wasserstein GAN to generate high quality adversarial examples

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

Generative models with both discrete and continuous latent variables are highly motivated

by the structure of many real-world data sets. They present, however, subtleties in training

often manifesting in the discrete latent being under leveraged. In this paper, we show that …

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various

machine learning tasks, in recent years, they are found to be vulnerable to so-called

adversarial examples Specifically, take x is an element of D on which a neural network has …

Equivalence Between Wasserstein and Value-Aware Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. Recently Farahmand et al.(2017) proposed …

Gradient Flows for Frame Potentials on the Wasserstein Space

C Wickman, K Okoudjou - arXiv preprint arXiv:1808.09319, 2018 - arxiv.org

In this paper we bring together some of the key ideas and methods of two very lively fields of

mathematical research, frame theory and optimal transport, using the methods of the second

to answer questions posed in the first. In particular, we construct gradient flows in the …

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

Convergence in the Wasserstein Distance

R Douc, E Moulines, P Priouret, P Soulier - Markov Chains, 2018 - Springer

In the previous chapters, we obtained rates of convergence in the total variation distance of

the iterates P^ n of an irreducible positive Markov kernel P to its unique invariant measure π

for π-almost every x ∈ X and for all x ∈ X if the kernel P is irreducible and positive Harris …

Convergence in the Wasserstein Distance

A proximal ALM method for computing Wasserstein barycenter in D2-clustering of discrete distributions

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

This paper concerns with the computation of a Wasserstein barycenter, the centroid of a

collection of discrete probability distributions that minimizes the average of the $\ell_2 $-

Wasserstein distance, for which the support points are not pre-specified. It is known to be a …

[PDF] Shape space in terms of Wasserstein geometry and applications to quantum physics

B Lessel - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

… 102 A.2.2 John Lott's geometric calculations on Wasserstein space … If the initial conditions are appropriately chosen, such a curve of probability measures stemming from a solution of the Schrödinger equation can naturally be regarded as a curve in Wasserstein space …

Zbl 1437.53005

<——2018 -——————— 2018 —————280—

Bayesian Learning with Wasserstein Barycenters

G Rios, J Backhoff-Veraguas, J Fontbona… - arXiv preprint arXiv …, 2018 - arxiv.org

In this work we introduce a novel paradigm for Bayesian learning based on optimal transport

theory. Namely, we propose to use the Wasserstein barycenter of the posterior law on

models, as an alternative to the maximum a posteriori estimator (MAP) and Bayes predictive …

[PDF] oregonstate.edu

Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

J McClelland - 2018 - ir.library.oregonstate.edu

The UniFrac metric (Definitions 1.1. 13 and 1.1. 14) is a robust and well-used β-diversity

metric in metagenomics. Evans and Matsen demonstrated in [28], using the dual formulation

of the 1-Wasserstein metric (Definition 1.2. 4), that the UniFrac metric is the 1-Wasserstein …

WGAN = Wasserstein GAN

arXiv:1807.08501 [pdf, other]

cs.LG stat.ML

Generalization Bounds for Unsupervised Cross-Domain Mapping with WGANs

Authors: Tomer Galanti, Sagie Benaim, Lior Wolf

Abstract: The recent empirical success of cross-domain mapping algorithms, between two domains that share common characteristics, is not well-supported by theoretical justifications. This lacuna is especially troubling, given the clear ambiguity in such mappings. We work with the adversarial training method called the Wasserstein GAN. We derive a novel generalization bound, which limits the risk between the… ▽ More

Submitted 26 July, 2018; v1 submitted 23 July, 2018; originally announced July 20

WGAN Latent Space Embeddings for Blast Identification in Childhood Acute Myeloid Leukaemia

R Licandro, T Schlegl, M Reiter, M Diem… - 2018 24th …, 2018 - ieeexplore.ieee.org

Acute Myeloid Leukaemia (AML) is a rare type of childhood acute leukaemia. During

treatment, the assessment of the number of cancer cells is particularly important to

determine treatment response and consequently adapt the treatment scheme if necessary …

Feature article by pat laMarche, former co-host of the WGAN-AM Morning Show, on

P LaMarche - 1997 - digitalcommons.portlandlibrary.com

Feature article by pat laMarche, former co-host of the WGAN-AM Morning Show, on her

experiences on the show and with talk radio in general. LaMarche worked for WGAN from

August 1996 to May 1997, at which time she says she resigned, rescinded her resignation …

WGAN 을 이용한 Data Augmentation 기법

임세호， 신용구， 유철환， 이한규， 고성제 - 대한전자공학회 학술대회, 2017 - dbpia.co.kr

최근 영상 dataset 을 이용하여 network 를 학습시키는 연구가 활발히 진행되면서 영상 dataset

구축의 중요성이 증가하고 있다. 이에 학습에 필요한 dataset 의 수가 부족한 경우에는 기존

dataset 을르거나 회전시키는 등의 방법을 통해 인위적으로 dataset 의 수를 늘리는 data …

Data Augmentation Technique using WGAN

Lim Se - ho, Kyeong - gu, Yoo, Chul - hwan, Lee, Han - gyu, Ko Sung - Je, Korea Electronics and Telecommunications Research Institute Conference, 2017 - dbpia.co.kr

Recently, as researches to learn network by using image dataset have progressed actively, image dataset

The importance of building is increasing. If the number of datasets required for learning is insufficient,

Increase the number of datasets artificially through methods such as rotating or rotating dataset data ...

Korean

WGAN Domain Adaptation for EEG-Based Emotion Recognition

Y Luo, SY Zhang, WL Zheng, BL Lu - International Conference on Neural …, 2018 - Springer

In this paper, we propose a novel Wasserstein generative adversarial network domain

adaptation (WGANDA) framework for building cross-subject electroencephalography (EEG)-

based emotion recognition models. The proposed framework consists of GANs-like …

<-—2018 ——————— 2018 -290—

基於 Wasserstein 生成對抗網絡進行可解析之臉部特徵學習

何岡秩 - 2018 - ir.lib.ntust.edu.tw

我們提出透過Wasserstein 損失函數的生成對抗網路輔助擷取人臉屬性特徵 (Disentangle

Represenetation of Generative Adversarial Network] 進行跨角度人臉辨識(Cross Pose Face

Recognition), DR-WGAN 藉由Wasserstein-1 距離以及梯度懲罰的訓練機制取代DRGAN …

[ransformation of Identity-Preserved Facial Features using Wasserstein Generative Adversarial Network with Gradient Penalty

Researchers at University of Texas Target Geophysics (Application of optimal transport and the quadratic Wasserstein metric

to full-waveform inversion)

Journal of Technology & Science, 05/2018

Findings in the Area of Potential Analysis Reported from Donghua University (Exponential Ergodicity for SDEs Driven by -Stable Processes with Markovian Switching in Wasserstein...

Journal of Technology & Science, 10/2018

Newsletter: Full Text Online

The optimal convergence rate of monotone schemes for conservation laws in the Wasserstein distance

AM Ruf, E Sande, S Solem - arXiv preprint arXiv:1808.04661, 2018 - arxiv.org

In 1994, Nessyahu, Tadmor and Tassa studied convergence rates of monotone finite volume

approximations of conservation laws. For compactly supported, $\Lip^+ $-bounded initial

data they showed a first-order convergence rate in the Wasserstein distance. Our main result …

Studies from University of Hamburg Yield New Data on Geophysics

(Evaluating a stochastic parametrization for a fast-slow system using the Wasserstein...

Journal of Technology & Science, 07/2018

Newsletter: Full Text Online

www.nonlin-processes-geophys.net › npg-25-413-2018

PDF

Jun 19, 2018 - Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance. Gabriele Vissio. 1,2 and Valerio Lucarini. 2,3,4.

New Mathematics Study Findings Recently Were Reported by Researchers at Beijing Normal University

(W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

Journal of Technology & Science, 08/2018

Newsletter: Full Text Online

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

New Mathematics Study Findings Recently Were Reported by Researchers at Beijing Normal University (W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds)
Journal of Technology & Science. (Aug. 26, 2018) From Global Issues in Context. Full Text Online

arXiv:1812.11026 [pdf, other] stat.ME

Hybrid Wasserstein Distance and Fast Distribution Clustering

Authors: Isabella Verdinelli, Larry Wasserman

Abstract: We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms. The first term --- which has a closed form --- measures the location-scale differ… ▽ More

Submitted 28 December, 2018; originally announced December 2018.

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

L Cited by 14 Related articles All 3 versions

arXiv:1812.10190 [pdf, ps, other] math.PR

Exponential Contraction in Wasserstein Distance for Diffusion Semigroups with Irregular Drifts

Authors: Shao-Qin Zhang

Abstract: The exponential contraction in standard Wasserstein distance

W_q(μ_1 P_t, μ_2 P_t)\leq ce^{-\ka t}W_q(μ_1,μ_2),~t\geq 0, q\geq 1

is proved for the transition semigroup Pt

associated with stochastic differential equations driven by multiplicative noise. Our first result is obtained by using the coupling by reflection and a new auxiliary function. Conditions on coefficients are explicit and c… ▽ More

Submitted 27 December, 2018; v1 submitted 25 December, 2018; originally announced December 2018.

Comments: 42 pages

MSC Class: 60H10

arXiv:1812.09808 [pdf, other] math.OC cs.SY

Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approach

Authors: Insoon Yang

Abstract: Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, we investigate the problem of designing a control policy that is robust against errors in the empirical distribution obtained from data. This problem can be formulated… ▽ More

Submitted 23 December, 2018; originally announced December 2018.

Irmation Technology; Researchers at Oklahoma State University Report New Data on Information Technology (Data-driven risk-averse stochastic optimization with Wasserstein metric)

Obesity, Fitness & Wellness Week; Atlanta [Atlanta]28 Apr 2018: 616.

Newspaper Article: Full Text Online

<——2018 ——————— 2018 -300—

Potential Analysis; Findings in the Area of Potential Analysis Reported from Donghua University

(Exponential Ergodicity for SDEs Driven by -Stable Processes with Markovian Switching in Wasserstein...

Journal of Technology & Science, Oct 28, 2018, 309

Newspaper Article: Full Text Online

MR3846693 Indexed Majewski, Szymon; Ciach, Michał Aleksander; Startek, Michał; Niemyska, Wanda; Miasojedow, Błażej; Gambin, Anna The Wasserstein distance as a dissimilarity measure for mass spectra with application to spectral deconvolution. 18th International Workshop on Algorithms in Bioinformatics, Art. No. 25, 21 pp., LIPIcs. Leibniz Int. Proc. Inform., 113, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2018. 92E10

The Wasserstein Distance as a Dissimilarity Measure for Mass Spectra with Application to Spectral Deconvolution

S Majewski, MA Ciach, M Startek… - … on Algorithms in …, 2018 - drops.dagstuhl.de

We propose a new approach for the comparison of mass spectra using a metric known in the

computer science under the name of Earth Mover's Distance and in mathematics as the

Wasserstein distance. We argue that this approach allows for natural and robust solutions to …

MR3826859 Pending Hanasusanto, Grani A.; Kuhn, Daniel Conic programming reformulations to two-stage distributionally robust linear programs over Wasserstein balls. Oper. Res. 66 (2018), no. 3, 849–869. 90C15

Review PDF Clipboard Journal Article 2 Citations

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and

distributionally robust linear programs can often be reformulated exactly as conic programs

that scale polynomially with the problem dimensions. Specifically, when the ambiguity set

constitutes 2-Wasserstein ball centered at a discrete distribution, the distributionally robust …

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

New Berry-Esseen and Wasserstein bounds in the CLT for …

Abstract. We prove abstract bounds on the Wasserstein and Kolmogorov dis-tances between non-randomly centered random sums of real i.i.d. random variables with a nite third moment and the standard normal distribution. Except for the case of mean zero summands, these bounds involve a coupling of the summation

MR3807589 Bolley, François; Gentil, Ivan; Guillin, Arnaud; Kuwada, Kazumasa Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), no. 3, 845–880. (Reviewer: Francesco Rossi) 58J65 (53B21 53C21 58J35)
Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

F Bolley, I Gentil, A Guillin, K Kuwada - 2018 - hal-clermont-univ.archives-ouvertes …

The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein …

MR3795449 Trashorras, José Large deviations for a matching problem related to the

∞-Wasserstein distance. ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), no. 1, 247–278. 60F10 (60B05 60C05)

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots, Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of empirical measures. We establish a Large Deviations Principle for $(W_ {\infty}(L^ X_n, L^ Y_n)) _ {n\geq 1} $ where $ W_ {\infty} $ is the $\infty $-Wasserstein distance.

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

MR3787206 Briani, Maya; Cristiani, Emiliano; Iacomini, Elisa Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance. Commun. Math. Sci. 16 (2018), no. 1, 123–144. 35R02 (35L45 35L65 90B20 90Cxx)

M Briani, E Cristiani, E Iacomini - Communications in Mathematical …, 2018 - intlpress.com

In this paper we investigate the sensitivity of the LWR model on network to its parameters

and to the network itself. The quantification of sensitivity is obtained by measuring the

Wasserstein distance between two LWR solutions corresponding to different inputs. To this …

Communications in Mathematical Sciences,Volume 16 (2018)Number 1

Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance Pages: 123 – 144

DOI: http://dx.doi.org/10.4310/CMS.2018.v16.n1.a6

Abstract Wasserstein distance between two LWR solutions corresponding to different inputs. To this end, we propose a numerical method to approximate the Wasserstein distance between two density distributions defined on a network. We found a large sensitivity to the traffic distribution at junctions, the network size, and the network topolog

Learning and Inference with Wasserstein Metrics

By Charles Albert Frogner · 2018 MIT

Learning and Inference with Wasserstein Metrics

books.google.com › books

Charles Albert Frogner · 2018 · ‎No preview

In this work, we describe a novel approximate inference method, which is based on a characterization of the diffusion as following a gradient flow in a space of probability densities endowed with a W

2018

Mobile Application Network Behavior Detection and Evaluation with WGAN and Bi-LSTM

S Wei, P Jiang, Q Yuan, J Wang - TENCON 2018-2018 IEEE …, 2018 - ieeexplore.ieee.org

In this paper, we present a modeling and learning method to analyze the network behavior

of mobile applications based on the Android platform. Various application system sand

environmental factors are simulated in order to trigger different categories of application …

[PDF] vsu.ru

[PDF] СТРОГАЯ ТЕОРИЯ ПОТОКОВ ГРАДИЕНТАИ ГЕОДЕЗИЧЕСКОЙ ВЫПУКЛОСТИ ОТНОСИТЕЛЬНО ГЕОМЕТРИЧЕСКОЙ СТРУКТУРЫ ТИПА ХЕЛЛИНГЕРА-КАНТОРОВИЧА-ВАССЕРШТЕЙНА НА ПРОСТРАНСТВЕ КОНЕЧНЫХ МЕР РАДОНА∗

ДА Воротников - 2018 - vestnik.vsu.ru

Мы развили строгую теорию потоков градиента и геодезической выпуклости относительно геометрической структуры типа Хеллингера-Канторовича-Вассерштейна на пространстве конечных мер Радона. Это даст нам возможность …

Related articles [Russian RIGOROUS THEORY OF GRADIENT AND GEODESIC CONVEX FLOWS WITH RESPECT TO THE GEOMETRIC STRUCTURE OF THE HELLINGER-KANTOROVICH-WASERSTEIN TYPE IN THE SPACE OF FINITE RADON MEASURES]

<——2018 ——————— 2018 —— -310 —

Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

G Auricchio, F Bassetti, S Gualandi… - arXiv preprint arXiv …, 2018 - arxiv.org

… the exact Kantorovich-Wasserstein distance between a pair of d-dimensional histograms

having n bins each. We prove that this problem is equivalent to an uncapacitated minimum cost

flow problem on a (d + 1)-partite graph with (d + 1)n nodes and dn d+1 d arcs, whenever the …

MR3922439 Agueh, Martial; Carlier, Guillaume; Igbida, Noureddine On the minimizing movement with the 1-Wasserstein distance. ESAIM Control Optim. Calc. Var. 24 (2018), no. 4, 1415–1427. 35K59 (35D30 49N15)

On the minimizing movement with the 1-Wasserstein distance

M Agueh, G Carlier, N Igbida - ESAIM: Control, Optimisation and …, 2018 - esaim-cocv.org

… www.esaim-cocv.org ON THE MINIMIZING MOVEMENT WITH THE 1-WASSERSTEIN DISTANCE Martial Agueh 1,2 , Guillaume Carlier 3,∗ and Noureddine Igbida 4 Abstract … Page 3. ON THE MINIMIZING MOVEMENT WITH THE 1-WASSERSTEIN DISTANCE 1417 …

MR3902631 Kaňková, Vlasta; Omelčenko, Vadim Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric. Kybernetika (Prague) 54 (2018), no. 6, 1231–1246. 90C15 (60A10 60E15)

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

V Kaňková, V Omelčenko - Kybernetika, 2018 - dml.cz

Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall eg, problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem ${\cal U} $ of the utility functions. Especially, considering ${\cal U}:={\cal U} _ {1} $(where ${\cal U} _ {1} $ is a system of non decreasing concave nonnegative utility functions) we …

MR3828791 Pending Rao, Dhvanita R.; Kolte, Sagar Odd orthogonal matrices and the non-injectivity of the Vaserstein symbol. J. Algebra 510 (2018), 458–468.

19G12 (13C10 14B20 14D06 19D99)

Odd orthogonal matrices and the non-injectivity of the Vaserstein symbol

DR Rao, S Kolte - Journal of Algebra, 2018 - Elsevier

RA Rao–W. van der Kallen showed that the Vaserstein symbol V Γ ( S R 3 ) from the orbit space

of unimodular rows of length three over the coordinate ring of the real three sphere S R 3 modulo

elementary action to the elementary symplectic Witt group W E ( Γ ( S R 3 ) ) is not injective. Dhvanita …

РАСПРЕДЕЛЕННОЕ ВЫЧИСЛЕНИЕ БАРИЦЕНТРА ВАСЕРШТЕЙНА

ДМ Двинских - soc-phys.ipu.ru

… p на i q . Барицентр Васерштейна для дискретных распределений определяется как

решение следующей задачи (2) ( ) 1 , 1 min ( ) i p S n … Литература 1. ALLEN-ZHU Z., ORECCHIA

L. Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent …

Количественные модели и методы в исследованиях сложных сетей … Двинских Д. М. (Московский

физико-технический институт, Москва; Сколковский институт науки и технологий,

Москва) … Определим энтропийно-регуляризованное расстояние Васерштейна, порожденное …

…

Центральная предельная теорема для барицентров Васерштейна от гауссовских мер

А Крошнин, А Суворикова - ИТиС 2018, 2018 - elibrary.ru

В работе рассматривается пространство многомерных нормальных распределений, снабженное транспортным расстоянием 2-Васерштейна. Исследуются дифференциальные свойства оптимального транспортного отображения между …

[Russian Central limit theorem for Wasserstein barycenters of Gaussian measures]

WGAN Based Edge Preserved De-Blurring Using Perceptual Style Similarity

M Hong, Y Choe - … on Computer, Consumer and Control (IS3C), 2018 - ieeexplore.ieee.org

Generative Adversarial Network (GAN) is an effective generative model and can be used for de-blurring. In this paper, we propose an edge preserved de-blurring method using Wasserstein generative adversarial network with gradient penalty (WGAN-GP), which is …

The Wonderful Wasserstein GAN

Jun 6, 2018 - From now on, "Wasserstein GAN" is referred as "The original WGAN," while "Towards Principled Methods for Training Generative Adversarial Networks" is referred as "Preliminaries on WGAN."

The Wonderful Wasserstein GAN - Peiyuan (Alexander) Liao ...

Zheng Huabin‘s 《令人拍案叫绝的Wasserstein GAN》originally posted on Zhihu. ... But this doesn’t help the big picture, except that Wasserstein GAN (WGAN) did. ... It completely solves the instability of GAN training, where concerns on balance between generative/discriminative model training are no ...

Apr 10, 2018 · 23 min read

Mggan: Solving mode collapse using manifold guided training

D Bang, H Shim - arXiv preprint arXiv:1804.04391, 2018 - arxiv.org

Mode collapse is a critical problem in training generative adversarial networks. To alleviate

mode collapse, several recent studies introduce new objective functions, network

architectures or alternative training schemes. However, their achievement is often the result …

Расстояние Вассерштейна: WGAN и 2 кучи земли | OTU

Accelerated discrete distribution clustering under wasserstein distance

Jun 20, 2018 - И в центре этой теории как раз и лежит расстояние Вассерштейна. Если подробно разобрать оригинальную статью, то окажется, что в ...

<——2018 ——————— 2018 -320—

2018 patent

J Ye, J Li, JZ Wang - US Patent 10,013,477, 2018 - Google Patents

Computationally efficient accelerated D2-clustering algorithms are disclosed for clustering discrete distributions under the Wasserstein distance with improved scalability. Three first-order methods include subgradient descent method with re-parametrization, alternating direction method of multipliers (ADMM), and a modified version of Bregman ADMM. The effects of the hyper-parameters on robustness, convergence, and speed of optimization are thoroughly examined. A parallel algorithm for the modified Bregman ADMM method is tested …

GAN — Wasserstein GAN & WGAN-GP - Jonathan Hui - Medium

Do cost functions matter in the GAN training? This article is part of the GAN series which looks into the Wasserstein GAN (WGAN) and the WGAN-Gradient ...

Jonathan Hui

Jun 14, 2018 · 10 min read

MR3876126 Belavkin, Roman V. Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence. Information geometry and its applications, 363–373, Springer Proc. Math. Stat., 252, Springer, Cham, 2018. 60B05 (28A33 49Q20 62B10)

Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence

RV Belavkin - 2018 - eprints.mdx.ac.uk

We discuss a relation between the Kantorovich-Wasserstein (KW) metric and the Kullback-

Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in

the Kantorovich formulation. The latter is used to define entropy and mutual information …

Remote Sensing Image Deblurring Algorithm Based on WGAN

H Xia, C Liu - International Conference on Service-Oriented …, 2018 - Springer

Remote sensing images are blurred due to large and wide imaging, long shooting distance,

fast scanning speed, interference from external light, etc. At the same time, because of that

remote sensing images have the characteristics of diverse and dense shooting objects …

[PDF] iitp.ru

[PDF] Построение вложений вершин графов с помощью максимизации расстояния Вассерштейна

С Цепа, К Славнов, М Панов - ИТиС 2018, 2018 - itas2018.iitp.ru

Аннотация В данной работе мы рассматриваем способы представления вершин графов в виде числовых признаков для дальнейшего использования в задачах машинного обучения. Мы вводим специальную функцию потерь, которая оценивает …

[Russian Construction of embeddings of graph vertices by maximizing the Wasserstein distance]

MR3974671 Pending Amari, Shun-ichi; Karakida, Ryo; Oizumi, Masafumi

Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem. Inf. Geom. 1 (2018), no. 1, 13–37. 62B99 (49Q20 58D17 60A10 62B10)

[HTML] Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

S Amari, R Karakida, M Oizumi - Information Geometry, 2018 - Springer

Two geometrical structures have been extensively studied for a manifold of probability

distributions. One is based on the Fisher information metric, which is invariant under

reversible transformations of random variables, while the other is based on the Wasserstein

distance of optimal transportation, which reflects the structure of the distance between

underlying random variables. Here, we propose a new information-geometrical theory that

provides a unified framework connecting the Wasserstein distance and Kullback–Leibler …

Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in

each of the following cases:(a) X and Y are geodesic spaces and Y is covered by X via a

finite-sheeted locally isometric covering,(b) Y is the quotient of X by a finite group of

isometries,(c) Y is the L^ p L p-Wasserstein space over X. As an application of (a) we show

that all compact flat manifolds have Markov type 2 with constant 1. In particular the circle with …

| Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

Oregon State U Ph.D/ 2018

In the following we develop metagenomic tools arising from the classic Wasserstein metric as applied to questions regarding the diversity between microbial ...

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

magnetic resonance images of the brain, represented as densities on a voxel grid. We aim

to use the Wasserstein distance for dimensionality reduction of MR images by using it as a …

Visual feature attribution using wasserstein gans

CF Baumgartner, LM Koch… - Proceedings of the …, 2018 - openaccess.thecvf.com

… Consequently, often post-processing of the predictions is required [12, 13, 43] … Wasserstein GANs …

Wasser- stein GANs are a modification to the classic GAN paradigm where the discriminator is

replaced by a critic which does not have an activation function in its final layer and …

<——2018 ——————— 2018 —— 330—

Wasserstein distance, Fourier series and applications

S Steinerberger - arXiv preprint arXiv:1803.08011, 2018 - arxiv.org

We study the Wasserstein metric $ W_p $, a notion of distance between two probability

distributions, from the perspective of Fourier Analysis and discuss applications. In particular,

we bound the Earth Mover Distance $ W_1 $ between the distribution of quadratic residues …

[CITATION] Wasserstein distance

S Steinerberger - Fourier series and applications, 2018

Mobile Application Network Behavior Detection and Evaluation with WGAN and Bi-LSTM

By: Wei, Songjie; Jiang, Pengfei; Yuan, Qiuzhuang; et al.

Conference: IEEE-Region-10 Conference (IEEE TENCON) Location: IEEE Reg 10, SOUTH KOREA Date: OCT 28-31, 2018

Sponsor(s): IEEE Korea Council; IEIE; KICS; KIEE; KIEES; KIPS

PROCEEDINGS OF TENCON 2018 - 2018 IEEE REGION 10 CONFERENCE Book Series: TENCON IEEE Region 10 Conference Proceedings Pages: 0044-0049 Published: 2018

Times Cited: 1

2018

WGAN based Edge Preserved De-Blurring using Perceptual Style Similarity

By: Hong, Minsoo; Choe, Yoonsik

Conference: 4th International Symposium on Computer, Consumer and Control (IS3C) / 15th International Conference on Automation Technology (Auto) Location: Natl Chin Yi Univ Technol, Taichung, TAIWAN Date: DEC 06-08, 2018

Sponsor(s): IEEE; Natl Kaohsiung Univ Sci & Technol; IEEE Comp Soc; IEEE Power Elect Soc; Xian Univ Sci & Technol; Univ Miami; Chiang Mai Rajabhat Univ; Technol Univ Philippines; Batangas State Univ; Waseda Univ; City Univ Hong Kong; Natl Chung Hsing Univ; Natl Taiwan Univ; Natil Cheng Kung Univ; Natl Chung Cheng Univ; Hebei Univ Technol

2018 INTERNATIONAL SYMPOSIUM ON COMPUTER, CONSUMER AND CONTROL (IS3C 2018) Book Series: International Symposium on Computer Consumer and Control Pages: 58-61 Published: 2018

WGAN method based on text generation

6 citations*

Zhou Zhiheng , Li Lijun 2018

WGAN Latent Space Embeddings for Blast Identification in Childhood Acute Myeloid Leukaemia

By: Licandro, Roxane; Schlegl, Thomas; Reiter, Michael; et al.

Conference: 24th International Conference on Pattern Recognition (ICPR) Location: Chinese Acad Sci, Inst Automat, Beijing, PEOPLES R CHINA Date: AUG 20-24, 2018

Sponsor(s): Int Assoc Pattern Recognit; Chinese Assoc Automat

2018 24TH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR) Book Series: International Conference on Pattern Recognition Pages: 3868-3873 Published: 2018

WGAN Latent Space Embeddings for Blast Identification in Childhood Acute Myeloid Leukaemia

Single Image Super-Resolution Based on Improved WGAN

By: Yu, Lei; Long, Xiang; Tong, Chao

Conference: International Conference on Advanced Control, Automation and Artificial Intelligence (ACAAI) Location: Shenzhen, PEOPLES R CHINA Date: JAN 21-22, 2018

PROCEEDINGS OF THE 2018 INTERNATIONAL CONFERENCE ON ADVANCED CONTROL, AUTOMATION AND ARTIFICIAL INTELLIGENCE (ACAAI 2018) Book Series: Advances in Intelligent Systems Research Volume: 155 Pages: 101-104 Published: 2018 Cited by 3 Related articles

Sliced wasserstein auto-encoders

S Kolouri, PE Pope, CE Martin, GK Rohde - 2018 - openreview.net

In this paper we use the geometric properties of the optimal transport (OT) problem and the

Wasserstein distances to define a prior distribution for the latent space of an auto-encoder.

We introduce Sliced-Wasserstein Auto-Encoders (SWAE), that enable one to shape the …

Cited by 20 Related articles

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

X Zha - pdfs.semanticscholar.org

The tools developed in Topological data analysis are built upon persistence homology

theory, and their main output is a descriptor called persistence diagram (PD), which encodes

the topology of a space at all scales in the form of a point cloud with multiplicities in the …

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

PDF) A partial Laplacian as an infinitesimal generator on the Wasserstein space

Jan 2, 2018 - PDF | We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled ...

<——2018 ——————— 2018 —— 340—

On the Wasserstein distance between mutually singular measures

Jan 17, 2018 - where W denotes the p-Wasserstein distance and 𝒜 is a class of Borel probabilities that are singular with respect to μ. For all the background ...

by G Buttazzo - ‎2020 - ‎Cited by 1 - ‎Related articles

‎Introduction · ‎Notation and preliminaries · ‎Some optimization problems

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as

uncertain factors. This paper proposes a data-driven distributionally robust optimization

model for the optimal gas-power flow problem with uncertain wind generation. The concept

of zonal line pack and line pack reserve are raised to topologically distinguish fuel suppliers …

Cited by 48 Related articles A

Deep learning framework DNN with conditional WGAN for protein solubility prediction

X Han, L Zhang, K Zhou, X Wang - arXiv preprint arXiv:1811.07140, 2018 - arxiv.org

Protein solubility plays a critical role in improving production yield of recombinant proteins in

biocatalyst and pharmaceutical field. To some extent, protein solubility can represent the

function and activity of biocatalysts which are mainly composed of recombinant proteins …

Odd orthogonal matrices and the non-injectivity of the Vaserstein symbol

DR Rao, S Kolte - Journal of Algebra, 2018 - Elsevier

RA Rao–W. van der Kallen showed that the Vaserstein symbol V Γ (SR 3) from the orbit

space of unimodular rows of length three over the coordinate ring of the real three sphere

SR 3 modulo elementary action to the elementary symplectic Witt group WE (Γ (SR 3)) is not …

Cited by 1 Re

[PDF] Центральная предельная теорема для барицентров Васерштейна от гауссовских мер

А Крошнин, А Суворикова - ИТиС 2018, 2018 - itas2018.iitp.ru

Объекты, которые можно рассматривать как вероÿтностные распределениÿ,

возникают в самых разных областÿх. Зачастую необходимо исследовать их, учитываÿ

геометрию пространства, на котором они определены. Так, один из естественных …

[PDF] … ОТНОСИТЕЛЬНО ГЕОМЕТРИЧЕСКОЙ СТРУКТУРЫ ТИПА ХЕЛЛИНГЕРА-КАНТОРОВИЧА-ВАССЕРШТЕЙНА НА ПРОСТРАНСТВЕ КОНЕЧНЫХ МЕР …

[Russian Central limit theorem for the Vaserstein biricenters of measures]

[PDF] vsu.ru

ДА Воротников - Вестник Воронежского государственного …, 2018 - vestnik.vsu.ru

Мы развили строгую теорию потоков градиента и геодезической выпуклости

относительно геометрической структуры типа Хеллингера-Канторовича-

Вассерштейна на пространстве конечных мер Радона. Это даст нам возможность …

Correcting Nuisance Variation using Wasserstein Distance

G Tabak, M Fan, SJ Yang, S Hoyer, G Davis - 2018 - openreview.net

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological

information resulting from various factors affecting the cells. One motivating application is

drug development: morphological cell features can be captured from images, from which …

基于 Wasserstein 直方图欧氏度量的图像重复区域盲检测算法

杜振龙，叶超，李晓丽，沈海洋，宋国美 - 光学与光电技术, 2018 - cnki.com.cn

提出了一种利用Wasserstein 重心坐标作为图像描述子的图像重复区域盲检测算法.

通过度量各图像块Wasserstein 重心坐标间的最小欧式距离确定图像重复区域初始搜索块,

再对初始搜索块进行扩展, 利用改进的PatchMatch 算法寻找相关度高的图像块 …

融合 Wasserstein 距离的图像生成循环对抗网络模型及其应用研究

[CHINESE Blind detection algorithm for image repeated region based on Wasserstein histogram Euclidean metric]

张春平 - 2018 - cdmd.cnki.com.cn

大多数图像处理方法都采用监督式学习算法, 而监督式学习对图像数据要求较高, 需要大量标签,

导致人工成本急剧上升, 而无监督学习则降低了对图像数据的人工标记要求.

生成模型即是一种无监督学习算法, 同时, 也是一种典型的深度学习算法, 具有很好的语义理解 …

[CHINESE Research on Image Generation Cyclic Adversarial Network Model and Its Application Based on Wasserstein Distance]

[PDF] Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DF Fonseca Valero - repositorio.uniandes.edu.co

En el presente trabajo estudiaremos los problemas de Optimización Robusta Distribucional

DRO, estos son problemas de optimización estocástica formulados desde una visión

robusta, esta visión consiste en asumir que la distribución verdadera de la variable aleatoria …

[CITATION] Wasserstein 거리를 이용한 feature selection

지종호， 신현정 - 한국정보과학회 학술발표논문집, 2018 - dbpia.co.kr

요 약그래프기반 준지도학습 (graph based semi-supervised learning) 은 그래프를 어떻게

만드냐에 따라 성능이 달라진다. 특히, 그래프의 엣지는 레코드 간 유사도로 생성되는데

유사도가 어떻게 정의되는가는 준지도학습의 성능에 상당한 영향을 미친다. 일반적으로 가장 …

[CITATION] Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DFF Valero - 2018 - Uniandes
<——2018 ——————— 2018———350-—

Wasserstein GANによるスタイル制御可能なフォント生成

https://www.ieice.org › ken › paper

https://www.ieice.org › ken › paper · Translate this page

Missing: (メディア ‎エクス ‎ペリ ‎エン

[CITATION] Wasserstein GAN によるスタイル制御可能なフォント生成 (メディアエクスペリエンス·バーチャル環境基礎)

阿部耕太郎，早志英朗，内田誠一 - 電子情報通信学会技術研究報告= IEICE …, 2018 - ci.nii.ac.jp

… 検索. すべて. 本文あり. すべて. 本文あり. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN.

巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. Wasserstein

GANによるスタイル制御可能なフォント生成 (メディアエクスペリエンス·バーチャル環境基礎) …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

[JAPANESE Style-controllable font generation with Wasserstein GAN (Media Experience Virtual Environment Foundation)]

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

… typical phenomenon of the system {µPt}t≥0,µ∈P(Rd) associated with some important models is the following exponential contraction in the Wasserstein distance … 1.2) with c =1(κ may be negative) is equivalent to that the curvature of the generator of the diffusion is bounded …

Dimension-free Wasserstein contraction of nonlinear filters - arXiv

by Whiteley, Nick

For a class of partially observed diffusions, sufficient conditions are given for the map from initial condition of the signal to filtering distribution to be...

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics...

by Hao Wu; Peter C. Ma; Yu Lv; More...

2018 AIAA Aerospace Sciences Meeting

Book ChapterFull Text Online

ентральная предельная теорема для барицентров Васерштейна ОТ ГАУССОВСКИХ МЕР

itas2018.iitp.ru › media › papers

- Translate this page

Аннотация. В работе рассматривается пространство многомерных нормальных распределений, снабженное транспортным расстояни-.

by А Крошнин - ‎Related articles

Распределенное вычисление барицентра Васерштейна

WGAN model method based on depth convolution nerve network

Перейти к основному содержанию. Вторая всероссийская междисциплинарная конференция «СОЦИОФИЗИКА И СОЦИОИНЖЕНЕРИЯ». Россия, Москва, ИПУ РАН, 23 - 25 мая 2018 г. Главное меню. Новости · Кратко · Тематика ...

конференция «СОЦИОФИЗИКА И СОЦИОИНЖЕНЕРИЯ». Россия, Москва, ИПУ РАН, 23 -

25 мая 2018 г. Главное меню. Новости · Кратко · Тематика ..

[RUSSIAN EXTENDED COMPUTATION OF WASSERSTEIN BARYCENTERS[
See 2020

Fuzzy-detection seed set generation method and generator based on WGAN (Wasserstein GAN) model

Zhou Zhiheng , Li Lijun 2018

[PDF] sjtu.edu.cn WGAN Domain Adaptation for EEG-Based Emotion Recognition

2018 Ji Shouling , Lyu Chenyang , Chen Jianhai , Li Yuwei

Y Luo, SY Zhang, WL Zheng, BL Lu - International Conference on Neural …, 2018 - Springer

In this paper, we propose a novel Wasserstein generative adversarial network domain

adaptation (WGANDA) framework for building cross-subject electroencephalography (EEG)-

based emotion recognition models. The proposed framework consists of GANs-like …

WGAN-based hyper-parameter dynamic adjustment method

WGAN-model-based hole convolution method

2018 Zhou Zhiheng , Li Lijun

<-—2018 — —2018———360—-

Wasserstein distributionally robust kalman filtering

2018 Zhou Zhiheng , Li Liju

by Soroosh Shafieezadeh-Abadeh profile imageSoroosh Shafieezadeh-Abadeh

Viet Anh Nguyen profile image Viet Anh Nguyen

Daniel Kuhn profile image Daniel Kuhn

Peyman Mohajerin Esfahani profile imagePeyman Mohajerin Esfahani

Publication: NIPS'18: Proceedings of the 32nd International Conference on Neural Information Processing Systems December 2018 Pages 8483–8492

Wasserstein Distributionally Robust Kalman Filtering

WGAN-model-based hole convolution method

Wasserstein discriminant analysis | SpringerLink

2018 Zhou Zhiheng , Li Lijun

May 18, 2018 — Wasserstein discriminant analysis (WDA) is a new supervised linear ... family of dimensionality reduction methods (Van Der Maaten et al. ... maximize the ratio of the regularized Wasserstein distances between inter ... 2015) have made them scalable to dimensions relevant to machine learning applications.

by R Flamary · ‎2018 · ‎Cited by 43 · ‎Related articles

Machine Learning volume 107, pages1923–1945(2018)

WGAN model-based decomposition convolution method

Image channel fusion method based on WGAN model

2018 Zhou Zhiheng , Li Lijun

How does the complexity of critic affect the performance of WGAN

2018 Zhou Zhiheng ,

Li Lijun

Iohara Akihiro , Tanaka Toshiyuki

2018 IEICE Technical Report; IEICE Tech. Rep.

WGAN model-based pedestrian detection method

On isometric embeddings of Wasserstein spaces--the discrete case

2018 Zhou Zhiheng , Li Lijun , Xu Jing , Zhu Xiangjun , Li Liping

see all 6 authors

The invention discloses a WGAN model-based pedestrian detection method, which belongs to the field of deep learning neural networks. The method comprises the following steps: S1, a primary generativeadversarial network model is constructed; S2, a Wasserstein distance is constructed as an evaluation index for the adversarial network model; S3, random noise are initialized and inputted to a generator; S4, a pedestrian image dataset is prepared and is inputted to a discriminator for training; and S5, a loss function obtained by pedestrian detection operation is inputted to the generator for follow-up training. According to the WGAN model-based pedestrian detection method, through introducing the Wasserstein distance, the training quality of the whole network can be evaluated, the pedestrianimage dataset is inputted to the discriminator, the ability of the discriminator is trained continuously, and the accurate position of a pedestrian can be accurately discriminated in a complex road image. Less

2018

G Pál Gehér, T Titkos, D Virosztek - arXiv, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

online

A Method to Accelerate the Training of WGAN

by Sun, Qi; Wang, Wei

2018 5th International Conference on Information Science and Control Engineering (ICISCE), 07/2018

Generative adversarial network draw much attention in recent years because of its impressive results. The idea of adversary was cleverly introduced to the...

Conference ProceedingFull Text Online

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A Method to Accelerate the Training of WGAN

by Qi Sun; Wei Wang

The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings, 01/2018

Conference Title: 2018 5th International Conference on Information Science and Control Engineering (ICISCE) Conference Start Date: 2018, July 20 Conference End...

Conference ProceedingCitation Online

Cited by 1 Related articles All 3 versions
<——2018——2018 — —370—

Improved AC-WGANs based unmanned aerial vehicle signal recognition detecting algorithm

by ZHAO CAIDAN; CHEN CAIYUN; HUANG LIANFEN

06/2018

An improved AC-WGANs based unmanned aerial vehicle signal recognition detecting algorithm includes steps: S1, acquiring radio-frequency signals of a wireless...

PatentCitation Online

WGAN model-based decomposition convolution method

by LI LIJUN; ZHOU ZHIHENG

04/2018

The invention discloses a WGAN model-based decomposition convolution method and belongs to the field of a deep learning neural network. The method comprises...

PatentCitation Online

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Odd orthogonal matrices and the non-injectivity of the Vaserstein symbol

By: Rao, Dhvanita R.; Kolte, Sagar

JOURNAL OF ALGEBRA Volume: ‏ 510 Pages: ‏ 458-468 Published: ‏ SEP 15 2018

wasserstein auto-encoders - OpenReview

openreview.net › pdf

We propose the Wasserstein Auto-Encoder (WAE)—a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of.

by I Tolstikhin · ‎2018 · ‎Cited by 457 · ‎Related articles

WGAN Based Edge Preserved De-Blurring Using Perceptual Style Similarity

M Hong, Y Choe - … on Computer, Consumer and Control (IS3C), 2018 - ieeexplore.ieee.org

Generative Adversarial Network (GAN) is an effective generative model and can be used for

de-blurring. In this paper, we propose an edge preserved de-blurring method using

Wasserstein generative adversarial network with gradient penalty (WGAN-GP), which is …

Remote Sensing Image Deblurring Algorithm Based on WGAN

2018

H Xia, C Liu - International Conference on Service-Oriented …, 2018 - Springer

Remote sensing images are blurred due to large and wide imaging, long shooting distance,

fast scanning speed, interference from external light, etc. At the same time, because of that

remote sensing images have the characteristics of diverse and dense shooting objects …

A Method to Accelerate the Training of WGAN

Q Sun, W Wang - 2018 5th International Conference on …, 2018 - ieeexplore.ieee.org

Generative adversarial network draw much attention in recent years because of its

impressive results. The idea of adversary was cleverly introduced to the training of the

network. And the result was used in the value function to evaluate the quality of the network …

Deep learning framework DNN with conditional WGAN for protein solubility prediction

X Han, L Zhang, K Zhou, X Wang - arXiv preprint arXiv:1811.07140, 2018 - arxiv.org

Protein solubility plays a critical role in improving production yield of recombinant proteins in

biocatalyst and pharmaceutical field. To some extent, protein solubility can represent the

function and activity of biocatalysts which are mainly composed of recombinant proteins …

WGAN latent space embeddings for blast identification in childhood acute myeloid leukaemia

R Licandro, T Schlegl, M Reiter, M Diem… - 2018 24th …, 2018 - ieeexplore.ieee.org

Acute Myeloid Leukaemia (AML) is a rare type of childhood acute leukaemia. During

treatment, the assessment of the number of cancer cells is particularly important to

determine treatment response and consequently adapt the treatment scheme if necessary …

[PDF] atlantis-press.com

Single image super-resolution based on improved WGAN

L Yu, X Long, C Tong - 2018 International Conference on …, 2018 - atlantis-press.com

SRGAN has successfully applied the Generative Adversarial Network to the single image

super-resolution reconstruction, which has achieved good results. But the loss function

based on feature space in SRGAN objectively sacrifices the pursuit of high peak signal-to …

WGAN domain adaptation for EEG-based emotion recognition

<-—2018 — —2018——380—

[PDF] sjtu.edu.cn

Y Luo, SY Zhang, WL Zheng, BL Lu - International Conference on Neural …, 2018 - Springer

In this paper, we propose a novel Wasserstein generative adversarial network domain

adaptation (WGANDA) framework for building cross-subject electroencephalography (EEG)-

based emotion recognition models. The proposed framework consists of GANs-like …

Uncoupled isotonic regression via minimum Wasserstein ...

Evaluating a stochastic parametrization for a fastslow system ...

Jun 27, 2018 — Uncoupled isotonic regression via minimum Wasserstein deconvolution. Authors:Philippe Rigollet, Jonathan Weed · Download PDF. Abstract: ...

by P Rigollet · ‎2018 · ‎Cited by 35 · ‎Related articles

centaur.reading.ac.uk › npg-25-413-2018-2

PDF

Jun 19, 2018 — Evaluating a stochastic parametrization for a fast–slow system using ... and constructed by coupling the Lorenz 84 (Lorenz, 1984) model with ...

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Generative model based on minimizing exact empirical wasserstein distance

A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

… They proposed instead using the Wasserstein-1 distance W1(q, p), which is defined as the

minimum cost of transporting mass in order to transform the distribution q into the distribution p…

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

… We show quantitative rates of exponential convergence to equilibrium in a well chosen Wasserstein-1 distance. We use the Wasserstein-1 version of Harris’s theorem introduced by …

2018

2018 patent

Human face gender discrimination algorithm based on Wasserstein distance

CN CN111046708A 徐江涛天津大学青岛海洋技术研究院

Priority 2018-10-15 • Filed 2018-10-15 • Published 2020-04-21

1. The human face gender discrimination algorithm based on the Wasserstein distance is characterized in that: the method comprises three steps, wherein the first step is to construct a comparison library, and select different genders to construct comparison libraries with different distributions;

[PDF] Центральная предельная теорема для барицентров Васерштейна от гауссовских мер

А Крошнин, А Суворикова - ИТиС 2018, 2018 - itas2018.iitp.ru

Объекты, которые можно рассматривать как вероÿтностные распределениÿ,

возникают в самых разных областÿх. Зачастую необходимо исследовать их, учитываÿ

геометрию пространства, на котором они определены. Так, один из естественных …

A note on reinforcement learning with Wasserstein distance ...

[Russian Central limit theorem for Vaserstein barycenters of gaussian measurees]

www.researchgate.net › publication › 323142105_A_note...

Request PDF | A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning | In this note we describe an ...

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

Sliced-Wasserstein Autoencoder: An Embarrassingly Simple ...

Apr 5, 2018 — Title:Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model. Authors:Soheil Kolouri, Phillip E. Pope, Charles E. Martin, ...

[CITATION] Sliced-wasserstein autoencoder: an embarrassingly simple generative model. arXiv e-prints

S Kolouri, PE Pope, CE Martin, GK Rohde - 2018

[CITATION] Sliced-wasserstein autoencoder: an embarrassingly simple generative model. arXiv e-prints

S Kolouri, PE Pope, CE Martin, GK Rohde - 2018

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

[PDF] osu.edu

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology

theory, and their main output is a descriptor called persistence diagram (PD), which encodes

the topology of a space at all scales in the form of a point cloud with multiplicities in the …

<ß——2018 –— —2018—————390—

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

Page 1. AMMI – Introduction to Deep Learning 10.2. Wasserstein GAN François Fleuret

https://fleuret.org/ammi-2018/ Wed Aug 29 16:57:14 CAT 2018 ÉCOLE POLYTECHNIQUE

FÉDÉRALE DE LAUSANNE Page 2. Arjovsky et al. (2017) point out that DJS does not …

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

W-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

Application of optimal transport and the quadratic Wasserstein ...

Nov 7, 2018 — Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties. Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions.

[CITATION] Laetita Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty.

“Fused Gromov-Wasserstein distance for structured objects: theoretical foundations …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

library.seg.org › doi › abs › geo2016-0663

Jan 5, 2018 — When the observed and predicted seismic data are considered to be two density functions, the quadratic Wasserstein metric corresponds to the ...

by Y Yang · ‎2018 · ‎Cited by 119 · ‎Related articles

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion: Geophysics, 83

Y Yang, B Engquist, J Sun, BF Hamfeldt - R43–R62, 2018

Application of optimal transport and the quadratic Wasserstein ...

https://library.seg.org › doi › abs › geo2016-0663

by Y Yang · 2018 · Cited by 128 — ABSTRACTConventional full-waveform inversion (FWI) using the least-squares norm as a misfit function is known to suffer fro

2018

2018 see 2019

wasserstein metric-driven bayesian inversion with ...

https://www.semanticscholar.org › paper

Jul 21, 2018 — We apply the new framework to a class of signal processing problems, that is, the inverse uncertainty quantification of waveforms, ...

[CITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018

Exact weights, path metrics, and algebraic Wasserstein distances

P Bubenik, J Scott, D Stanley - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

… We use this distance to define Wasserstein distances, which coincide with the previously

defined Wasserstein distances for one-parameter persistence modules. For one-parameter …

S Cited by 1

Adversarial Lipschitz Regularization \| OpenReview	Oct 3, 2019
On Convergence and Stability of GANs \| OpenReview	Nov 14, 2017
DISTRIBUTIONAL CONCAVITY REGULARIZATION FOR GANS	Oct 3, 2018
Improving the Improved Training of Wasserstein GANs: A ...	Nov 16, 2017
More results from openreview.net

ON THE REGULARIZATION OF WASSERSTEIN GANS

openreview.net › pdf

by H Petzka · 2018 · Cited by 104 — Accordingly, this version of GAN was called. Wasserstein GAN (WGAN). The change of

201[PDF] neurips.cc

Distilled wasserstein learning for word embedding and topic modeling

H Xu, W Wang, W Liu, L Carin - Advances in Neural …, 2018 - proceedings.neurips.cc

… 21] use the same framework as ours, computing underlying distances based on … Feature Metric

Dim … pooling of the code embeddings and calculate the Euclidean distance between them …

Malliavin-Stein Method: a Survey of Recent Developments

E Azmoodeh, G Peccati - arXiv preprint arXiv:1809.01912, 2018 - arxiv.org

… In particular, the Malliavin-Stein approach captures and amplifies the essence of [C09], where Stein's … hand, we aim at presenting the essence of the Malliavin-Stein's method for functionals … the connection between Malliavin calculus and the version Stein's method presented in …

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

Wasserstein Divergence for GANs | SpringerLink

<——2018 — —2018——— 400—

link.springer.com › chapter

by J Wu · 2018 · Cited by 44 — Benefiting from the non-challenging constraint required by the W-div, we introduce Wasserstein divergence GANs (WGAN-div) as its practical ...

[CITATION] Wasserstein divergence for gans

W Jiqing, H Zhiwu, T Janine, A Dinesh, VG Luc - ECCV, 2018

Wasserstein Divergence for GANs

2018 PDF
Spatial-aware Network using Wasserstein Distance for Unsupervised Domain Adaptation
by Y Chen · 2018 · Cited by 1 — tEuclidean, metric, and Wassersteinu gradient flows: an overview. Bulletin of Mathematical Sciences 7 87–154. Shang, H. L. and Hyndman, ...

[PDF] osu.edu

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Γ-convergence of Entropy Regularized Wasserstein …

S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized

optimal transport (OT) problem to the non-regularized OT problem, as described in

[CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

2018

Zakai-Type Bound for Periodic Stochastic Filtering - IEEE Xplore

https://ieeexplore.ieee.org › iel7ß

by E Nitzan · 2018 · Cited by 3 — We derive a Bobrovsky-Zakai-type bound for mixed periodic and nonperi- odic stochastic filtering. Then, we derive a recursive computation method ...

[CITATION] … –Zakai-Type Bound for Periodic Stochastic Filtering............ E. Nitzan, T. Routtenberg, and J. Tabrikian 1460 Wasserstein-Distance-Based Gaussian …

S Khanna, CR Murthy, L Hu, J Zhang, X Wang, S Wang… - ieeexplore.ieee.org

LETTERS Digital and Multirate Signal Processing Recovery of the Starting Times of Delayed

Signals . . . . . . . . . . . . . . . . . . . . . . . . LC Perotti, D. Vrinceanu, and D. Bessis … An Optimal-Dimensionality

Sampling for Spin-s Functions on the Sphere …

[CITATION] … –Zakai-Type Bound for Periodic Stochastic Filtering............ E. Nitzan, T. Routtenberg, and J. Tabrikian 1460 Wasserstein-Distance-Based Gaussian …

S Khanna, CR Murthy, L Hu, J Zhang, X Wang, S Wang… - ieeexplore.ieee.org

LETTERS Digital and Multirate Signal Processing Recovery of the Starting Times of Delayed

Signals . . . . . . . . . . . . . . . . . . . . . . . . LC Perotti, D. Vrinceanu, and D. Bessis … An Optimal-Dimensionality

Sampling for Spin-s Functions on the Sphere …

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

Using Wasserstein GAN to generate high quality adversarial examples

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various

machine learning tasks, in recent years, they are found to be vulnerable to so-called

adversarial examples Specifically, take x is an element of D on which a neural network has …

On the Convergence and Robustness of Training GANs with ...

Feb 22, 2018 — A popular GAN formulation is based on the use of Wasserstein distance as ... to stationarity for a proposed class of GAN optimization algorithms. ... our algorithm only requires solving the discriminator to approximate optimality.

[CITATION] Solving approximate Wasserstein GANs to stationarity

M Sanjabi, J Ba, M Razaviyayn, JD Lee - arXiv preprint arXiv:1802.08249, 2018

[PDF] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018 - imo.universite-paris-saclay.fr

We study the numerical implementation of a minimizing movement scheme using the 1-

Wasserstein distance introduced in [1]. We implement this scheme using two different primal

dual algorithm: a Augmented Lagrangian technique with the ADMM algorithm and the …

[PDF] crest.science

[PDF] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

This article introduces a new non-linear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so called displacement interpolations (aka Wasserstein …

[PDF] impa.br

[PDF] Large Deviations for a matching problem related to the∞-Wasserstein distance

J Trashorras - ALEA, 2018 - alea.impa.br

Abstract. Let (E,d) be a compact metric space, X = (X1,...,Xn,... ) and Y = (Y1,...,Yn,... ) two independent

sequences of independent E-valued random variables and (LX n )n≥1 and (LY n )n≥1 the associated

sequences of empirical mea- sures. We establish a Large Deviation Principle for (W∞(LX …

[PDF] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

<——2018 — —2018——————410 —

G Vissio, V Lucarini - pdfs.semanticscholar.org

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modelling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

H Farooq, Y Chen, T Georgiou, C Lenglet - Computational Diffusion MRI, 2018 - Springer

Several studies have used structural connectivity information to parcellate brain areas like

the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult

to achieve using conventional MRI techniques. They typically employ diffusion MRI (dMRI) …

Wasserstein distance guided representation learning for domain adaptation

[PDF] aaai.org

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

domain via utilizing the knowledge distilled from a source domain which has a different but

related data distribution. One solution to domain adaptation is to learn domain invariant …

Graph clustering and the nuclear Wasserstein metric

D Roux Uribe - 2018 - repositorio.uniandes.edu.co

INTRODUCTION: one of the most relevant situations in public health in Colombia is child

stunting and in parallel, the social effects caused by armed conflict. Currently, it is unknown if

exposure to armed conflict is related to child stunting. OBJECTIVES: identify if significant …

Type spaces and Wasserstein spaces

S Song - Journal of the Korean Mathematical Society, 2018 - koreascience.or.kr

Abstract Types (over parameters) in the theory of atomless random variable structures

correspond precisely to (conditional) distributions in probability theory. Moreover, the logic

(resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) …

2018

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

Résumé Cette thèse se concentre sur l'analyse de données présentées sous forme de

mesures de probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension

des outils statistiques usuels sur cet espace muni de la distance de Wasserstein. Une …

Diffusing Policies: Towards Wasserstein Policy Gradient Flows

PH Richemond, B Maginnis - 2018 - openreview.net

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

[PDF] Wasserstein GAN: Technical Report

C Eteke - pdfs.semanticscholar.org

Even though the introduction of Generative Adversarial Nets lead to amazing applications

and results, the training of these models are highly instable and always regarded as a black

box. This is a technical report for the term project of the course COMP 541: Deep Learning …

Discrete Wasserstein Generative Adversarial Networks (DWGAN)

R Fathony, N Goela - 2018 - openreview.net

Generating complex discrete distributions remains as one of the challenging problems in

machine learning. Existing techniques for generating complex distributions with high

degrees of freedom depend on standard generative models like Generative Adversarial …

[PDF] ON WASSERSTEIN ISOMETRIES OF PROBABILITY MEASURES ON UNIT SPHERES

D VIROSZTEK - arXiv preprint arXiv:1802.03305, 2018 - researchgate.net

We consider the space of all Borel probability measures on the unit sphere of a Euclidean

space endowed with the Wasserstein metric Wp for arbitrary p≥ 1. Our goal is to describe

the isometry group of this metric space. We make some progress in the direction of a Banach …

<——2018 ——2018 — —420—

Wasserstein Adversarial Mixture Clustering

W Harchaoui, A Almansa, PA Mattei, C Bouveyron - 2018 - hal.archives-ouvertes.fr

Clustering complex data is a key element of unsupervised learning which is still a

challenging problem. In this work, we introduce a deep approach for unsupervised

clustering based on a latent mixture living in a low-dimensional space. We achieve this …

Cited by 57 Related articles

[CITATION] Yong Yu. Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang - Thirty-Second AAAI Conference on Artificial …, 2018 see 2017

On the minimizing movement with the 1-Wasserstein distance

M Agueh, G Carlier, N Igbida - ESAIM: Control, Optimisation and …, 2018 - esaim-cocv.org

We consider a class of doubly nonlinear constrained evolution equations which may be

viewed as a nonlinear extension of the growing sandpile model of [L. Prigozhin, Eur. J. Appl.

Math. 7 (1996) 225–235.]. We prove existence of weak solutions for quite irregular sources …

[PDF] aimsciences.org

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

[PDF] Wasserstein natural gradient in statistical manifolds with continuous sample space

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - pdfs.semanticscholar.org

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample spaces. Our approach is to pull back the L2-Wasserstein metric tensor in the

probability density space to a parameter space, equipping the latter with a positive definite …

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

[PDF] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018 - imo.universite-paris-saclay.fr

We study the numerical implementation of a minimizing movement scheme using the 1-

Wasserstein distance introduced in [1]. We implement this scheme using two different primal

dual algorithm: a Augmented Lagrangian technique with the ADMM algorithm and the …

[PDF] hse.ru

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

[PDF] oregonstate.edu

Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

J McClelland - 2018 - ir.library.oregonstate.edu

The UniFrac metric (Definitions 1.1. 13 and 1.1. 14) is a robust and well-used β-diversity

metric in metagenomics. Evans and Matsen demonstrated in [28], using the dual formulation

of the 1-Wasserstein metric (Definition 1.2. 4), that the UniFrac metric is the 1-Wasserstein …

<——2018 -—— —2018——430-—

[PDF] Bregman and Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond

GANR Wasserstein - wwwf.imperial.ac.uk

Page 1. Bregman Divergence Function Generative Adversarial Networks (GANs) Wasserstein

Divergence and GANs Relaxed Wasserstein Empirical Results Conclusions Bregman and

Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond Xin Guo …

Exponential Ergodicity for SDEs Driven by α-Stable Processes with Markovian Switching in Wasserstein Distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

[PDF] episciences.org

Free complete Wasserstein algebras

GD Plotkin, P Panangaden… - Logical Methods in …, 2018 - lmcs.episciences.org

We present an algebraic account of the Wasserstein distances $ W_p $ on complete metric

spaces, for $ p\geq 1$. This is part of a program of a quantitative algebraic theory of effects

in programming languages. In particular, we give axioms, parametric in $ p $, for algebras …

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in

each of the following cases:(a) X and Y are geodesic spaces and Y is covered by X via a …

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

Learning and inference with Wasserstein metrics

CCA Frogner - 2018 - dspace.mit.edu

This thesis develops new approaches for three problems in machine learning, using tools

from the study of optimal transport (or Wasserstein) distances between probability

distributions. Optimal transport distances capture an intuitive notion of similarity between …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

[PDF] stanford.edu

[PDF] Using Wasserstein GAN to Generate Adversarial Examples

Z Xiong, P Moulin - stanford.edu

Abstract Although Deep Neural Networks (DNNs) have state-of-the-art performance in

various machine learning tasks, in recent years, they are found to be vulnerable to socalled

adversarial examples. Specifically, take x∈ D on which a neural network has very high …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PEC de Raynal, N Frikha - arXiv preprint arXiv:1811.06904, 2018 - arxiv.org

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

<——2018 — —2018——440 —

A Fast Proximal Point Method for Computing Exact ...

by Y Xie · 2018 · Cited by 54 — A Fast Proximal Point Method for Computing Exact Wasserstein Distance. Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing.

[CITATION] A fast proximal point method for Wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

The Wasserstein Distance and its Application to Generative Adversarial Networks

[PDF] univie.ac.at

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

2[PDF] uni-muenster.de

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

… We aim to use the Wasserstein … the Wasserstein distance can indeed be used to train autoencoders. However, we also address the question whether the application of the Wasserstein …

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space

of Wasserstein in the framework of mean field control problems. The main motivation for this

study is given by the control of multi-agent systems, where the number of the agents is so …

Sketch-based 3D object retrieval using Wasserstein Center Loss

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using

human-drawn sketches as query. In this paper, we propose a new method of using Sketch

CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search …

[PDF] harchaoui.org

[PDF] Wasserstein Adversarial Mixture for Deep Generative Modeling and Clustering

W Harchaoui, PA Mattei, A Almansa, C Bouveyron - harchaoui.org

Unsupervised learning, and in particular clustering, is probably the most central problem in

learning theory nowadays. This work focuses on the clustering of complex data by

introducing a deep generative approach for both modeling and clustering. The proposed …

Central Limit Theorem for Wasserstein type distances ...

2018 see 2017 2020

projecteuclid.org › euclid.aihp

"A Central Limit Theorem for Wasserstein type distances between two distinct ... Received: 2 February 2018; Revised: 6 March 2019; Accepted: 29 March 2019; ...

[CITATION] A central limit theorem for Wasserstein type distances between two different real distributions

P Berthet, JC Fort, T Klein - Ann. Inst. Henri Poincaré Probab. Stat., hal-01526879, 2018

https://projecteuclid.org › journalArticle › Download › 19...

Received 2 February 2018; revised 6 March 2019; accepted 29 March 2019 ... We prove a central limit theorem under general conditions relating the tails and the ... of estimating the distance between two different distributions with respect to a ... The p-Wasserstein distance between two univariate probability distributions ...

[CITATION] A central limit theorem for Wasserstein type distances between two different real distributions

P Berthet, JC Fort, T Klein - Ann. Inst. Henri Poincaré Probab. Stat., hal-01526879, 2018

Perturbation theory for Markov chains via Wasserstein distance

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in

each of the following cases:(a) X and Y are geodesic spaces and Y is covered by X via a …

Evolution of the Wasserstein distance between the marginals of two Markov processes

A Alfonsi, J Corbetta, B Jourdain - Bernoulli, 2018 - projecteuclid.org

In this paper, we are interested in the time derivative of the Wasserstein distance between

the marginals of two Markov processes. As recalled in the introduction, the Kantorovich

duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the …

ited by 8 Related articles All 6 versions
<-—2018 — — —2018————450 —

Peer-reviewed
Large Deviations for a matching problem related to the ∞-Wasserstein distance
Author:Trashorras J
Article, 2018
Publication:Alea, 15, 2018, 247
Publisher:2018

Conference Paper Citation/Abstract

EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN

Luo, Yun.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Gaussian word embedding with a wasserstein distance loss

C Sun, H Yan, X Qiu, X Huang - arXiv preprint arXiv:1808.07016, 2018 - arxiv.org

Compared with word embedding based on point representation, distribution-based word

embedding shows more flexibility in expressing uncertainty and therefore embeds richer

semantic information when representing words. The Wasserstein distance provides a …

Wasserstein Riemannian geometry of Gaussian densities

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

Generative models with both discrete and continuous latent variables are highly motivated

by the structure of many real-world data sets. They present, however, subtleties in training

often manifesting in the discrete latent being under leveraged. In this paper, we show that …

L Malagò, L Montrucchio, G Pistone - Information Geometry, 2018 - Springer

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Cited by 69 Related articles

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

minimizing the sliced-Wasserstein … landscape for the sliced-Wasserstein distance is more well-…

Wasserstein-distance-based Gaussian mixture reduction

A Assa, KN Plataniotis - IEEE Signal Processing Letters, 2018 - ieeexplore.ieee.org

Gaussian mixtures (GMs) are widely used in signal processing applications to capture the

multimodal behavior of dynamic systems. Due to an exponential increase in the number of

GM components in such applications, Gaussian mixture reduction (GMR) approaches are …

[CITATION] … Stochastic Filtering............ E. Nitzan, T. Routtenberg, and J. Tabrikian 1460 Wasserstein-Distance-Based Gaussian Mixture Reduction............................. A …

S Khanna, CR Murthy, L Hu, J Zhang, X Wang, S Wang… - ieeexplore.ieee.org

OCTOBER 2018 VOLUME 25 NUMBER 10 ISPLEM (ISSN 1070-9908) Digital and Multirate

Signal Pro

Wasserstein-Distance-Based Gaussian Mixture Reduction ...

ieeexplore.ieee.org › document

Aug 20, 2018 — For such applications, this work prescribes the use of the Wasserstein distance (WD), which quantifies the minimum cost of converting one density into another and, therefore, is mostly concerned with the shape difference between the densities.

by A Assa · ‎2018 · ‎Cited by 8 · ‎Related articles

Wasserstein-Distance-Based Gaussian Mixture Reduction ...

ieeexplore.ieee.org › document

by A Assa · ‎2018 · ‎Cited by 8 · ‎Related articles

[CITATION] … Wasserstein-Distance-Based Gaussian Mixture Reduction............................. A. Assa and KN Plataniotis 1465

2018

Title: Regularized Wasserstein Distances and Barycenters
Author Marcel Klatt May 4, 2018

Type Package

<——2018 ———— 2018—————460——

Wasserstein Riemannian geometry of Gaussian densities

L Malagò, L Montrucchio, G Pistone - Information Geometry, 2018 - Springer

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Wasserstein riemannian geometry of positive definite matrices

L Malagò, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

W-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

G Auricchio, F Bassetti, S Gualandi… - Advances in Neural …, 2018 - papers.nips.cc

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance

between a pair of $ d $-dimensional histograms having $ n $ bins each. We prove that this

problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+ 1) $-partite …

On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order

one between a pair of two-dimensional histograms. Recent works in Computer Vision and

Machine Learning have shown the benefits of measuring Wasserstein distances of order …

[CITATION] On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows (2018). arXiv preprint

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

We consider doing Bayesian inference by minimizing the KL divergence on the 2-

Wasserstein space P2. By exploring the Riemannian structure of P2, we develop two

inference methods by simulating the gradient flow on P2 via updating particles, and an …

Wasserstein metric-driven Bayesian inversion with application ...

www.researchgate.net › publication › 326621570_Wasser...

Jul 26, 2018 — We apply the new framework to the inverse uncertainty quantification of wave propagation problems and demonstrate its advantages compared ...

[CITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018

[CITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems. ArXiv e-prints, 7 2018

M Motamed, D Appelö - arXiv preprint arXiv:1807.09682

Bayesian learning with Wasserstein barycenters

J Backhoff-Veraguas, J Fontbona, G Rios… - arXiv preprint arXiv …, 2018 - arxiv.org

We introduce a novel paradigm for Bayesian learning based on optimal transport theory.

Namely, we propose to use the Wasserstein barycenter of the posterior law on models as a

predictive posterior, thus introducing an alternative to classical choices like the maximum a

posteriori estimator and the Bayesian model average. We exhibit conditions granting the

existence and statistical consistency of this estimator, discuss some of its basic and specific

properties, and provide insight into its theoretical advantages. Finally, we introduce a novel …

Bayesian learning with wasserstein barycenters
<——2018 ———2018———————470—

Sliced wasserstein distance for learning gaussian mixture models

[PDF] Bayesian learning with wasserstein barycenters

G Rios, J Backhoff-Veraguas, J Fontbona, F Tobar - ArXiv e-prints, 1805 - researchgate.net

In this work we introduce a novel paradigm for Bayesian learning based on optimal transport

theory. Namely, we propose to use the Wasserstein barycenter of the posterior law on

models, as an alternative to the maximum a posteriori estimator (MAP) and Bayes predictive …

2018 [PDF] thecvf.com

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

M Di Francesco, M Wunsch - Monatshefte für Mathematik, 2008 - Springer

We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems

arising in semiconductor device modeling and plasma physics in one space dimension. In

particular, we prove that, under certain structural assumptions on the external potentials and …

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

DT Zhou, J Chen, H Wu, DH Yang, LY Qiu - arXiv preprint arXiv …, 2018 - arxiv.org

In our previous work [Chen el al., J. Comput. Phys., 373 (2018)], the quadratic Wasserstein

metric is successfully applied to the earthquake location problem. The actual earthquake

hypocenter can be accurately recovered starting from initial values very far from the true …

2018

-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

2018

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

[PDF] mit.edu

[PDF] Wasserstein coresets for lipschitz costs

S Claici, J Solomon - stat, 2018 - people.csail.mit.edu

Sparsification is becoming more and more relevant with the proliferation of huge data sets.

Coresets are a principled way to construct representative weighted subsets of a data set that

have matching performance with the full data set for specific problems. However, coreset …

2018

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

We present upper bounds for the Wasserstein distance of order $ p $ between the marginals

of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the

convolution structure, we further derive upper bounds for the total variation distance …

Cited by 10 Related articles All 3 versions
<——2018—-— —2018——480—

Propagation of chaos, Wasserstein gradient flows and toric Kähler–Einstein metrics

RJ Berman, M Önnheim - Analysis & PDE, 2018 - msp.org

Motivated by a probabilistic approach to Kähler–Einstein metrics we consider a general

nonequilibrium statistical mechanics model in Euclidean space consisting of the stochastic

Wasserstein distributionally robust kalman filtering

SS Abadeh, VA Nguyen, D Kuhn… - Advances in Neural …, 2018 - papers.nips.cc

We study a distributionally robust mean square error estimation problem over a nonconvex

Wasserstein ambiguity set containing only normal distributions. We show that the optimal

estimator and the least favorable distribution form a Nash equilibrium. Despite the non …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

2018

W-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

Sketch-based 3D object retrieval using Wasserstein Center Loss

2018

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

… 499-515, 2016. https://doi.org/10.1007/978-3-319-46478-7_31; A. Rolet, M. Cuturi, and G.

Peyr'e. "Fast dictionary learning with a smoothed wasserstein loss," International Conference

on Artificial Intelligence and Statistics, Cadiz, Spain, pp. 630-638, 2016 …

2018

Wasserstein Loss 를 이용한 모델 파라미터 학습에 대한 학술자료
The guideline of diagnosis and treatment of attention- … - ‎Lee - Cited by 6

[CITATION] Wasserstein Loss 를 이용한 모델 파라미터 학습

지종호， 신현정 - 한국정보과학회 학술발표논문집, 2018 - dbpia.co.kr

요 약그래프기반 준지도학습 (graph based semi-supervised learning) 은 그래프를 어떻게

만드냐에 따라 성능이 달라진다. 특히, 그래프의 엣지는 레코드 간 유사도로 생성되는데

유사도가 어떻게 정의되는가는 준지도학습의 성능에 상당한 영향을 미친다. 일반적으로 가장 …

[Korean Model parameter learning using Wasserstein Loss ]

2018

Distilled wasserstein learning for word embedding and topic modeling

H Xu, W Wang, W Liu, L Carin - Advances in Neural Information …, 2018 - papers.nips.cc

We propose a novel Wasserstein method with a distillation mechanism, yielding joint

learning of word embeddings and topics. The proposed method is based on the fact that the

Euclidean distance between word embeddings may be employed as the underlying …

2018 [PDF] projecteuclid.org

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

This paper is focused on the statistical analysis of probability measures $\boldsymbol {\nu} _

{1},\ldots,\boldsymbol {\nu} _ {n} $ on ${\mathbb {R}} $ that can be viewed as independent

realizations of an underlying stochastic process. We consider the situation of practical …

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

Decentralize and randomize: Faster algorithm for Wasserstein barycenters

2018 [PDF] nips.cc

P Dvurechenskii, D Dvinskikh, A Gasnikov… - Advances in Neural …, 2018 - papers.nips.cc

We study the decentralized distributed computation of discrete approximations for the

regularized Wasserstein barycenter of a finite set of continuous probability measures

distributedly stored over a network. We assume there is a network of agents/machines …

Stochastic wasserstein barycenters

S Claici, E Chien, J Solomon - arXiv preprint arXiv:1802.05757, 2018 - arxiv.org

We present a stochastic algorithm to compute the barycenter of a set of probability

distributions under the Wasserstein metric from optimal transport. Unlike previous

approaches, our method extends to continuous input distributions and allows the support of …

[CITATION] Stochastic Wasserstein Barycenters (2018). arXiv preprint

S Claici, E Chien, J Solomon - arXiv preprint arXiv:1802.05757

Distributed computation of Wasserstein barycenters over networks

CA Uribe, D Dvinskikh, P Dvurechensky… - … IEEE Conference on …, 2018 - ieeexplore.ieee.org

We propose a new class-optimal algorithm for the distributed computation of Wasserstein

Barycenters over networks. Assuming that each node in a graph has a probability

distribution, we prove that every node reaches the barycenter of all distributions held in the …

Propriétés statistiques du barycentre dans l'espace de Wasserstein

E Cazelles - 2018 - tel.archives-ouvertes.fr

Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de

probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension des outils

statistiques usuels sur cet espace muni de la distance de Wasserstein. Une première notion …

A fast globally linearly convergent algorithm for the computation of Wasserstein barycenters

L Yang, J Li, D Sun, KC Toh - arXiv preprint arXiv:1809.04249, 2018 - arxiv.org

In this paper, we consider the problem of computing a Wasserstein barycenter for a set of

discrete probability distributions with finite supports, which finds many applications in areas

such as statistics, machine learning and image processing. When the support points of the …

[CITATION] A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters. eprint

L Yang, J Li, D Sun, KC Toh - arXiv preprint arXiv:1809.04249, 2019

Bayesian learning with Wasserstein barycenters

J Backhoff-Veraguas, J Fontbona, G Rios… - arXiv preprint arXiv …, 2018 - arxiv.org

We introduce a novel paradigm for Bayesian learning based on optimal transport theory.

Namely, we propose to use the Wasserstein barycenter of the posterior law on models as a

predictive posterior, thus introducing an alternative to classical choices like the maximum a …

[CITATION] Bayesian learning with Wasserstein barycenters (2018)

J Backhoff-Veraguas, J Fontbona, G Rios, F Tobar - arXiv preprint arXiv:1805.10833

[CITATION] Bayesian learning with Wasserstein barycenters (2018)

J Backhoff-Veraguas, J Fontbona, G Rios, F Tobar - arXiv preprint arXiv:1805.10833

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity …

2018 [PDF] jmlr.org

Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - dl.acm.org

2018 [PDF] shichuan.org

Deep variational network embedding in wasserstein space

D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

Network embedding, aiming to embed a network into a low dimensional vector space while preserving the inherent structural properties of the network, has attracted considerable attentions recently. Most of the existing embedding methods embed nodes as point vectors …

2018 [PDF] nips.cc

Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - Advances in Neural Information Processing …, 2018 - papers.nips.cc

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability distributions, namely distributions …

2018

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

We consider doing Bayesian inference by minimizing the KL divergence on the 2-Wasserstein space P2. By exploring the Riemannian structure of P2, we develop two inference methods by simulating the gradient flow on P2 via updating particles, and an …

<——2018—-— 2018———500—

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org

This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric classes of random probability measures with …

Extremal flows in Wasserstein space

G Conforti, M Pavon - Journal of Mathematical Physics, 2018 - aip.scitation.org

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein space. We show that the flows associated with the Schrödinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as …

2018 [PDF] projecteuclid.org

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2018 - projecteuclid.org

We introduce a general theory for a consensus-based combination of estimations of probability measures. Potential applications include parallelized or distributed sampling schemes as well as variations on aggregation from resampling techniques like boosting or …

2018 see 2019

ION] From the Backward Kolmogorov PDE on the Wasserstein space to propagation of chaos for McKean-Vlasov SDEs

PEC de Raynal, N Frikha - arXiv preprint arXiv:1907.01410, 2018

[CITATION] From the Backward Kolmogorov PDE on the Wasserstein space to propagation of chaos for McKean-Vlasov SDEs

PEC de Raynal, N Frikha - arXiv preprint arXiv:1907.01410, 2018

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Gradient flows for frame potentials on the Wasserstein space

C Wickman, K Okoudjou - arXiv preprint arXiv:1808.09319, 2018 - arxiv.org

In this paper we bring together some of the key ideas and methods of two very lively fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular, we construct gradient flows in the …

year 2018

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space of Wasserstein in the framework of mean field control problems. The main motivation for this study is given by the control of multi-agent systems, where the number of the agents is so …

2018 [PDF] theses.fr

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

Résumé Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension des outils statistiques usuels sur cet espace muni de la distance de Wasserstein. Une …

[PDF] Wasserstein natural gradient in statistical manifolds with continuous sample space

2018 [PDF] semanticscholar.org

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - pdfs.semanticscholar.org

Page 1. WASSERSTEIN NATURAL GRADIENT IN STATISTICAL MANIFOLDS WITH CONTINUOUS SAMPLE SPACE YIFAN CHEN AND WUCHEN LI Abstract. We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces …

Wasserstein Riemannian geometry of Gaussian densities

[PDF] Multi-Level Metric Learning via Smoothed Wasserstein Distance.

J Xu, L Luo, C Deng, H Huang - IJCAI, 2018 - ijcai.org

Traditional metric learning methods aim to learn a single Mahalanobis distance matrix M,

which, however, is not discriminative enough to characterize the complex and …

<——2018—-— 2018———510—

L Malagò, L Montrucchio, G Pistone - Information Geometry, 2018 - Springer

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Wasserstein riemannian geometry of positive definite matrices

L Malagò, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

2018 [HTML] springer.com

[HTML] Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

S Amari, R Karakida, M Oizumi - Information Geometry, 2018 - Springer

2018

Wasserstein geometry of quantum states and optimal transport of matrix-valued measures

Y Chen, TT Georgiou, A Tannenbaum - Emerging Applications of Control …, 2018 - Springer

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices and of matrix-valued distributions, as well as some extensions of the theory to vector-valued distributions …

2018

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the description of nature. This idea, inspired by Mach's principle, says that it should be possible to describe the dynamics of matter without resorting to a notion of space, in particular to a …

2018

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

We propose in this paper a construction of a diffusion process on the space $\mathcal P_2

(\mathbb R) $ of probability measures with a second-order moment. This process was

introduced in several papers by Konarovskyi (see eg [12]) and consists of the limit as $ N …

2018

Wasserstein divergence for gans

J Wu, Z Huang, J Thoma, D Acharya… - Proceedings of the …, 2018 - openaccess.thecvf.com

In many domains of computer vision, generative adversarial networks (GANs) have

achieved great success, among which the family of Wasserstein GANs (WGANs) is

considered to be state-of-the-art due to the theoretical contributions and competitive …

[CITATION] Wasserstein divergence for gans (2018) 653–668

J Wu, Z Huang, J Thoma, D Acharya, L Van Gool - Conflict of Interest

[CITATION] Wasserstein divergence for gans

W Jiqing, H Zhiwu, T Janine, A Dinesh, VG Luc - ECCV, 2018

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

2012018 [PDF] neurips.cc

Wasserstein distributionally robust Kalman filtering

S Shafieezadeh Abadeh, VA Nguyen… - Advances in …, 2018 - proceedings.neurips.cc

… respect to the type-2 Wasserstein distance. The Wasserstein distance has seen widespread

… In the following, we propose to use the Wasserstein distance in order to construct ambiguity …

Generative modeling using the sliced wasserstein distance

I Deshpande, Z Zhang… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Abstract Generative Adversarial Nets (GANs) are very successful at modeling distributions

from given samples, even in the high-dimensional case. However, their formulation is also

known to be hard to optimize and often not stable. While this is particularly true for early GAN …

<——2018—-— 2018———520 —

Sliced Wasserstein auto-encoders

S Kolouri, PE Pope, CE Martin… - … Conference on Learning …, 2018 - openreview.net

In this paper we use the geometric properties of the optimal transport (OT) problem and the

Wasserstein distances to define a prior distribution for the latent space of an auto-encoder.

We introduce Sliced-Wasserstein Auto-Encoders (SWAE), that enable one to shape the …

Cited by 33 Related articles

2018

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

Report for CSE 5339 2018 — (OTMLSA) Optimal Transport in ...

2018

people.math.osu.edu › courses › reports › xiao-zha

PDF

Optimal Transport in Machine Learning and Shape Analysis. Report on ”Sliced Wasserstein Distance for Persistence Diagram”. Xiao Zha. 1 Motivation and ...

Mapper Comparison with Wasserstein Metrics

M McCabe - arXiv preprint arXiv:1812.06232, 2018 - arxiv.org

The challenge of describing model drift is an open question in unsupervised learning. It can

be difficult to evaluate at what point an unsupervised model has deviated beyond what

would be expected from a different sample from the same population. This is particularly true …

2018

Learning and inference with Wasserstein metrics

CCA Frogner - 2018 - dspace.mit.edu

This thesis develops new approaches for three problems in machine learning, using tools

from the study of optimal transport (or Wasserstein) distances between probability

distributions. Optimal transport distances capture an intuitive notion of similarity between …

2018

Semantic image inpainting through improved wasserstein generative adversarial networks

P Vitoria, J Sintes, C Ballester - arXiv preprint arXiv:1812.01071, 2018 - arxiv.org

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image.

In this work we tackle this problem not only by using the available visual data but also by

incorporating image semantics through the use of generative models. Our contribution is …

2018 [HTML] springer.com

[HTML] Improved Wasserstein conditional generative adversarial network speech enhancement

S Qin, T Jiang - EURASIP Journal on Wireless Communications and …, 2018 - Springer

The speech enhancement based on the generative adversarial network has achieved

excellent results with large quantities of data, but performance in the low-data regime and

tasks like unseen data learning still lag behind. In this work, we model Wasserstein …

2018

Aero-engine faults diagnosis based on K-means improved wasserstein GAN and relevant vector machine

Z Zhao, R Zhou, Z Dong - 2019 Chinese Control Conference …, 2019 - ieeexplore.ieee.org

The aero-engine faults diagnosis is essential to the safety of the long-endurance aircraft.

The problem of fault diagnosis for aero-engines is essentially a sort of model classification

problem. Due to the difficulty of the engine faults modeling, a data-driven approach is used …

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

2018 [PDF] eg.org

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

-Wasserstein distances of tracial -algebras and their disintegration problem

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with

multiplication operators arising as the logarithmic mean under a functional calculus …

[PDF] iitp.ru

[PDF] Центральная предельная теорема для барицентров Васерштейна от гауссовских мер

А Крошнин, А Суворикова - ИТиС 2018, 2018 - itas2018.iitp.ru

Объекты, которые можно рассматривать как вероÿтностные распределениÿ,

возникают в самых разных областÿх. Зачастую необходимо исследовать их, учитываÿ

геометрию пространства, на котором они определены. Так, один из естественных …

Gromov-wasserstein alignment of word embedding spaces

D Alvarez-Melis, TS Jaakkola - arXiv preprint arXiv:1809.00013, 2018 - arxiv.org

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from

machine translation to transfer learning. Recently, purely unsupervised methods operating

on monolingual embeddings have become effective alignment tools. Current state-of-the-art …

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

T Vayer, L Chapel, R Flamary, R Tavenard… - arXiv preprint arXiv …, 2018 - arxiv.org

Optimal transport theory has recently found many applications in machine learning thanks to

its capacity for comparing various machine learning objects considered as distributions. The

Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the …

[CITATION] Laetita Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty. Fused gromov-wasserstein distance for structured objects: theoretical foundations …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

Snowflake universality of Wasserstein spaces

A Andoni, A Naor, O Neiman - … Scientifiques de l'Ecole …, 2018 - collaborate.princeton.edu

Abstract For p∈(1;∞) let P p (ℝ3) denote the metric space of all p-integrable Borel

probability measures on ℝ 3, equipped with the Wasserstein p metric W p. We prove that for

every ϵ> 0, every θ∈(0; 1/p] and every finite metric space (X, d X), the metric space (X; d X …

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in

each of the following cases:(a) X and Y are geodesic spaces and Y is covered by X via a …

[PDF] Differential properties of sinkhorn approximation for learning with wasserstein distance

G Luise, A Rudi, M Pontil, C Ciliberto - Advances in Neural …, 2018 - papers.nips.cc

Applications of optimal transport have recently gained remarkable attention as a result of the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation to the Wasserstein distance is replaced by a regularized version …

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

Data-driven risk-averse stochastic optimization with Wasserstein metric

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

In this paper, we study a data-driven risk-averse stochastic optimization approach with

Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we

can successfully reformulate the risk-averse two-stage stochastic optimization problem with …

Minimax statistical learning with wasserstein distances

J Lee, M Raginsky - Advances in Neural Information Processing …, 2018 - papers.nips.cc

As opposed to standard empirical risk minimization (ERM), distributionally robust

optimization aims to minimize the worst-case risk over a larger ambiguity set containing the

original empirical distribution of the training data. In this work, we describe a minimax …

Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In the presence of

VRE uncertainties, this paper discusses a distributionally robust chance constrained …

<——2018—-— 2018———540—

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so …

Gaussian mixture models with Wasserstein distance

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

Generative models with both discrete and continuous latent variables are highly motivated

by the structure of many real-world data sets. They present, however, subtleties in training

often manifesting in the discrete latent being under leveraged. In this paper, we show that …

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

Data-driven distributionally robust chance-constrained optimization with Wasserstein metric

R Ji, M Lejeune - Available at SSRN 3201356, 2018 - papers.ssrn.com

We study distributionally robust chance-constrained programming (DRCCP) optimization

problems with data-driven Wasserstein ambiguity sets. We consider DRCCP problems with

random right-hand side and technology vector under two types of uncertainties called …

[CITATION] Data-driven distributionally robust chance-constrained programming with Wasserstein metric

R Ji, M Lejeune - Available at Optimization Online, 2018

Non-local texture optimization with wasserstein regularization under convolutional neural network

[PDF] Learning disentangled representations with wasserstein auto-encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

Page 1. Workshop track - ICLR 2018 LEARNING DISENTANGLED REPRESENTATIONS WITH

WASSERSTEIN AUTO-ENCODERS Paul Rubenstein∗, Bernhard Schölkopf, Ilya Tolstikhin

Empirical Inference Max Planck Institute for Intelligent Systems, Tübingen 1paul.rubenstein,bs …

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

Anomaly detection with Wasserstein GAN

I Haloui, JS Gupta, V Feuillard - arXiv preprint arXiv:1812.02463, 2018 - arxiv.org

Generative adversarial networks are a class of generative algorithms that have been widely

used to produce state-of-the-art samples. In this paper, we investigate GAN to perform

anomaly detection on time series dataset. In order to achieve this goal, a bibliography is …

Bayesian learning with Wasserstein barycenters

J Backhoff-Veraguas, J Fontbona, G Rios… - arXiv preprint arXiv …, 2018 - arxiv.org

We introduce a novel paradigm for Bayesian learning based on optimal transport theory.

Namely, we propose to use the Wasserstein barycenter of the posterior law on models as a

predictive posterior, thus introducing an alternative to classical choices like the maximum a …

Free complete Wasserstein algebras

R Mardare, P Panangaden, GD Plotkin - arXiv preprint arXiv:1802.07366, 2018 - arxiv.org

We present an algebraic account of the Wasserstein distances $ W_p $ on complete metric

spaces, for $ p\geq 1$. This is part of a program of a quantitative algebraic theory of effects

in programming languages. In particular, we give axioms, parametric in $ p $, for algebras …

[PDF] episciences.org

Free complete Wasserstein algebras

GD Plotkin, P Panangaden… - Logical Methods in …, 2018 - lmcs.episciences.org

We present an algebraic account of the Wasserstein distances $ W_p $ on complete metric

spaces, for $ p\geq 1$. This is part of a program of a quantitative algebraic theory of effects

in programming languages. In particular, we give axioms, parametric in $ p $, for algebras …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

<——2018—-— 2018———550

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

Motion-blind blur removal for CT images with wasserstein generative adversarial networks

Y Lyu, W Jiang, Y Lin, L Voros, M Zhang… - … Congress on Image …, 2018 - ieeexplore.ieee.org

Advanced deblurring techniques for computed tomography (CT) images are necessary and

crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup

and treatment response assessment in radiation oncology. Currently, medical image …

Mapper Comparison with Wasserstein Metrics

M McCabe - arXiv preprint arXiv:1812.06232, 2018 - arxiv.org

The challenge of describing model drift is an open question in unsupervised learning. It can

be difficult to evaluate at what point an unsupervised model has deviated beyond what

would be expected from a different sample from the same population. This is particularly true …

Measuring distributional asymmetry with Wasserstein distance and Rademacher symmetrization

AB Kashlak - Electronic Journal of Statistics, 2018 - projecteuclid.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

asymmetry of the given measure. An empirical bound on this asymmetric correction term is …

Learning and inference with Wasserstein metrics

CCA Frogner - 2018 - dspace.mit.edu

This thesis develops new approaches for three problems in machine learning, using tools

from the study of optimal transport (or Wasserstein) distances between probability

distributions. Optimal transport distances capture an intuitive notion of similarity between …

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

[PDF] uma.es

A Esteban-Pérez, JM Morales - 2018 - riuma.uma.es

We consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

[CITATION] Probabilistic natural language generation with wasserstein autoencoders

H Bahuleyan, L Mou, K Vamaraju, H Zhou… - arXiv preprint arXiv …, 2018

Policy optimization as wasserstein gradient flows

R Zhang, C Chen, C Li, L Carin - arXiv preprint arXiv:1808.03030, 2018 - arxiv.org

Policy optimization is a core component of reinforcement learning (RL), and most existing

RL methods directly optimize parameters of a policy based on maximizing the expected total

reward, or its surrogate. Though often achieving encouraging empirical success, its …

Propagation of chaos, Wasserstein gradient flows and toric Kähler–Einstein metrics

RJ Berman, M Önnheim - Analysis & PDE, 2018 - msp.org

Motivated by a probabilistic approach to Kähler–Einstein metrics we consider a general

nonequilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasiconvex N-particle interaction energy. We …

<——2018—-— 2018———560—

Minimax statistical learning with wasserstein distances

J Lee, M Raginsky - Advances in Neural Information Processing …, 2018 - papers.nips.cc

As opposed to standard empirical risk minimization (ERM), distributionally robust

optimization aims to minimize the worst-case risk over a larger ambiguity set containing the

original empirical distribution of the training data. In this work, we describe a minimax …

Generalization error bounds using Wasserstein distances

AT Lopez, V Jog - 2018 IEEE Information Theory Workshop …, 2018 - ieeexplore.ieee.org

Generalization error of a learning algorithm characterizes the gap between an algorithm's

performance on test data versus performance on training data. In recent work, Xu &

Raginsky [1] showed that generalization error may be upper-bounded using the mutual …

Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

G Auricchio, F Bassetti, S Gualandi… - Advances in Neural …, 2018 - papers.nips.cc

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance

between a pair of $ d $-dimensional histograms having $ n $ bins each. We prove that this

problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+ 1) $-partite …

Computing Kantorovich-Wasserstein Distances on $ d ...

by G Auricchio · 2018 · Cited by 15 — ... Distances on d-dimensional histograms using (d+1)-partite graphs ... novel method to compute the exact Kantorovich-Wasserstein distance ...

Missing: (d+ ‎| Must include: (d+

[CITATION] Computing Kantorovich-Wasserstein Distances on d-dimensional histograms using (d+ 1)-partite graphs

GAFBS Gualandiand, M Veneroni - arXiv preprint arXiv:1805.07416, 2018

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so …

On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order

one between a pair of two-dimensional histograms. Recent works in Computer Vision and

Machine Learning have shown the benefits of measuring Wasserstein distances of order …

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

-Wasserstein distances of tracial -algebras and their disintegration problem

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with

multiplication operators arising as the logarithmic mean under a functional calculus …

Exponential Ergodicity for SDEs Driven by α-Stable Processes with Markovian Switching in Wasserstein Distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

Inference for empirical Wasserstein distances on finite spaces Series B Statistical methodology

M Sommerfeld, A Munk - 2018 - pubag.nal.usda.gov

The Wasserstein distance is an attractive tool for data analysis but statistical inference is

hindered by the lack of distributional limits. To overcome this obstacle, for probability

measures supported on finitely many points, we derive the asymptotic distribution of …

Improving the improved training of wasserstein gans: A consistency term and its dual effect

X Wei, B Gong, Z Liu, W Lu, L Wang - arXiv preprint arXiv:1803.01541, 2018 - arxiv.org

Despite being impactful on a variety of problems and applications, the generative

adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed

by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the …

<——2018—-— 2018———570—

Visual feature attribution using wasserstein gans

CF Baumgartner, LM Koch… - Proceedings of the …, 2018 - openaccess.thecvf.com

Attributing the pixels of an input image to a certain category is an important and well-studied

problem in computer vision, with applications ranging from weakly supervised localisation to

understanding hidden effects in the data. In recent years, approaches based on interpreting …

Towards high resolution video generation with progressive growing of sliced Wasserstein GANs

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

since the temporal dimension of videos introduces an extra challenge during the generation

process. Besides, due to the limitation of memory and training stability, the generation …

Cited by 19 Related articles

Classification of small UAVs based on auxiliary classifier wasserstein GANs

C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Beyond their benign uses, the small Unmanned Aerial Vehicles (UAVs) are expected to take

the major role in future smart cities that have attracted the attention of the public and

authorities. Therefore, detecting, tracking and classifying the type of UAVs is important for …

Single image super-resolution based on wasserstein GANs

T Pinetz, D Soukup, T Pock - … of the 23rd Computer Vision Winter …, 2018 - researchgate.net

Wasserstein Generative Adversarial Networks (GANs) work by approximating the

Wasserstein distance using large Neural Networks (NNs) with specific architectures,

hyperparameter and regularization techniques. We show that those networks severely …

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network

and Wasserstein generative adversarial nets is proposed aiming at generating a photo-

realistic image with finer texture details. Specifically, we construct a framework consisting of …

[PDF] Automatic Liver Segmentation Using U-Net with Wasserstein GANs

2018

[PDF] joig.org

Y Enokiya, Y Iwamoto, YW Chen, XH Han - Journal of Image and Graphics, 2018 - joig.org

Automatic liver segmentation in CT images is an important step for computer-aided

diagnosis and computeraided hepatic surgery. Recently, though numerous methods based

on deep learning such as U-Net have been proposed for automatic liver segmentation, it is …

Sparse-view CT reconstruction using wasserstein GANs

F Thaler, K Hammernik, C Payer, M Urschler… - … Workshop on Machine …, 2018 - Springer

We propose a 2D computed tomography (CT) slice image reconstruction method from a

limited number of projection images using Wasserstein generative adversarial networks

(wGAN). Our wGAN optimizes the 2D CT image reconstruction by utilizing an adversarial …

Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

necessary. Computer aided diagnosis offers an objective score that is independent of …

[PDF] imperial.ac.uk

[PDF] Bregman and Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond

GANR Wasserstein - wwwf.imperial.ac.uk

Page 1. Bregman Divergence Function Generative Adversarial Networks (GANs) Wasserstein

Divergence and GANs Relaxed Wasserstein Empirical Results Conclusions Bregman and

Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond Xin Guo …

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

<——2018—–— 2018———580—-

On the Convergence and Robustness of Training GANs with ...

anjabi · 2018 · Cited by 53 — A popular GAN formulation is based on the use of Wasserstein distance as ... to stationarity for a proposed class of GAN optimization algorithms. ... our algorithm only requires solving the discriminator to approximate optimality.

[CITATION] Solving approximate Wasserstein GANs to stationarity

M Sanjabi, J Ba, M Razaviyayn, JD Lee - arXiv preprint arXiv:1802.08249, 2018

On the regularization of Wasserstein GANs | OpenReview

2018 see 2017

https://openreview.net › forum

by H Petzka · 2018 · Cited by 186 — Review: This paper proposes a novel regularization scheme for Wasserstein GAN based on a relaxation of the constraints on the Lipschitz constant of 1. The ...

[CITATION] On the regularization of Wasserstein GANs

S Augustin - Proc. Int. Conf. Learn. Representations, 2018

On the regularization of Wasserstein GANs | OpenReview

openreview.net › forum

by H Petzka · 2018 · Cited by 101 — Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms ...

Adversarial Lipschitz Regularization \| OpenReview	Oct 3, 2019
Improving the Improved Training of Wasserstein GANs: A ...	Nov 16, 2017
More results from openreview.net

[CITATION] On the regularization of Wasserstein GANs

S Augustin - Proc. Int. Conf. Learn. Representations, 2018

On the regularization of Wasserstein GANs | OpenReview

openreview.net › forum

by H Petzka · 2018 · Cited by 104 — These arguments are supported by experimental results on several data sets. TL;DR: A new regularization term can improve your training of wasserstein gans.

Banach wasserstein gan

J Adler, S Lunz - Advances in Neural Information Processing …, 2018 - papers.nips.cc

Abstract Wasserstein Generative Adversarial Networks (WGANs) can be used to generate

realistic samples from complicated image distributions. The Wasserstein metric used in

WGANs is based on a notion of distance between individual images, which induces a notion …

Hashgan: Deep learning to hash with pair conditional wasserstein gan

Y Cao, B Liu, M Long, J Wang - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Deep learning to hash improves image retrieval performance by end-to-end representation

learning and hash coding from training data with pairwise similarity information. Subject to

the scarcity of similarity information that is often expensive to collect for many application …

EEG data augmentation for emotion recognition using a conditional wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Primal-dual wasserstein gan

M Gemici, Z Akata, M Welling - arXiv preprint arXiv:1805.09575, 2018 - arxiv.org

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent

variable models of the data distribution based on the primal and the dual formulations of the

optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference …

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

Anomaly detection with Wasserstein GAN

I Haloui, JS Gupta, V Feuillard - arXiv preprint arXiv:1812.02463, 2018 - arxiv.org

Generative adversarial networks are a class of generative algorithms that have been widely

used to produce state-of-the-art samples. In this paper, we investigate GAN to perform

anomaly detection on time series dataset. In order to achieve this goal, a bibliography is …

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

Using Wasserstein GAN to generate high quality adversarial examples

[PDF] Wasserstein GAN: Technical Report

C Eteke - pdfs.semanticscholar.org

Even though the introduction of Generative Adversarial Nets lead to amazing applications

and results, the training of these models are highly instable and always regarded as a black

box. This is a technical report for the term project of the course COMP 541: Deep Learning …

<——2018—-— 2018———590 —

[PDF] stanford.edu

[PDF] Using Wasserstein GAN to Generate Adversarial Examples

Z Xiong, P Moulin - stanford.edu

Abstract Although Deep Neural Networks (DNNs) have state-of-the-art performance in

various machine learning tasks, in recent years, they are found to be vulnerable to socalled

adversarial examples. Specifically, take x∈ D on which a neural network has very high …

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various

machine learning tasks, in recent years, they are found to be vulnerable to so-called

adversarial examples Specifically, take x is an element of D on which a neural network has …

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

Page 1. AMMI – Introduction to Deep Learning 10.2. Wasserstein GAN François Fleuret

https://fleuret.org/ammi-2018/ Wed Aug 29 16:57:14 CAT 2018 ÉCOLE POLYTECHNIQUE

FÉDÉRALE DE LAUSANNE Page 2. Arjovsky et al. (2017) point out that DJS does not …

Wasserstein GAN によるスタイル制御可能なフオント生成

阿部耕太郎，早志英朗，内田誠一 - 研究報告コンピュータビジョンと …, 2018 - ipsj.ixsq.nii.ac.jp

論文抄録本研究では, Wasserstein GAN を用いてスタイル制御可能なフォント生成を試みる.

Wasserstein GAN は, 学習パターンと生成パターンの確率分布間の距離を定義し,

それを最小化するように学習される構成の GAN である. ランダムノイズに文字情報付与を付与した …

Wasserstein GANによるスタイル制御可能な ... - CiNii 論文

[Japonese Style-controllable font generation by Wasserstein GAN]

ci.nii.ac.jp › naid

by 阿部耕太郎 · 2018 — Wasserstein GANによるスタイル制御可能なフォント生成 (メディアエクスペリエンス・バーチャル環境基礎). 阿部耕太郎 · 早志英朗 · 内田誠一 ... キーワード. GAN · Wasserstein GAN · フォント生成 · 深層学習 ...

[CITATION] Wasserstein GAN によるスタイル制御可能なフォント生成 (メディアエクスペリエンス・バーチャル環境基礎)

阿部耕太郎，早志英朗，内田誠一 - 電子情報通信学会技術研究報告= IEICE …, 2018 - ci.nii.ac.jp

… 検索. すべて. 本文あり. すべて. 本文あり. タイトル. 著者名. 著者ID. 著者所属. 刊行物名. ISSN.

巻号ページ. 出版者. 参考文献. 出版年. 年から年まで. 検索. 閉じる. 検索. 検索. Wasserstein

GANによるスタイル制御可能な

[Japonese Style-controllable font generation by GAN (Media Experience]

2018

Malliavin…Stein method: a survey of some recent developments

https://www.vmsta.org › article › file › pdf

PDF

by E Azmoodeh · 2021 · Cited by 2 — The approximation will be performed with respect to the total variation and 1-Wasserstein distances between the distributions.

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

[CITATION] Multivariate Stein Factors from Wasserstein Decay

MA Erdogdu, L Mackey, O Shamir - 2019 - preparation

[PDF] Differential properties of sinkhorn approximation for learning with wasserstein distance

G Luise, A Rudi, M Pontil, C Ciliberto - Advances in Neural …, 2018 - papers.nips.cc

Applications of optimal transport have recently gained remarkable attention as a result of the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation to the Wasserstein distance is replaced by a regularized version …

[PDF] aaai.org

Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

domain via utilizing the knowledge distilled from a source domain which has a different but

related data distribution. One solution to domain adaptation is to learn domain invariant …

CITATION] Yong Yu. Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang - Thirty-Second AAAI Conference on Artificial …, 2018

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Generative modeling using the sliced wasserstein distance

I Deshpande, Z Zhang… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Abstract Generative Adversarial Nets (GANs) are very successful at modeling distributions

from given samples, even in the high-dimensional case. However, their formulation is also

known to be hard to optimize and often not stable. While this is particularly true for early GAN …

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

<——2018—-— 2018———600 ——

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

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A two-step computation of the exact gan wasserstein distance

H Liu, GU Xianfeng, D Samaras - … Conference on Machine …, 2018 - proceedings.mlr.press

In this paper, we propose a two-step method to compute the Wasserstein distance in

Wasserstein Generative Adversarial Networks (WGANs): 1) The convex part of our objective

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Minimax distribution estimation in Wasserstein distance

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

The Wasserstein metric is an important measure of distance between probability

distributions, with applications in machine learning, statistics, probability theory, and data

analysis. This paper provides upper and lower bounds on statistical minimax rates for the …

Perturbation theory for Markov chains via Wasserstein distance

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

[ [PDF] arxiv.org

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

… to the 2-Wasserstein distance between probability measures. To this end, we propose comparing the methods of log-PCA and geodesic PCA in the Wasserstein space as introduced in […

[HTML] Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

S Amari, R Karakida, M Oizumi - Information Geometry, 2018 - Springer

Two geometrical structures have been extensively studied for a manifold of probability

distributions. One is based on the Fisher information metric, which is invariant under

reversible transformations of random variables, while the other is based on the Wasserstein …

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

T Vayer, L Chapel, R Flamary, R Tavenard… - arXiv preprint arXiv …, 2018 - arxiv.org

Optimal transport theory has recently found many applications in machine learning thanks to

its capacity for comparing various machine learning objects considered as distributions. The

Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the …

CITATION] Laetita Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty.“Fused Gromov-Wasserstein distance for structured objects: theoretical foundations …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

Gaussian mixture models with Wasserstein distance

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

Generative models with both discrete and continuous latent variables are highly motivated

by the structure of many real-world data sets. They present, however, subtleties in training

often manifesting in the discrete latent being under leveraged. In this paper, we show that …

Computing Wasserstein distance for persistence diagrams on a quantum computer

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to

provide a concise description of a filtered topological space. What makes them even more

useful in practice is that they come with a notion of a metric, the Wasserstein distance …

<——2018—-— 2018———610—

[PDF] usc.edu

Wasserstein distance and the distributionally robust TSP

JG Carlsson, M Behroozi, K Mihic - Operations Research, 2018 - pubsonline.informs.org

Recent research on the robust and stochastic traveling salesman problem and the vehicle

routing problem has used many different approaches for describing the region of ambiguity

including taking convex combinations of observed demand vectors or imposing constraints …

Gaussian word embedding with a wasserstein distance loss

C Sun, H Yan, X Qiu, X Huang - arXiv preprint arXiv:1808.07016, 2018 - arxiv.org

Compared with word embedding based on point representation, distribution-based word

embedding shows more flexibility in expressing uncertainty and therefore embeds richer

semantic information when representing words. The Wasserstein distance provides a …

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

Cross-lingual document retrieval using regularized Wasserstein distance

G Balikas, C Laclau, I Redko, MR Amini - European Conference on …, 2018 - Springer

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

Cross-Lingual Document Retrieval Using Regularized Wasserstein Distance

MR Amini - Advances in Information Retrieval: 40th European …, 2018 - books.google.com

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

[PDF] Multi-Level Metric Learning via Smoothed Wasserstein Distance.

J Xu, L Luo, C Deng, H Huang - IJCAI, 2018 - pdfs.semanticscholar.org

Traditional metric learning methods aim to learn a single Mahalanobis distance matrix M,

which, however, is not discriminative enough to characterize the complex and

heterogeneous data. Besides, if the descriptors of the data are not strictly aligned …

Model risk measurement under Wasserstein distance

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018 - arxiv.org

The paper proposes a new approach to model risk measurement based on the Wasserstein

distance between two probability measures. It formulates the theoretical motivation resulting

from the interpretation of fictitious adversary of robust risk management. The proposed …

[CITATION] Model risk measurement under Wasserstein distance. arXiv

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018

Evaluating a stochastic parametrization for a fast--slow system using the Wasserstein distance

[PDF] reading.ac.uk

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - centaur.reading.ac.uk

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modeling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

The exponential contraction in $ L^ 1$-Wasserstein distance and exponential convergence

in $ L^ q $-Wasserstein distance ($ q\geq 1$) are considered for stochastic differential

equations with irregular drift. When the irregular drift drift is locally bounded, the exponential …

Learning to optimize via wasserstein deep inverse optimal control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

… • We design a novel Wasserstein inverse optimal control framework by using Wasserstein … To overcome this limitation, next we propose to use the Wasserstein distance as the metric …

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - Journal of Statistical Computation …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

sets in the size of millions of entries. We consider the situation when the information on a

large univariate data set or sample needs to be preserved, stored or transferred. We suggest …

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[PDF] dagstuhl.de

The wasserstein distance as a dissimilarity measure for mass spectra with application to spectral deconvolution

S Majewski, MA Ciach, M Startek… - … on Algorithms in …, 2018 - drops.dagstuhl.de

We propose a new approach for the comparison of mass spectra using a metric known in the

computer science under the name of Earth Mover's Distance and in mathematics as the

Wasserstein distance. We argue that this approach allows for natural and robust solutions to …

Evolution of the Wasserstein distance between the marginals of two Markov processes

A Alfonsi, J Corbetta, B Jourdain - Bernoulli, 2018 - projecteuclid.org

In this paper, we are interested in the time derivative of the Wasserstein distance between

the marginals of two Markov processes. As recalled in the introduction, the Kantorovich

duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the …

Cross-Domain Text Sentiment Classification Based on Wasserstein Distance

G Cai, Q Lin, N Chen - International Conference on Security with Intelligent …, 2018 - Springer

Text sentiment analysis is mainly to detect the sentiment polarity implicit in text data. Most

existing supervised learning algorithms are difficult to solve the domain adaptation problem

in text sentiment analysis. The key of cross-domain text sentiment analysis is how to extract …

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Wasserstein distance for generalized persistence modules and abelian categories

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018 - arxiv.org

In persistence theory and practice, measuring distances between modules is central. The

Wasserstein distances are the standard family of L^ p distances for persistence modules.

They are defined in a combinatorial way for discrete invariants called persistence diagrams …

[CITATION] Wasserstein distance for generalized persistence modules and abelian categories

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018

[CITATION] Wasserstein distance for generalized persistence modules and abelian categories

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

Lifted and geometric differentiability of the squared quadratic Wasserstein distance

A Alfonsi, B Jourdain - arXiv preprint arXiv:1811.07787, 2018 - arxiv.org

In this paper, we remark that any optimal coupling for the quadratic Wasserstein distance $

W^ 2_2 (\mu,\nu) $ between two probability measures $\mu $ and $\nu $ with finite second

order moments on $\mathbb {R}^ d $ is the composition of a martingale coupling with an …

Saliency detection based on aggregated Wasserstein distance

F Sun, W Li - Journal of Electronic Imaging, 2018 - spiedigitallibrary.org

This paper proposes a saliency detection method based on the aggregated Wasserstein

distance. A multidimensional Gaussian mixture model is used to model the superpixels,

whereby the color information of different color spaces is combined. To overcome the lack of …

Accelerated discrete distribution clustering under wasserstein distance

[PDF] googleapis.com

J Ye, J Li, JZ Wang - US Patent 10,013,477, 2018 - Google Patents

Computationally efficient accelerated D2-clustering algorithms are disclosed for clustering

discrete distributions under the Wasserstein distance with improved scalability. Three first-

order methods include subgradient descent method with re-parametrization, alternating …

<——2018—-— 2018———630—

Generative model based on minimizing exact empirical wasserstein distance

A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

Generative Adversarial Networks (GANs) are a very powerful framework for generative

modeling. However, they are often hard to train, and learning of GANs often becomes

unstable. Wasserstein GAN (WGAN) is a promising framework to deal with the instability …

[HTML] Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

J Tugaut - Comptes Rendus Mathematique, 2018 - Elsevier

It is well-known (see Bolley et al.[3]) that there exists a contraction in Wasserstein distance

between the solution to the granular media equation and its unique steady state, provided

that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is …

Measuring distributional asymmetry with Wasserstein distance and Rademacher symmetrization

AB Kashlak - Electronic Journal of Statistics, 2018 - projecteuclid.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

asymmetry of the given measure. An empirical bound on this asymmetric correction term is …

Constructing misfit function for full waveform inversion based on sliced Wasserstein distance

F Chen, D Peter - 80th EAGE Conference and Exhibition 2018, 2018 - earthdoc.org

It has been proven that full waveform inversion (FWI) based on optimal transport (OT) is

robust against noise and contains less local minima. The accurate solution to OT problem on

the real line (1D) is analytical with the selected distance function which can be effectively …

Convergence in the Wasserstein Distance

R Douc, E Moulines, P Priouret, P Soulier - Markov Chains, 2018 - Springer

In the previous chapters, we obtained rates of convergence in the total variation distance of

the iterates P^ n of an irreducible positive Markov kernel P to its unique invariant measure π

for π-almost every x ∈ X and for all x ∈ X if the kernel P is irreducible and positive Harris …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

Topological data assimilation using Wasserstein distance

L Li, A Vidard, FX Le Dimet, J Ma - Inverse Problems, 2018 - iopscience.iop.org

This work combines a level-set approach and the optimal transport-based Wasserstein

distance in a data assimilation framework. The primary motivation of this work is to reduce

assimilation artifacts resulting from the position and observation error in the tracking and …

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

<——2018—-— 2018———640—

[PDF] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

G Vissio, V Lucarini - pdfs.semanticscholar.org

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modelling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

[CITATION] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

magnetic resonance images of the brain, represented as densities on a voxel grid. We aim

to use the Wasserstein distance for dimensionality reduction of MR images by using it as a …

2018 zzz 39

[CITATION] Supplementary materials “Approximate Bayesian computation with the Wasserstein distance”

E Bernton, PE Jacob, M Gerber, CP Robert

[CITATION] Supplementary materials for “On point estimation with the Wasserstein distance”

E Bernton, PE Jacob, M Gerber, CP Robert

[CITATION] Supplementary materials for “On point estimation with the Wasserstein distance”

E Bernton, PE Jacob, M Gerber, CP Robert

The Wasserstein Distance and its Application to Generative Adversarial Networks

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

[PDF] impa.br 2018

[PDF] Large Deviations for a matching problem related to the∞-Wasserstein distance

J Trashorras - ALEA, 2018 - alea.impa.br

Abstract. Let (E,d) be a compact metric space, X = (X1,...,Xn,... ) and Y = (Y1,...,Yn,... ) two independent

sequences of independent E-valued random variables and (LX n )n≥1 and (LY n )n≥1 the associated

sequences of empirical mea- sures. We establish a Large Deviation Principle for (W∞(LX …

hal.archives-ouvertes.fr › document

by J Trashorras · 2018 — Large Deviations for a matching problem related to the ∞-Wasserstein distance. José Trashorras ∗. February 15, 2017. Abstract. Let (E,d) be a ...

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

[

[PDF] … for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence Diagram”

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology

theory, and their main output is a descriptor called persistence diagram (PD), which encodes

the topology of a space at all scales in the form of a point cloud with multiplicities in the …

[PDF] … for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Γ-convergence of Entropy Regularized Wasserstein Distance

S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized

optimal transport (OT) problem to the non-regularized OT problem, as described in

[CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

A fast Proximal Point Method for Computing Exact ...

by Y Xie · 2018 · Cited by 51 — A Fast Proximal Point Method for Computing Exact Wasserstein Distance. Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing.

[CITATION] A fast proximal point method for Wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

Fast Proximal Point Method for Computing Exact ...

by Y Xie · 2018 · Cited by 51 — A Fast Proximal Point Method for Computing Exact Wasserstein Distance. ... We address this challenge by developing an Inexact Proximal point method for exact Optimal Transport problem (IPOT) with the proximal operator approximately evaluated at each iteration using projections to the probability simplex.

[CITATION] A fast proximal point method for computing wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

Multivariate approximations in Wasserstein distance by Stein's ...

2018

link.springer.com › article › shared-article-renderer

Sep 28, 2018 — In particular, we provide an error bound for the Wasserstein distance ... CLT in $\cal{W}_2$ distance with near optimal convergence rate.

[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

MGAN: Training generative adversarial nets with multiple generators

<——2018—-— 2018———650—

Q Hoang, TD Nguyen, T Le, D Phung - International conference on …, 2018 - openreview.net

… our approach over GAN, UnrolledGAN and D2GAN wrt both distances (lower is better); notably

the Wasserstein distances from … The rationale is that for each feature map, the ReLU gates will

open for about 50 … Finally, we try SeLU (Klambauer et al., 2017) but fail to train our model …

\ Cited by 20 Related articles All 5 versions

[HTML] Improved Wasserstein conditional generative adversarial network speech enhancement

S Qin, T Jiang - EURASIP Journal on Wireless Communications and …, 2018 - Springer

… such as conditional GAN and Wasserstein GAN to solve those disadvantages. … the Wasserstein

GAN to improve the learning stability [7] and Ishaan Gulrajani improves the Wasserstein …

2018 see 2016, 2020

The Wasserstein distance between stationary measures ...

by I Cipriano · 2016 · Cited by 3 — Title:The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval.

[CITATION] The Wasserstein distance between stationary measures

I Cipriano - arXiv preprint arXiv:1611.00092, 2018

2018 see 2019 zzz 40

[CITATION] Optimal transport and wasserstein distance

L Wasserman - 2018

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between the distribution of mappings of trajectories of a policy into some metric space, and some other fixed distribution (which may, for example …

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

2018

[PDF] upmc.fr

[PDF] Barycentres de Wasserstein pour les abstractions topologiques

J Tierny - edb.upmc.fr

Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui

permet en pratique d'introduire une mesure de bruit sur les structures topologiques, comme

les singularités (sphères de couleur) dans cet exemple de carte d'élévation. Cette mesure …

Data-driven risk-averse stochastic optimization with Wasserstein metric

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

In this paper, we study a data-driven risk-averse stochastic optimization approach with

Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we

can successfully reformulate the risk-averse two-stage stochastic optimization problem with …

[PDF] Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - jmlr.org

Divide-and-conquer based methods for Bayesian inference provide a general approach for

tractable posterior inference when the sample size is large. These methods divide the data

into smaller subsets, sample from the posterior distribution of parameters in parallel on all …

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function

is known to suffer from cycle-skipping issues that increase the risk of computing a local

rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to …

rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to …

The quadratic Wasserstein metric for earthquake location

J Chen, Y Chen, H Wu, D Yang - Journal of Computational Physics, 2018 - Elsevier

Abstract In Engquist et al.(2016)[8], the Wasserstein metric was successfully introduced to

the full waveform inversion. We apply this method to the earthquake location problem. For

this problem, the seismic stations are far from each other. Thus, the trace by trace …

<——2018—-— 2018———660 —

2018 [PDF] arxiv.org

Mapper Comparison with Wasserstein Metrics

M McCabe - arXiv preprint arXiv:1812.06232, 2018 - arxiv.org

The challenge of describing model drift is an open question in unsupervised learning. It can

be difficult to evaluate at what point an unsupervised model has deviated beyond what

would be expected from a different sample from the same population. This is particularly true …

On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order one between a pair of two-dimensional histograms. Recent works in Computer Vision and Machine Learning have shown the benefits of measuring Wasserstein distances of order …

Distributionally robust games: Wasserstein metric

J Gao, H Tembine - 2018 International Joint Conference on …, 2018 - ieeexplore.ieee.org

Deep generative models are powerful but difficult to train due to its instability, saturation

problem and high dimensional data distribution. This paper introduces a game theory

framework with Wasserstein metric to train generative models, in which the unknown data …

[HTML] nature.com

[HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with

asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian

dynamics and the collective motion of living organisms. In this study, we found that particles …

Classification of small UAVs based on auxiliary classifier wasserstein GANs

C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Beyond their benign uses, the small Unmanned Aerial Vehicles (UAVs) are expected to take

the major role in future smart cities that have attracted the attention of the public and

authorities. Therefore, detecting, tracking and classifying the type of UAVs is important for …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

… Compared with Wasserstein-metric and Moment-metric, WM-metric considers more probabilistic

information and thus can further mitigate the conservativeness of ambiguity set.The performance

of the proposed approach is tested by a 6-bus system for illustrative purpose …

Risk-based Distributionally Robust Energy and Reserve Dispatch with Wasserstein-Moment Metric

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation

H Wu, PC Ma, Y Lv, M Ihme - 2018 AIAA Aerospace Sciences Meeting, 2018 - arc.aiaa.org

The objective of this work is to address the need for assessing the quality of large-eddy

simulations with particular application to turbulent reacting flows. Such assessments include

the consideration of resolution requirements and the quantitative evaluation of the accuracy …

[PDF] hse.ru

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

Graph clustering and the nuclear Wasserstein metric

D Roux Uribe - 2018 - repositorio.uniandes.edu.co

INTRODUCTION: one of the most relevant situations in public health in Colombia is child

stunting and in parallel, the social effects caused by armed conflict. Currently, it is unknown if

exposure to armed conflict is related to child stunting. OBJECTIVES: identify if significant …

<——2018—-— 2018———670—

[PDF] uma.es

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

A Esteban-Pérez, JM Morales - 2018 - riuma.uma.es

We consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

A two-step computation of the exact gan wasserstein distance

H Liu, GU Xianfeng, D Samaras - … Conference on Machine …, 2018 - proceedings.mlr.press

In this paper, we propose a two-step method to compute the Wasserstein distance in

Wasserstein Generative Adversarial Networks (WGANs): 1) The convex part of our objective

can be solved by linear programming; 2) The non-convex residual can be approximated by …

Free complete Wasserstein algebras

R Mardare, P Panangaden, GD Plotkin - arXiv preprint arXiv:1802.07366, 2018 - arxiv.org

We present an algebraic account of the Wasserstein distances $ W_p $ on complete metric

spaces, for $ p\geq 1$. This is part of a program of a quantitative algebraic theory of effects

in programming languages. In particular, we give axioms, parametric in $ p $, for algebras …

[PDF] episciences.org

Free complete Wasserstein algebras

GD Plotkin, P Panangaden… - Logical Methods in …, 2018 - lmcs.episciences.org

We present an algebraic account of the Wasserstein distances $ W_p $ on complete metric

spaces, for $ p\geq 1$. This is part of a program of a quantitative algebraic theory of effects

in programming languages. In particular, we give axioms, parametric in $ p $, for algebras …

Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary

Learning

Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel, Fred Ngolè, David Coeurjolly, Marco Cuturi, Gabriel Peyré, and Jean-Luc Starck

SIAM Journal on Imaging Sciences Vol. 11, No. 1, pp. 643–6782018
Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein …

W-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

2018 [PDF] uni-muenster.de

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

magnetic resonance images of the brain, represented as densities on a voxel grid. We aim

to use the Wasserstein distance for dimensionality reduction of MR images by using it as a …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

2018 [HTML] springer.com

[HTML] Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

S Amari, R Karakida, M Oizumi - Information Geometry, 2018 - Springer

Two geometrical structures have been extensively studied for a manifold of probability

distributions. One is based on the Fisher information metric, which is invariant under

reversible transformations of random variables, while the other is based on the Wasserstein …

2018 zzz 41 see 2020 book with introduction -> invitation

[CITATION] Introduction to statistics in the Wasserstein space

VM Panaretos, Y Zemel - 2018 - … and Mathematical Statistics. To …

[CITATION] Introduction to statistics in the Wasserstein space

VM Panaretos, Y Zemel - 2018 - Springer Briefs in Probability and …

[CITATION] Introduction to statistics in the Wasserstein space

VM Panaretos, Y Zemel - 2018 - Springer Briefs in Probability and …

Cited by 2 Related articles7
[CITATION] Introduction to statistics in the Wasserstein space

VM Panaretos, Y Zemel - 2018 - … and Mathematical Statistics. To …

amazon

Anomaly detection with Wasserstein GAN

I Haloui, JS Gupta, V Feuillard - arXiv preprint arXiv:1812.02463, 2018 - arxiv.org

… Instead of clipping the weights, some authors suggest to use another technique to ensure the …

The loss curve converges towards zero thus the Wasserstein distance between Pr and Pθ tends

to … the optimal discriminator will always return 1/2 ∀x ∈ X. Moreover, the author of the …

Primal-dual wasserstein gan

M Gemici, Z Akata, M Welling - arXiv preprint arXiv:1805.09575, 2018 - arxiv.org

… Corresponding author … In Wasserstein GANs (WGAN, [5]), the potential f ∈ FLip is represented

by a critic network with parameters that lie within a compact … Authors of [15] use this property of

optimal potentials to motivate their choice of regularization for the critic network in their …

<——2018—–—2018———680—

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

… The algorithm resembles the Polyak's momentum [26] ∗This work was done when the author

was visiting Duke University … JZ and LC are corresponding authors … In this work, we propose to

minimize the KLD on the 2-Wasserstein space P2, which is general enough to contain all …

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

We consider doing Bayesian inference by minimizing the KL divergence on the 2-

Wasserstein space P2. By exploring the Riemannian structure of P2, we develop two

inference methods by simulating the gradient flow on P2 via updating particles, and an …

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

A multivariate CLT in Wasserstein distance with near optimal ...

2018 see 2017

https://www.semanticscholar.org › paper › A-multivariate-...

Let $X_1, \ldots , X_n$ be i.i.d. random vectors in $\mathbb{R}^d$ with $\|X_1\| \le \beta$. Then, we show that $\frac{1}{\sqrt{n}}(X_1 + \ldots + X_n)$ converges ...

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[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

Page 1. AMMI – Introduction to Deep Learning 10.2. Wasserstein GAN François Fleuret

https://fleuret.org/ammi-2018/ Wed Aug 29 16:57:14 CAT 2018 ÉCOLE POLYTECHNIQUE

FÉDÉRALE DE LAUSANNE Page 2. Arjovsky et al. (2017) point out that DJS does not account

[much] for the metric structure of the space. François Fleuret AMMI – Introduction to Deep Learning /

10.2. Wasserstein GAN 1 / 16 Page 3. Arjovsky et al. (2017) point out that DJS does not account

[much] for the metric structure of the space. δ x 1 2 1 2δ 1 µ µ François Fleuret AMMI – Introduction …

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

… Wasserstein GAN 16 / 16 Page 34. So instead of looking for argmax DL≤1 EX∼µ [ D(X) ] −

EX∼µG [ D(X) ] , Gulrajani et al. propose to solve argmax D EX∼µ [ D(X) ] − EX∼µG [ D(X) ] −

λEX∼µp [ ( ∇D(X) − 1)2 ] where µp is the distribution of a point B sampled uniformly between …

Gradient flows for frame potentials on the Wasserstein space

C Wickman, K Okoudjou - arXiv preprint arXiv:1808.09319, 2018 - arxiv.org

… In particular, we construct gradient flows in the Wasserstein … to subdifferentials in the Wasserstein space will likely prove … If F : P2pRdq Ñ p8,8s is a functional on the 2-Wasserstein …

2018

A note on reinforcement learning with Wasserstein distance ...

https://www.semanticscholar.org › paper › A-note-on-rein...

Feb 12, 2018 — An application of Wasserstein distance to Reinforcement Learning is described, ... regularisation, with applications to multipolicy learning.

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

[CITATION] Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls. under review, 2016

GA Hanasusanto, D Kuhn

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

<——2018—-—2018———690 —

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

2018

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

Learning Joint Wasserstein Auto-Encoders for Joint Distribution Matching

2018

J Cao, Y Guo, L Mo, P Zhao, J Huang, M Tan - 2018 - openreview.net

We study the joint distribution matching problem which aims at learning bidirectional

mappings to match the joint distribution of two domains. This problem occurs in

unsupervised image-to-image translation and video-to-video synthesis tasks, which …

2018

multivariate CLT in Wasserstein distance with near optimal ...

www.researchgate.net › publication › 301846996_A_mul...

Download Citation | A multivariate CLT in Wasserstein distance with near optimal convergence rate | Let $X_1, \ldots , X_n$ be i.i.d. random vectors in ...

[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

ITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

Minimax distribution estimation in Wasserstein distance

2018

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

The Wasserstein metric is an important measure of distance between probability

distributions, with applications in machine learning, statistics, probability theory, and data

analysis. This paper provides upper and lower bounds on statistical minimax rates for the …

Fast discrete distribution clustering using Wasserstein barycenter with sparse support

J Ye, P Wu, JZ Wang, J Li - IEEE Transactions on Signal …, 2017 - ieeexplore.ieee.org

In a variety of research areas, the weighted bag of vectors and the histogram are widely

used descriptors for complex objects. Both can be expressed as discrete distributions. D2-

clustering pursues the minimum total within-cluster variation for a set of discrete distributions …

2018 [PDF] googleapis.com

Accelerated discrete distribution clustering under wasserstein distance

J Ye, J Li, JZ Wang - US Patent 10,013,477, 2018 - Google Patents

Computationally efficient accelerated D2-clustering algorithms are disclosed for clustering

discrete distributions under the Wasserstein distance with improved scalability. Three first-

order methods include subgradient descent method with re-parametrization, alternating …

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

[PDF] wiley.com

Data-driven affinely adjustable distributionally robust framework for unit commitment based on Wasserstein metric

W Hou, R Zhu, H Wei, H TranHoang - IET Generation, Transmission & …, 2018 - IET

This study proposes a data-driven distributionally robust framework for unit commitment

based on Wasserstein metric considering the wind power generation forecasting errors. The

objective of the constructed model is to minimise the expected operating cost, including the …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

<——2018—-— 2018———700 —

ngle image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network

and Wasserstein generative adversarial nets is proposed aiming at generating a photo-

realistic image with finer texture details. Specifically, we construct a framework consisting of …

Cross-domain text sentiment classification based on Wasserstein distance

G Cai, Q Lin, N Chen - International Conference on Security with Intelligent …, 2018 - Springer

Text sentiment analysis is mainly to detect the sentiment polarity implicit in text data. Most

existing supervised learning algorithms are difficult to solve the domain adaptation problem

in text sentiment analysis. The key of cross-domain text sentiment analysis is how to extract …

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

Geometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

J Li, F Zhang - Journal of Computational and Graphical …, 2018 - amstat.tandfonline.com

An ensemble of forecasts generated by different model simulations provides rich information

for meteorologists about impending weather such as precipitating clouds. One major form of

forecasts presents cloud images created by multiple ensemble members. Common features …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

Page 1. Accelerated First-order Methods on the Wasserstein Space for Bayesian Inference Chang

Liu1∗, Jingwei Zhuo1, Pengyu Cheng2, Ruiyi Zhang2, Jun Zhu1†, Lawrence Carin2† 1 Dept.

of Comp. Sci. & Tech., TNList Lab, State Key Lab for Intell. Tech …

-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

[PDF] ON WASSERSTEIN ISOMETRIES OF PROBABILITY MEASURES ON UNIT SPHERES

D VIROSZTEK - arXiv preprint arXiv:1802.03305, 2018 - researchgate.net

We consider the space of all Borel probability measures on the unit sphere of a Euclidean

space endowed with the Wasserstein metric Wp for arbitrary p≥ 1. Our goal is to describe

the isometry group of this metric space. We make some progress in the direction of a Banach …

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

… distance, ie, dij = |i − j|. III. PROPOSED ALGORITHM BASED ON WASSERSTEIN

DISTANCE We propose smooth sparse representation based on Wasser- stein distance

for face image super-resolution. We reviews the face image …

Improving the improved training of wasserstein gans: A consistency term and its dual effect

X Wei, B Gong, Z Liu, W Lu, L Wang - arXiv preprint arXiv:1803.01541, 2018 - arxiv.org

Despite being impactful on a variety of problems and applications, the generative

adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed

by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the …

<——2018—-— 2018———710 —

On the latent space of wasserstein auto-encoders

PK Rubenstein, B Schoelkopf, I Tolstikhin - arXiv preprint arXiv …, 2018 - arxiv.org

We study the role of latent space dimensionality in Wasserstein auto-encoders (WAEs).

Through experimentation on synthetic and real datasets, we argue that random encoders

should be preferred over deterministic encoders. We highlight the potential of WAEs for …

Distributed computation of Wasserstein barycenters over networks

CA Uribe, D Dvinskikh, P Dvurechensky… - … IEEE Conference on …, 2018 - ieeexplore.ieee.org

We propose a new class-optimal algorithm for the distributed computation of Wasserstein

Barycenters over networks. Assuming that each node in a graph has a probability

distribution, we prove that every node reaches the barycenter of all distributions held in the …

Snowflake universality of Wasserstein spaces

A Andoni, A Naor, O Neiman - … Scientifiques de l'Ecole …, 2018 - collaborate.princeton.edu

Abstract For p∈(1;∞) let P p (ℝ3) denote the metric space of all p-integrable Borel

probability measures on ℝ 3, equipped with the Wasserstein p metric W p. We prove that for

every ϵ> 0, every θ∈(0; 1/p] and every finite metric space (X, d X), the metric space (X; d X …

A fast globally linearly convergent algorithm for the computation of Wasserstein barycenters

L Yang, J Li, D Sun, KC Toh - arXiv preprint arXiv:1809.04249, 2018 - arxiv.org

In this paper, we consider the problem of computing a Wasserstein barycenter for a set of

discrete probability distributions with finite supports, which finds many applications in areas

such as statistics, machine learning and image processing. When the support points of the …

Speech enhancement based on a new architecture of wasserstein generative adversarial networks

S Ye, T Jiang, S Qin, W Zou… - 2018 11th International …, 2018 - ieeexplore.ieee.org

Most conventional speech enhancement methods work poorly at low SNRs. And the speech

enhancement method based on generative adversarial network (SEGAN) gets lower speech

quality though it has lots of parameters in its generator. To solve these problems, we …

Classification of small UAVs based on auxiliary classifier wasserstein GANs

2018

C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Page 1. Classification of Small UAVs based on Auxiliary Classifier Wasserstein GANs Caidan

Zhao1, Caiyun Chen1, Zhibiao Cai1, Mingxian Shi1, Xiaojiang Du2, Mohsen Guizani3 1Dept.

of Communication Engineering, Xiamen University, Xiamen, China. 2Dept …

Classification of Small UAVs Based on Auxiliary Classifier Wasserstein GANs

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

Y Chen, HG Müller - arXiv preprint arXiv:1809.03498, 2018 - arxiv.org

… We make the following assumption regarding the discrepancy of the estimated and true

probability distributions for the theoretical analysis on the estimation of Wasserstein temporal

gradients, where we note that this assumption can be easily satisfied …

Wasserstein gradients for the temporal evolution of probability distributions

<——2018—-— 2018———720 —

Scene classification using hierarchical Wasserstein CNN

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

… We address this issue by coupling CNN with a hierarchical Wasserstein (HW) loss—the …

(GANs) and proved to play a prominent role in Wasserstein GAN [43]. WD can be intuitively …

Save Cite Cited by 49 Related articles All 2 versions

[PDF] aimsciences.org

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

Minimax distribution estimation in Wasserstein distance

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

… The Wasserstein metric is an important measure of distance … a probability distribution under

Wasserstein loss. Specifically, we … The main object of study in this paper is the Wasserstein …

Policy optimization as wasserstein gradient flows

R Zhang, C Chen, C Li, L Carin - … Conference on Machine …, 2018 - proceedings.mlr.press

Policy optimization is a core component of reinforcement learning (RL), and most existing

RL methods directly optimize parameters of a policy based on maximizing the expected total

reward, or its surrogate. Though often achieving encouraging empirical success, its …

2018

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

Variational wasserstein clustering

L Mi, W Zhang, X Gu, Y Wang - Proceedings of the …, 2018 - openaccess.thecvf.com

We propose a new clustering method based on optimal transportation. We discuss the

connection between optimal transportation and k-means clustering, solve optimal

transportation with the variational principle, and investigate the use of power diagrams as …

Lp-WGAN: Using Lp-norm normalization to stabilize Wasserstein generative adversarial networks

C Zhou, J Zhang, J Liu - Knowledge-Based Systems, 2018 - Elsevier

Wasserstein generative adversarial networks (Wasserstein GANs, WGAN) improve the

performance of GANs significantly by imposing the Lipschitz constraints on the critic, which

is implemented by weight clipping. In this work, we argue that weight clipping could result in …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

…, X Wang, C Duan, X Wu, W Zhang - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

The exponential contraction in $ L^ 1$-Wasserstein distance and exponential convergence

in $ L^ q $-Wasserstein distance ($ q\geq 1$) are considered for stochastic differential

equations with irregular drift. When the irregular drift drift is locally bounded, the exponential …

<——2018—-— 2018———730 —

Motion-blind blur removal for CT images with Wasserstein generative adversarial networks

Y Lyu, W Jiang, Y Lin, L Voros, M Zhang… - … Congress on Image …, 2018 - ieeexplore.ieee.org

Advanced deblurring techniques for computed tomography (CT) images are necessary and

crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup

and treatment response assessment in radiation oncology. Currently, medical image …

Wasserstein generative recurrent adversarial networks for image generating

C Zhang, Y Feng, B Qiang… - 2018 24th International …, 2018 - ieeexplore.ieee.org

Most generative models are generating images at a time, but in fact, painting is usually done

iteratively and repeatedly. Generative Adversarial Networks (GAN) are well known for

generating images, however, it is hard to train stably. To tackle this problem, we propose a …

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

[PDF] Regularized Wasserstein Means Based on Variational Transportation

L Mi, W Zhang, Y Wang - CoRR, 2018 - public.asu.edu

We raise the problem of regularizing Wasserstein means and propose several terms tailored

to tackle different problems. Our formulation is based on the variational transportation to

distribute a sparse discrete measure into the target domain without mass splitting. The …

Graph clustering and the nuclear Wasserstein metric

D Roux Uribe - 2018 - repositorio.uniandes.edu.co

INTRODUCTION: one of the most relevant situations in public health in Colombia is child

stunting and in parallel, the social effects caused by armed conflict. Currently, it is unknown if

exposure to armed conflict is related to child stunting. OBJECTIVES: identify if significant …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

The exponential contraction in $ L^ 1$-Wasserstein distance and exponential convergence

in $ L^ q $-Wasserstein distance ($ q\geq 1$) are considered for stochastic differential

equations with irregular drift. When the irregular drift drift is locally bounded, the exponential …

[HTML] Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

J Tugaut - Comptes Rendus Mathematique, 2018 - Elsevier

It is well-known (see Bolley et al.[3]) that there exists a contraction in Wasserstein distance

between the solution to the granular media equation and its unique steady state, provided

that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is …

Policy optimization as wasserstein gradient flows

R Zhang, C Chen, C Li, L Carin - … Conference on Machine …, 2018 - proceedings.mlr.press

Policy optimization is a core component of reinforcement learning (RL), and most existing

RL methods directly optimize parameters of a policy based on maximizing the expected total

reward, or its surrogate. Though often achieving encouraging empirical success, its …

<——2018—-— 2018———740—

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as …

On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order

one between a pair of two-dimensional histograms. Recent works in Computer Vision and

Machine Learning have shown the benefits of measuring Wasserstein distances of order …

Propagation of chaos, Wasserstein gradient flows and toric Kähler–Einstein metrics

RJ Berman, M Önnheim - Analysis & PDE, 2018 - msp.org

Motivated by a probabilistic approach to Kähler–Einstein metrics we consider a general

nonequilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasiconvex N-particle interaction energy. We …

Extremal flows in Wasserstein space

G Conforti, M Pavon - Journal of Mathematical Physics, 2018 - aip.scitation.org

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein

space. We show that the flows associated with the Schrödinger bridge with general prior,

with optimal mass transport, and with the Madelung fluid can all be characterized as …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

2018

Gradient flows for frame potentials on the Wasserstein space

C Wickman, K Okoudjou - arXiv preprint arXiv:1808.09319, 2018 - arxiv.org

In this paper we bring together some of the key ideas and methods of two very lively fields of

mathematical research, frame theory and optimal transport, using the methods of the second

to answer questions posed in the first. In particular, we construct gradient flows in the …

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation

H Wu, PC Ma, Y Lv, M Ihme - 2018 AIAA Aerospace Sciences Meeting, 2018 - arc.aiaa.org

The objective of this work is to address the need for assessing the quality of large-eddy

simulations with particular application to turbulent reacting flows. Such assessments include

the consideration of resolution requirements and the quantitative evaluation of the accuracy …

Diffusing Policies: Towards Wasserstein Policy Gradient Flows

PH Richemond, B Maginnis - 2018 - openreview.net

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

machine learning and computer vision. Such an image can be generated at pixel level by

learning from a large collection of images. Learning to generate colorful cartoon images …

Scene classification using hierarchical Wasserstein CNN

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

In multiclass classification, convolutional neural network (CNN) is generally coupled with the

cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a

ground truth class and ignores the interclass relationship. We argue that CNN can be …

<——2018—-— 2018———750—

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org

This paper is concerned by the study of barycenters for random probability measures in the

Wasserstein space. Using a duality argument, we give a precise characterization of the

population barycenter for various parametric classes of random probability measures with …

Bayes and maximum likelihood for L 1 -Wasserstein deconvolution of Laplace mixtures

C Scricciolo - Statistical Methods & Applications, 2018 - Springer

We consider the problem of recovering a distribution function on the real line from

observations additively contaminated with errors following the standard Laplace distribution.

Assuming that the latent distribution is completely unknown leads to a nonparametric …

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

distributions with a set of particles. In this paper we introduce a new particle-based

variational inference method based on the theory of semi-discrete optimal transport. Instead …

[PDF] eg.org

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

A two-step computation of the exact gan wasserstein distance

H Liu, GU Xianfeng, D Samaras - … Conference on Machine …, 2018 - proceedings.mlr.press

In this paper, we propose a two-step method to compute the Wasserstein distance in

Wasserstein Generative Adversarial Networks (WGANs): 1) The convex part of our objective

can be solved by linear programming; 2) The non-convex residual can be approximated by …

Wasserstein divergence for gans

J Wu, Z Huang, J Thoma, D Acharya… - Proceedings of the …, 2018 - openaccess.thecvf.com

In many domains of computer vision, generative adversarial networks (GANs) have

achieved great success, among which the family of Wasserstein GANs (WGANs) is

considered to be state-of-the-art due to the theoretical contributions and competitive …

CITATION] Wasserstein divergence for gans

W Jiqing, H Zhiwu, T Janine, A Dinesh, VG Luc - ECCV, 2018

Wasserstein Center 손실을 이용한 스케치 기반 3 차원 물체 검색

지명근， 전준철， 김남기 - 인터넷정보학회논문지, 2018 - dbpia.co.kr

… 마지막으로, 추출한 3차원 물체의 특징과 스케치의 특징을 본 논문에서 제안한 Wasserstein Center

손실을 이용하여 학습하고 스케치 기반의 3차원 물체 … In this paper, we propose a new method of

using Sketch CNN, Wasserstein CNN and Wasserstein center loss for sketch …

관련 학술자료 전체 3개의 버전

[Korean 3D object search based on sketch using Wasserstein Center loss]

Bayes and maximum likelihood for L 1 -Wasserstein deconvolution of Laplace mixtures

C Scricciolo - Statistical Methods & Applications, 2018 - Springer

We consider the problem of recovering a distribution function on the real line from

observations additively contaminated with errors following the standard Laplace distribution.

Assuming that the latent distribution is completely unknown leads to a nonparametric …

<——2018—-— 2018———760—

Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

G Auricchio, F Bassetti, S Gualandi… - arXiv preprint arXiv …, 2018 - arxiv.org

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance

between a pair of $ d $-dimensional histograms having $ n $ bins each. We prove that this

problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+ 1) $-partite …

-Wasserstein distances of tracial -algebras and their disintegration problem

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with

multiplication operators arising as the logarithmic mean under a functional calculus …

On the minimizing movement with the 1-Wasserstein distance

M Agueh, G Carlier, N Igbida - ESAIM: Control, Optimisation and …, 2018 - esaim-cocv.org

We consider a class of doubly nonlinear constrained evolution equations which may be

viewed as a nonlinear extension of the growing sandpile model of [L. Prigozhin, Eur. J. Appl.

Math. 7 (1996) 225–235.]. We prove existence of weak solutions for quite irregular sources …

Bayes and maximum likelihood for L 1 -Wasserstein deconvolution of Laplace mixtures

C Scricciolo - Statistical Methods & Applications, 2018 - Springer

We consider the problem of recovering a distribution function on the real line from

observations additively contaminated with errors following the standard Laplace distribution.

Assuming that the latent distribution is completely unknown leads to a nonparametric …

[PDF] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

…, G CARLIER, E référent ENSTA, P CARPENTIER… - 2018 - imo.universite-paris-saclay.fr

We study the numerical implementation of a minimizing movement scheme using the 1-

Wasserstein distance introduced in [1]. We implement this scheme using two different primal

dual algorithm: a Augmented Lagrangian technique with the ADMM algorithm and the …

[CITATION] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018

[PDF] crest.science

[PDF] Sliced Wasserstein Kernel for Persistence Diagrams M. CARRIÈRE M. CUTURI 2

S OUDOT - crest.science

Persistence diagrams play a key role in topological data analysis (TDA), in which they are

routinely used to describe topological properties of complicated shapes. persistence

diagrams enjoy strong stability properties and have proven their utility in various learning …

[CITATION] Wasserstein-1 in generative models

A Nowak - 2018

2018

The Vaserstein symbol on real smooth affine threefolds

by Fasel, Jean K-Theory, 2018

Book Chapter: Citation Online

The aserstein symbol on real smooth affine threefolds

by J Fasel - ‎2016 - ‎Cited by 1 - ‎Related articles

May 30, 2016 - More precisely, we show that the Vaserstein symbol is a bijection for such a threefold X if and only if the set of compact connected components of the real points of X (endowed with the Euclidean topology) is empty.

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

Graph clustering and the nuclear Wasserstein metric

2018 book [PDF] uniandes.edu.co

D Roux Uribe - 2018 - repositorio.uniandes.edu.co

INTRODUCTION: one of the most relevant situations in public health in Colombia is child

stunting and in parallel, the social effects caused by armed conflict. Currently, it is unknown if

exposure to armed conflict is related to child stunting. OBJECTIVES: identify if significant …

Graph clustering and the nuclear Wasserstein metric

<——2018—-— 2018———770—

[PDF] harchaoui.org

[PDF] Wasserstein Adversarial Mixture for Deep Generative Modeling and Clustering

W Harchaoui, PA Mattei, A Almansa, C Bouveyron - harchaoui.org

Unsupervised learning, and in particular clustering, is probably the most central problem in

learning theory nowadays. This work focuses on the clustering of complex data by

introducing a deep generative approach for both modeling and clustering. The proposed …

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical practice has raised a public concern over the associated radiation dose to the patient. Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

Minimax distribution estimation in Wasserstein distance

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on statistical minimax rates for the …

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in machine learning and computer vision. Such an image can be generated at pixel level by learning from a large collection of images. Learning to generate colorful cartoon images …

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under wasserstein distance

Y Han, J Jiao, T Weissman - Conference On Learning …, 2018 - proceedings.mlr.press

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance. We construct an efficiently computable estimator that achieves the minimax rates in estimating …

2018

Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator

VA Nguyen, D Kuhn, PM Esfahani - arXiv preprint arXiv:1805.07194, 2018 - arxiv.org

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $ p $-dimensional Gaussian random vector from $ n $ independent samples. The proposed model minimizes …

Semantic image inpainting through improved wasserstein generative adversarial networks

P Vitoria, J Sintes, C Ballester - arXiv preprint arXiv:1812.01071, 2018 - arxiv.org

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image. In this work we tackle this problem not only by using the available visual data but also by incorporating image semantics through the use of generative models. Our contribution is …

Image labeling based on graphical models using wasserstein messages and geometric assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete graphical models. By utilizing local Wasserstein distances for coupling assignment measures across edges of the underlying graph, a given discrete objective function is …

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an alternative to vocoders and achieved very high-quality synthetic speech in terms of both naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

Single image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network and Wasserstein generative adversarial nets is proposed aiming at generating a photo-realistic image with finer texture details. Specifically, we construct a framework consisting of …

Wasserstein generative recurrent adversarial networks for image generating

<——2018—-— 2018———780—

C Zhang, Y Feng, B Qiang… - 2018 24th International …, 2018 - ieeexplore.ieee.org

Most generative models are generating images at a time, but in fact, painting is usually done iteratively and repeatedly. Generative Adversarial Networks (GAN) are well known for generating images, however, it is hard to train stably. To tackle this problem, we propose a …

Cross-domain text sentiment classification based on Wasserstein distance

G Cai, Q Lin, N Chen - International Conference on Security with Intelligent …, 2018 - Springer

Text sentiment analysis is mainly to detect the sentiment polarity implicit in text data. Most existing supervised learning algorithms are difficult to solve the domain adaptation problem in text sentiment analysis. The key of cross-domain text sentiment analysis is how to extract …

Image inpainting using wasserstein generative adversarial network

P Hua, X Liu, M Liu, L Dong, M Hui… - Optics and Photonics …, 2018 - spiedigitallibrary.org

Recent advances in convolution neural networks have shown promising results for the challenging task of filling large missing regions in an image with semantically plausible and context aware details. These learning-based methods are significantly more effective in …

[PDF] eg.org

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D RGB image. We consider the light field synthesis problem equivalent to image super-resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have been proposed. However, these approaches only perform well under the condition that the input is noiseless or has small noise. These existing approaches think the measure of …

2018

Generalization error bounds using Wasserstein distances

AT Lopez, V Jog - 2018 IEEE Information Theory Workshop …, 2018 - ieeexplore.ieee.org

Generalization error of a learning algorithm characterizes the gap between an algorithm's performance on test data versus performance on training data. In recent work, Xu & Raginsky [1] showed that generalization error may be upper-bounded using the mutual …

Towards high resolution video generation with progressive growing of sliced wasserstein gans

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task, since the temporal dimension of videos introduces an extra challenge during the generation process. Besides, due to the limitation of memory and training stability, the generation …

Cited by 20 Related articles

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

This paper is focused on the statistical analysis of probability measures $\boldsymbol {\nu} _ {1},\ldots,\boldsymbol {\nu} _ {n} $ on ${\mathbb {R}} $ that can be viewed as independent realizations of an underlying stochastic process. We consider the situation of practical …

Using Wasserstein GAN to generate high quality adversarial examples

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various machine learning tasks, in recent years, they are found to be vulnerable to so-called adversarial examples Specifically, take x is an element of D on which a neural network has …

2018 Index IEEE Signal Processing Letters Vol. 25 - IEEE Xplore

ieeexplore.ieee.org › iel7

by M Abdoli · 2018 — Mandic, D.P., see Talebi, S.P., LSP Oct. 2018 1450-1454. Manton, J.H., see Pauley, ... Bobrovsky–Zakai-Type Bound for Periodic Stochastic Filtering. Nitzan, E.,.
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[PDF] Computing Kantorovich-Wasserstein Distances on d ...

https://www.semanticscholar.org › paper › Computing-Ka...

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of $d$-dimensional histograms having $n$ bins each.

Missing: (d+ ‎| Must include: (d+

[CITATION] Computing Kantorovich-Wasserstein Distances on d-dimensional histograms using (d+ 1)-partite graphs

GAFBS Gualandiand, M Veneroni - arXiv preprint arXiv:1805.07416, 2018

Propriétés statistiques du barycentre dans l’espace de Wasserstein

2018 online

by Cazelles, Elsa

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Computing Wasserstein distance for persistence diagrams on a quantum computer

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to

provide a concise description of a filtered topological space. What makes them even more

useful in practice is that they come with a notion of a metric, the Wasserstein distance …

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

L²-Wasserstein distances of tracial W²-algebras and their disintegration problem

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with

multiplication operators arising as the logarithmic mean under a functional calculus …

2018

[PDF] aimsciences.org

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - ALEA: Latin American Journal of Probability …, 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

Decentralize and randomize: Faster algorithm for Wasserstein barycenters

P Dvurechensky, D Dvinskikh, A Gasnikov… - arXiv preprint arXiv …, 2018 - arxiv.org

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of agents/machines …

Lifted Wasserstein matcher for fast and robust topology tracking

M Soler, M Plainchault, B Conche… - 2018 IEEE 8th …, 2018 - ieeexplore.ieee.org

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on …All 16 versions

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[PDF] copernicus.org

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modeling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

A fast globally linearly convergent algorithm for the computation of Wasserstein barycenters

L Yang, J Li, D Sun, KC Toh - arXiv preprint arXiv:1809.04249, 2018 - arxiv.org

In this paper, we consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the support points of the …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - … IEEE Power & Energy …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-based distributionally robust approach to address the wind power uncertainty in the energy and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

[PDF] dml.cz

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

V Kaňková, V Omelčenko - Kybernetika, 2018 - dml.cz

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

2018

A note on reinforcement learning with Wasserstein distance ...

Feb 12, 2018 — In this note we describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between ...

Missing: A2018 ‎| Must include: A2018

CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

Evaluating a Parametrization of the Coupling in a Fast-Slow System ...

npg.copernicus.org › npg-2018-16-manuscript-version3

coupled system on the subspace spanned by the variables of the Lorenz 84 model with the actual ... discussing the Wasserstein distance and in particular a) whether it is efficient in ... forcings are set as F0 = 8 (corresponding to the so-called winter conditions) and G = 1. ... parametrization (e.g. Vissio and Lucarini (2018)) is:.

[CITATION] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Evaluating a stochastic parametrization for a fast–slow system ...

pdfs.semanticscholar.org › ...

by G Vissio · 2018 · Cited by 8 — ... for a fast–slow system using the Wasserstein distance ... G. Vissio and V. Lucarini: Evaluating a stochastic parametrization for a fast–slow system ... and constructed by coupling the Lorenz 84 (Lorenz, 1984) model with the ...

Missing: Vizio, ‎| Must include: Vizio,

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

2018 aaa
A high-dimensional CLT in W 2 distance with near optimal convergence rate

A Zhai - Probability Theory and Related Fields, 2018 - Springer

… A high-dimensional CLT in $\mathcal {W}_2$ distance with near optimal convergence rate … In the multivariate setting, the recent work of Bonis [10] proves a \(O(1/\sqrt{n … distance is perhaps the most widely studied metric in the high-dimensional central limit theorem literature (see …

[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

Wasserstein cnn: Learning invariant features for nir-vis face recognition

R He, X Wu, Z Sun, T Tan - IEEE transactions on pattern …, 2018 - ieeexplore.ieee.org

Heterogeneous face recognition (HFR) aims at matching facial images acquired from different sensing modalities with mission-critical applications in forensics, security and commercial sectors. However, HFR presents more challenging issues than traditional face …

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EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion recognition model with high accuracy from EEG signals using machine learning approach. Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity …

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

The exponential contraction in $ L^ 1$-Wasserstein distance and exponential convergence in $ L^ q $-Wasserstein distance ($ q\geq 1$) are considered for stochastic differential equations with irregular drift. When the irregular drift drift is locally bounded, the exponential …

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data, we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - Unknown Journal, 2018 - experts.umn.edu

Wasserstein auto-encoders: Latent dimensionality and random encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

OpenReview is created by the Information Extraction and Synthesis Laboratory, College of Information and Computer Science, University of Massachusetts Amherst. We gratefully acknowledge the support of the OpenReview sponsors: Google, Facebook, NSF, the University of Massachusetts …

[HTML] Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

J Tugaut - Comptes Rendus Mathematique, 2018 - Elsevier

It is well-known (see Bolley et al.[3]) that there exists a contraction in Wasserstein distance between the solution to the granular media equation and its unique steady state, provided that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is …

Convergence in the Wasserstein Distance

R Douc, E Moulines, P Priouret, P Soulier - Markov Chains, 2018 - Springer

In the previous chapters, we obtained rates of convergence in the total variation distance of the iterates P^ n of an irreducible positive Markov kernel P to its unique invariant measure π for π-almost every x ∈ X and for all x ∈ X if the kernel P is irreducible and positive Harris …

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Visual feature attribution using wasserstein gans

CF Baumgartner, LM Koch… - Proceedings of the …, 2018 - openaccess.thecvf.com

Attributing the pixels of an input image to a certain category is an important and well-studied problem in computer vision, with applications ranging from weakly supervised localisation to understanding hidden effects in the data. In recent years, approaches based on interpreting …

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We present the critic and map generator functions as Python-inspired pseudo code, which we found easier to interpret than a graphical representation. The layer parameters are specified …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the so …

Geometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

J Li, F Zhang - Journal of Computational and Graphical …, 2018 - amstat.tandfonline.com

An ensemble of forecasts generated by different model simulations provides rich information for meteorologists about impending weather such as precipitating clouds. One major form of forecasts presents cloud images created by multiple ensemble members. Common features …

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology theory, aDistributionally robust mean–variance portfolio selection with Wasserstein distancesnd their main output is a descriptor called persistence diagram (PD), which encodes the topology of a space at all scales in the form of a point cloud with multiplicities in the …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Γ-convergence of Entropy Regularized Wasserstein …

S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized optimal transport (OT) problem to the non-regularized OT problem, as described in [CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the so-called Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend recent inference methodology in order to select the size of the distributional uncertainty as well as …

[CITATION] Distributionally robust mean–variance portfolio selection with Wasserstein distances. arXiv

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018

istributionally robust mean-variance portfolio selection with wasserstein distances

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Computing Wasserstein distance for persistence diagrams on a quantum computer

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a metric, the Wasserstein distance …

Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

G Auricchio, F Bassetti, S Gualandi… - arXiv preprint arXiv …, 2018 - arxiv.org

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of $ d $-dimensional histograms having $ n $ bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+ 1) $-partite …

Classification of small UAVs based on auxiliary classifier wasserstein GANs

C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Beyond their benign uses, the small Unmanned Aerial Vehicles (UAVs) are expected to take the major role in future smart cities that have attracted the attention of the public and authorities. Therefore, detecting, tracking and classifying the type of UAVs is important for …

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

We consider doing Bayesian inference by minimizing the KL divergence on the 2-Wasserstein space P2. By exploring the Riemannian structure of P2, we develop two inference methods by simulating the gradient flow on P2 via updating particles, and an …

Speech enhancement based on a new architecture of wasserstein generative adversarial networks

S Ye, T Jiang, S Qin, W Zou… - … Symposium on Chinese …, 2018 - ieeexplore.ieee.org

Most conventional speech enhancement methods work poorly at low SNRs. And the speech enhancement method based on generative adversarial network (SEGAN) gets lower speech quality though it has lots of parameters in its generator. To solve these problems, we …

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Single image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network and Wasserstein generative adversarial nets is proposed aiming at generating a photo-realistic image with finer texture details. Specifically, we construct a framework consisting of …

Geometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

J Li, F Zhang - Journal of Computational and Graphical …, 2018 - amstat.tandfonline.com

Gradient flows for frame potentials on the Wasserstein space

C Wickman, K Okoudjou - arXiv preprint arXiv:1808.09319, 2018 - arxiv.org

Generative model based on minimizing exact empirical wasserstein distance

A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

Generative Adversarial Networks (GANs) are a very powerful framework for generative modeling. However, they are often hard to train, and learning of GANs often becomes unstable. Wasserstein GAN (WGAN) is a promising framework to deal with the instability …

Saliency detection based on aggregated Wasserstein distance

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F Sun, W Li - Journal of Electronic Imaging, 2018 - spiedigitallibrary.org

This paper proposes a saliency detection method based on the aggregated Wasserstein distance. A multidimensional Gaussian mixture model is used to model the superpixels, whereby the color information of different color spaces is combined. To overcome the lack of …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - … Conference on …, 2018 - ieeexplore.ieee.org

[PDF] Regularized Wasserstein Means Based on Variational Transportation

L Mi, W Zhang, Y Wang - CoRR, 2018 - public.asu.edu

We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the variational transportation to distribute a sparse discrete measure into the target domain without mass splitting. The …

Bathymetric data processing based on denoising autoencoder Wasserstein generative adversarial network

R Zhang, Y Chen, S Bian, D Gao - Global Intelligence Industry …, 2018 - spiedigitallibrary.org

In view of the complexity and variability of bathymetric data, the paper introduces a new algorithm named DAE-WGAN to construct sea bottom trend surface. This new model is an alternative to traditional GAN training method, combined with the advantages of Denoising …

Inference for empirical Wasserstein distances on finite spaces Series B Statistical methodology

M Sommerfeld, A Munk - 2018 - pubag.nal.usda.gov

2018

On the minimizing movement with the 1-Wasserstein distance

M Agueh, G Carlier, N Igbida - ESAIM: Control, Optimisation and …, 2018 - esaim-cocv.org

We consider a class of doubly nonlinear constrained evolution equations which may be viewed as a nonlinear extension of the growing sandpile model of [L. Prigozhin, Eur. J. Appl. Math. 7 (1996) 225–235.]. We prove existence of weak solutions for quite irregular sources …

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X}) $, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

W-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

Reinforcement Learning with Wasserstein Distance ...

Phonocardiogram Signal Denoising Based on Non-negative ...

by MA Abdullah · 2018 · Cited by 1 — Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning. ... Changing the sign of the regularisation parameter, one can learn a policy for which its trajectory mapping distribution is attracted to a given fixed distributio

hal.archives-ouvertes.fr › hal-01855855 › document

by DH Pham · 2018 · Cited by 7 — It relies on the successive combination of a denoising procedure based on NMF, followed by ACRC. The principle of the denoising technique using NMF is to determine a Wiener filter to apply to the STFT of the original signal to get a first denoised signal.

Phonocardiogram Signal Denoising Based on …

S Khanna, CR Murthy, L Hu, J Zhang, X Wang, S Wang… - ieeexplore.ieee.org

LETTERS Digital and Multirate Signal Processing Recovery of the Starting Times of Delayed Signals . . . . . . . . . . . . . . . . . . . . . . . . LC Perotti, D. Vrinceanu, and D. Bessis … An Optimal-Dimensionality Sampling for Spin-s Functions on the Sphere …

<——2018—-— 2018———850—	2018Oct 3, 2019
Improving the Improved Training of Wasserstein GANs: A ...	Nov 16, 2017
On Convergence and Stability of GANs \| OpenReview	Nov 14, 2017
DISTRIBUTIONAL CONCAVITY REGULARIZATION FOR GANS	Oct 3, 2018
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[CITATION] On the regularization of Wasserstein GANs

S Augustin - Proc. Int. Conf. Learn. Representations, 2018

Wasserstein distance for generalized persistence modules ...

2018

open.library.ubc.ca › collections › items

Aug 7, 2018 — For $p=1$ it generalizes to abelian categories and for arbitrary $p$ it generalizes to Krull-Schmidt categories. These distances may be useful for ...

differential game on Wasserstein space. Application to weak approachability with partial monitoring

preprint Nov 2018 Vianney Perchet Marc Quincampoix

[PDF] Natural gradient in Wasserstein statistical manifold

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - math.ucla.edu

We study the Wasserstein natural gradient in parametric statistical models with continuous sample space. Our approach is to pull back the L2-Wasserstein metric tensor in probability density space to parameter space, under which the parameter space become a Riemannian …

2018

Improving the improved training of wasserstein gans: A consistency term and its dual effect

X Wei, B Gong, Z Liu, W Lu, L Wang - arXiv preprint arXiv:1803.01541, 2018 - arxiv.org

Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the …

Primal-dual wasserstein gan

M Gemici, Z Akata, M Welling - arXiv preprint arXiv:1805.09575, 2018 - arxiv.org

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference …

[PDF] Natural gradient in Wasserstein statistical manifold

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - math.ucla.edu

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample space. Our approach is to pull back the L2-Wasserstein metric tensor in probability

density space to parameter space, under which the parameter space become a Riemannian …

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

Inference for empirical Wasserstein distances on finite spaces Series B Statistical methodology

M Sommerfeld, A Munk - 2018 - pubag.nal.usda.gov

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of …

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2018 modified

Supplementary Materials: Wasserstein Dictionary Learning ...

perso.liris.cnrs.fr/nicolas.bonneel/supplementW...

SUPPLEMENTARY MATERIALS: Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning Morgan A. Schmitzy, Matthieu Heitzz, Nicolas Bonneelz, Fred Ngol ex, David Coeurjollyz, Marco Cuturi{, Gabriel Peyr ek, and Jean-Luc Starcky SM1. Detailed derivations. Let us rst introduce the notation: ’: RN RN!RN b s ...

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with volatile renewable generations. The deepened system interdependence calls for elaborate consideration of network models of both natural gas and power systems, as well as …

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein …

-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead …

Wasserstein geometry of quantum states and optimal transport of matrix-valued measures

Y Chen, TT Georgiou, A Tannenbaum - Emerging applications of control …, 2018 - Springer

Learning to optimize via wasserstein deep inverse optimal control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to fit the behavioral data, we …

[PDF] theses.fr

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

2018 modified

[PDF] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so called displacement interpolations (aka Wasserstein …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology theory, and their main output is a descriptor called persistence diagram (PD), which encodes the topology of a space at all scales in the form of a point cloud with multiplicities in the …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Γ-convergence of Entropy Regularized Wasserstein …

S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized optimal transport (OT) problem to the non-regularized OT problem, as described in [CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

<——2018—-— 2018———870—

[PDF] shichuan.org

Deep variational network embedding in wasserstein space

D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

Network embedding, aiming to embed a network into a low dimensional vector space while preserving the inherent structural properties of the network, has attracted considerable attentions recently. Most of the existing embedding methods embed nodes as point vectors …

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning. Though learning a good model in the tabular setting is a simple task, learning a useful model in the approximate setting is challenging. In this context, an important question is the …

[HTML] Improved Wasserstein conditional generative adversarial network speech enhancement

S Qin, T Jiang - EURASIP Journal on Wireless Communications and …, 2018 - Springer

The speech enhancement based on the generative adversarial network has achieved excellent results with large quantities of data, but performance in the low-data regime and tasks like unseen data learning still lag behind. In this work, we model Wasserstein …

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

Wasserstein Measure Coresets

S Claici, A Genevay, J Solomon - arXiv preprint arXiv:1805.07412, 2018 - arxiv.org

The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the performance of the full data set on specific …

One-dimensional data augmentation using a Wasserstein generative adversarial network with supervised signal

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains; however, there is still some difficulties in training the network, which are mainly caused by mode collapse, vanishing gradient of generator and indirect assessment criteria of …

Non-local texture optimization with wasserstein regularization under convolutional neural network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture and has long been drawing attention in the fields of computer graphics, computer vision, and image processing. Nevertheless, synthesizing structured textures remains a challenging …

Image inpainting using wasserstein generative adversarial network

P Hua, X Liu, M Liu, L Dong, M Hui… - Optics and Photonics …, 2018 - spiedigitallibrary.org

2018 22

A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS

G Degottex, M Gales - 2018 IEEE Spoken Language …, 2018 - ieeexplore.ieee.org

Generative networks can create an artificial spectrum based on its conditional distribution estimate instead of predicting only the mean value, as the Least Square (LS) solution does. This is promising since the LS predictor is known to oversmooth features leading to muffling …

Sketch-based 3D object retrieval using Wasserstein Center Loss

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using human-drawn sketches as query. In this paper, we propose a new method of using Sketch CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search …

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Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function is known to suffer from cycle-skipping issues that increase the risk of computing a local rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to …

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion: Geophysics, 83

Y Yang, B Engquist, J Sun, BF Hamfeldt - R43–R62, 2018

Odd orthogonal matrices and the non-injectivity of the Vaserstein symbol

2018

DR Rao, S Kolte - Journal of Algebra, 2018 - Elsevier

RA Rao–W. van der Kallen showed that the Vaserstein symbol V Γ (SR 3) from the orbit space of unimodular rows of length three over the coordinate ring of the real three sphere SR 3 modulo elementary action to the elementary symplectic Witt group WE (Γ (SR 3)) is not …

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

We present upper bounds for the Wasserstein distance of order $ p $ between the marginals of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the convolution structure, we further derive upper bounds for the total variation distance …

Cited by 155 Related articles

An algebraic Wasserstein distance for generalized persistence modules

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018 - arxiv.org

The Wasserstein distances are a family of $ L^ p $ distances, with $1\leq p\leq\infty $, for persistence diagrams. We define Wasserstein distances for persistence modules, the algebraic counterpart to persistence diagrams, and prove the following isometry theorem …

Measuring distributional asymmetry with Wasserstein distance and Rademacher symmetrization

AB Kashlak - Electronic Journal of Statistics, 2018 - projecteuclid.org

We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the asymmetry of the given measure. An empirical bound on this asymmetric correction term is …

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

2018 [PDF] ieee.org

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

We propose in this paper a construction of a diffusion process on the space $\mathcal P_2 (\mathbb R) $ of probability measures with a second-order moment. This process was introduced in several papers by Konarovskyi (see eg [12]) and consists of the limit as $ N …

[PDF] shichuan.org

Deep variational network embedding in wasserstein space

D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

<——2018————2018———890—

Hashgan: Deep learning to hash with pair conditional wasserstein gan

Y Cao, B Liu, M Long, J Wang - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Deep learning to hash improves image retrieval performance by end-to-end representation learning and hash coding from training data with pairwise similarity information. Subject to the scarcity of similarity information that is often expensive to collect for many application …

ITATION] HashGAN: Deep Learning to Hash with Pair Conditional Wasserstein GAN [C]

C Yue, L Bin, L Mingsheng - IEEE/CVF Conference on Computer Vision & Pattern …, 2018

2018

Learning to optimize via wasserstein deep inverse optimal control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to fit the behavioral data, we …

2018[PDF] arxiv.org

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

[PDF] Wasserstein Adversarial Mixture for Deep Generative Modeling and Clustering

2018 [PDF] harchaoui.org

W Harchaoui, PA Mattei, A Almansa, C Bouveyron - harchaoui.org

Unsupervised learning, and in particular clustering, is probably the most central problem in learning theory nowadays. This work focuses on the clustering of complex data by introducing a deep generative approach for both modeling and clustering. The proposed …

[HTML] Wasserstein discriminant analysis

R Flamary, M Cuturi, N Courty, A Rakotomamonjy - Machine Learning, 2018 - Springer

Wasserstein discriminant analysis (WDA) is a new supervised linear dimensionality reduction algorithm. Following the blueprint of classical Fisher Discriminant Analysis, WDA selects the projection matrix that maximizes the ratio of the dispersion of projected points …

2018

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

2018

Wasserstein stationary subspace analysis

S Kaltenstadler, S Nakajima, KR Müller… - IEEE Journal of …, 2018 - ieeexplore.ieee.org

Learning under nonstationarity can be achieved by decomposing the data into a subspace that is stationary and a nonstationary one [stationary subspace analysis (SSA)]. While SSA has been used in various applications, its robustness and computational efficiency have …

2018

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity …

2018

Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - Unknown Journal, 2018 - experts.umn.edu

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

2018[PDF] dml.cz

V Kaňková, V Omelčenko - Kybernetika, 2018 - dml.cz

<-––018—-—2018———900—

2018

[HTML] nature.com

[HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian dynamics and the collective motion of living organisms. In this study, we found that particles …

[PDF] Natural gradient in Wasserstein statistical manifold

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - math.ucla.edu

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample space. Our approach is to pull back the L2-Wasserstein metric tensor in probability

density space to parameter space, under which the parameter space become a Riemannian …

2018

[PDF] WASSERSTEIN NATURAL GRADIENT IN STATISTICAL MANIFOLDS WITH CONTINUOUS SAMPLE SPACE

Y Chen, W LI - arXiv preprint arXiv:1805.08380, 2018 - researchgate.net

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample spaces. Our approach is to pull back the L2-Wasserstein metric tensor in the

probability density space to a parameter space, equipping the latter with a positive definite …

2018

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a

data distribution and sample distribution. Recent studies have proposed stabilizing the

training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

[PDF] Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - jmlr.org

Divide-and-conquer based methods for Bayesian inference provide a general approach for

tractable posterior inference when the sample size is large. These methods divide the data

into smaller subsets, sample from the posterior distribution of parameters in parallel on all …

2018

A canonical barycenter via Wasserstein regularization

YH Kim, B Pass - SIAM Journal on Mathematical Analysis, 2018 - SIAM

We introduce a weak notion of barycenter of a probability measure μ on a metric measure

space (X,d,\bfm), with the metric d and reference measure \bfm. Under the assumption that

all optimal transport plans transporting \bfm to any probability measure ν on X are induced …

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

This paper is concerned with the statistical analysis of datasets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the principal component analysis (PCA) of histograms with …

2018 BOOK [PDF] d-nb.info

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

Perturbation theory for Markov chains via Wasserstein distance

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

2018 [PDF] nsf.gov

Data-driven risk-averse stochastic optimization with Wasserstein metric

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

In this paper, we study a data-driven risk-averse stochastic optimization approach with

Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we

can successfully reformulate the risk-averse two-stage stochastic optimization problem with …

<——2018—-— 2018———910—

Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

We provide an exact deterministic reformulation for data-driven chance constrained

programs over Wasserstein balls. For individual chance constraints as well as joint chance

constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer …

2018 [PDF] sjtu.edu.cn

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

One-dimensional data augmentation using a Wasserstein generative adversarial network with supervised signal

2018

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains;

however, there is still some difficulties in training the network, which are mainly caused by

mode collapse, vanishing gradient of generator and indirect assessment criteria of …

2018 [PDF] uma.es

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

A Esteban-Pérez, JM Morales - 2018 - riuma.uma.es

We consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

Mobile Application Network Behavior Detection and Evaluation with WGAN and Bi-LSTM

S Wei, P Jiang, Q Yuan, J Wang - TENCON 2018-2018 IEEE …, 2018 - ieeexplore.ieee.org

In this paper, we present a modeling and learning method to analyze the network behavior

of mobile applications based on the Android platform. Various application system sand

environmental factors are simulated in order to trigger different categories of application …

onathan-hui.medium.com › gan-wasserstein-gan-wgan...

基于 WGAN 的图像修复应用

哈文全 - 收藏, 2018 - cnki.com.cn

近年来深度学习在图像处理, 音频处理以及NLP 领域取得了令人瞩目的成绩,

特别在图像处理领域, 深度学习已然成为主流方法. 本文介绍深度学习方法在图像修复领域的

应用, 通过使用WGAN 来生成破损图像中缺失的部分. 通过从可用的大批量的数据集中生成对应 …

[Chinese Image restoration application based on WGAN

Below is the inception score using different methods. The experiment from the WGAN-GP paper demonstrates better image quality and convergence comparing ...

[CITATION] GAN–Wasserstein GAN & WGAN-GP

J Hui - … . com/@ jonathanhui/gan− wasserstein− gan− wgan …, 2018

[PDF] Robust Hypothesis Testing Using Wasserstein Uncertainty Sets.

R Gao, L Xie, Y Xie, H Xu - NeurIPS, 2018 - papers.nips.cc

We develop a novel computationally efficient and general framework for robust hypothesis

testing. The new framework features a new way to construct uncertainty sets under the null

and the alternative distributions, which are sets centered around the empirical distribution …

Wasserstein distributionally robust Kalman filtering

S Shafieezadeh-Abadeh, VA Nguyen, D Kuhn… - arXiv preprint arXiv …, 2018 - arxiv.org

We study a distributionally robust mean square error estimation problem over a nonconvex

Wasserstein ambiguity set containing only normal distributions. We show that the optimal

estimator and the least favorable distribution form a Nash equilibrium. Despite the non …

Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In the presence of

VRE uncertainties, this paper discusses a distributionally robust chance constrained …

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Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

We propose in this paper a construction of a diffusion process on the space $\mathcal P_2

(\mathbb R) $ of probability measures with a second-order moment. This process was

introduced in several papers by Konarovskyi (see eg [12]) and consists of the limit as $ N …

Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator

VA Nguyen, D Kuhn, PM Esfahani - arXiv preprint arXiv:1805.07194, 2018 - arxiv.org

We introduce a distributionally robust maximum likelihood estimation model with a

Wasserstein ambiguity set to infer the inverse covariance matrix of a $ p $-dimensional

Gaussian random vector from $ n $ independent samples. The proposed model minimizes …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

2018

Distributionally robust games: Wasserstein metric

J Gao, H Tembine - 2018 International Joint Conference on …, 2018 - ieeexplore.ieee.org

Deep generative models are powerful but difficult to train due to its instability, saturation

problem and high dimensional data distribution. This paper introduces a game theory

framework with Wasserstein metric to train generative models, in which the unknown data …

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

Y Chen, HG Müller - arXiv preprint arXiv:1809.03498, 2018 - arxiv.org

Many studies have been conducted on flows of probability measures, often in terms of

gradient flows. We utilize a generalized notion of derivatives with respect to time to model

the instantaneous evolution of empirically observed one-dimensional distributions that vary …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so-

called Wasserstein distance. We reduce this problem into an empirical variance

minimization problem with an additional regularization term. Moreover, we extend recent

inference methodology in order to select the size of the distributional uncertainty as well as …

Showing the best result for this search. See all results

[CITATION] Distributionally robust mean–variance portfolio selection with Wasserstein distances. arXiv

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018

Gromov-Wasserstein alignment of word embedding spaces

D Alvarez-Melis, TS Jaakkola - arXiv preprint arXiv:1809.00013, 2018 - arxiv.org

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from

machine translation to transfer learning. Recently, purely unsupervised methods operating

on monolingual embeddings have become effective alignment tools. Current state-of-the-art …

2018 [PDF] koreascience.or.kr

Type spaces and Wasserstein spaces

S Song - Journal of the Korean Mathematical Society, 2018 - koreascience.or.kr

Abstract Types (over parameters) in the theory of atomless random variable structures

correspond precisely to (conditional) distributions in probability theory. Moreover, the logic

(resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) …

Wasserstein distance guided representation learning for domain adaptation

<––2018—-—–2018———930—

2018 [PDF] aaai.org

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

domain via utilizing the knowledge distilled from a source domain which has a different but

related data distribution. One solution to domain adaptation is to learn domain invariant

feature representations while the learned representations should also be discriminative in

prediction. To learn such representations, domain adaptation frameworks usually include a

domain invariant representation learning approach to measure and reduce the domain …

Showing the best result for this search. See all results

반 3 차원 물체 검색

지명근， 전준철， 김남기 - 인터넷정보학회논문지, 2018 - dbpia.co.kr

… Wasserstein Center 손실을 이용한 스케치 기반 3차원 물체 검색 … Center 손실이란 각 물체의

클래스(category)의 중심을 학습하고, 동일한 클래스의 특징과 중심 간의 Wasserstein 거리가

작아지도록 … 첫 번째로, 3차원 물체의 특징은 3차원 물체를 여러 방향에서 촬영된 2차원 영상의 …

관련 학술자료 전체 3개의 버전

[Korean Sketcher using Wasserstein Center loss]

2018

Wasserstein 거리를 이용한 feature selection - 한국정보과학회 ...

Distance de Wasserstein d'une imagea une mesure quelconque

Wasserstein 거리를 이용한 feature selection. Feature Selection with Wasserstein Distance ... 추천 논문. Wasserstein Loss를 이용한 모델 파라미터 학습.

[CITATION] Wasserstein 거리를 이용한 feature selection

지종호， 신현정 - 한국정보과학회 학술발표논문집, 2018 - dbpia.co.kr

Page 1. Wasserstein 거리를 이용한 feature selection 지종호, 신현정* 아주대학교

산업공학과 {baical77, shin}@ajou.ac.kr Feature Selection with Wasserstein Distance

Jong Ho Jhee, Hyunjung Shin* Industrial Engineering, Ajou University …

{Korean Feature selection using Wasserstein distance ]

F de GOURNAY, L LEBRAT, J KHAN, P WEISS - smai.emath.fr

… Mots-clés : Transport optimal, distance de Wasserstein, … et de mani`ere stable la distance de Wasserstein 2. Apr`es nous être … au sens de la distance de Wasserstein i sur l’ensemble des …

Semi-supervised biomedical translation with cycle wasserstein regression GANs

M McDermott, T Yan, T Naumann, N Hunt… - Proceedings of the …, 2018 - ojs.aaai.org

The biomedical field offers many learning tasks that share unique challenges: large amounts

of unpaired data, and a high cost to generate labels. In this work, we develop a method to

address these issues with semi-supervised learning in regression tasks (eg, translation from …

[PDF] oregonstate.edu

[PDF] Wasserstein Proximal of GANs

A Tong Lin, W Li, S Osher, G Montúfar - 2018 - mis.mpg.de

We introduce a new method for training GANs by applying the Wasserstein-2 metric

proximal on the generators. This approach is based on the gradient operator induced by

optimal transport theory, which connects the geometry of the sample space and the …

Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

J McClelland - 2018 - ir.library.oregonstate.edu

The UniFrac metric (Definitions 1.1. 13 and 1.1. 14) is a robust and well-used β-diversity

metric in metagenomics. Evans and Matsen demonstrated in [28], using the dual formulation

of the 1-Wasserstein metric (Definition 1.2. 4), that the UniFrac metric is the 1-Wasserstein …

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

DT Zhou, J Chen, H Wu, DH Yang, LY Qiu - arXiv preprint arXiv …, 2018 - arxiv.org

In our previous work [Chen el al., J. Comput. Phys., 373 (2018)], the quadratic Wasserstein

metric is successfully applied to the earthquake location problem. The actual earthquake

hypocenter can be accurately recovered starting from initial values very far from the true …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

[PDF] uma.es

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints A Esteban-Pérez, JM Morales - 2018 - riuma.uma.esWe consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

On the latent space of wasserstein auto-encoders

<——2018—-— 2018———940—

PK Rubenstein, B Schoelkopf, I Tolstikhin - arXiv preprint arXiv …, 2018 - arxiv.org

… We study the role of latent space dimensionality in Wasserstein auto-encoders (WAEs).

Through experimentation on synthetic and real datasets, we argue that random encoders should …

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

Application of optimal transport and the quadratic Wasserstein ...

library.seg.org › doi › abs › geo2016-0663

by Y Yang · ‎2018 · ‎Cited by 124 · ‎Related articles

Jan 5, 2018 — ABSTRACTConventional full-waveform inversion (FWI) using the ... Application of optimal transport and the quadratic Wasserstein metric to ...

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion: Geophysics, 83

Y Yang, B Engquist, J Sun, BF Hamfeldt - R43–R62, 2018

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Wasserstein introspective neural networks

K Lee, W Xu, F Fan, Z Tu - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

We present Wasserstein introspective neural networks (WINN) that are both a generator and

a discriminator within a single model. WINN provides a significant improvement over the

recent introspective neural networks (INN) method by enhancing INN's generative modeling …

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

2018

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

machine learning and computer vision. Such an image can be generated at pixel level by

learning from a large collection of images. Learning to generate colorful cartoon images …

Distributed computation of Wasserstein barycenters over networks

CA Uribe, D Dvinskikh, P Dvurechensky… - … IEEE Conference on …, 2018 - ieeexplore.ieee.org

We propose a new class-optimal algorithm for the distributed computation of Wasserstein

Barycenters over networks. Assuming that each node in a graph has a probability

distribution, we prove that every node reaches the barycenter of all distributions held in the …

Semantic image inpainting through improved wasserstein generative adversarial networks

P Vitoria, J Sintes, C Ballester - arXiv preprint arXiv:1812.01071, 2018 - arxiv.org

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image.

In this work we tackle this problem not only by using the available visual data but also by

incorporating image semantics through the use of generative models. Our contribution is …

Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

necessary. Computer aided diagnosis offers an objective score that is independent of …

Lp-WGAN: Using Lp-norm normalization to stabilize Wasserstein generative adversarial networks

C Zhou, J Zhang, J Liu - Knowledge-Based Systems, 2018 - Elsevier

Wasserstein generative adversarial networks (Wasserstein GANs, WGAN) improve the

performance of GANs significantly by imposing the Lipschitz constraints on the critic, which

is implemented by weight clipping. In this work, we argue that weight clipping could result in …

<——2018—–— 2018———950—

Application of auxiliary classifier wasserstein generative adversarial networks in wireless signal classification of illegal unmanned aerial vehicles

C Zhao, C Chen, Z He, Z Wu - Applied Sciences, 2018 - mdpi.com

Recently, many studies have reported on image synthesis based on Generative Adversarial

Networks (GAN). However, the use of GAN does not provide much attention on the signal

classification problem. In the context of using wireless signals to classify illegal Unmanned …

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

Speech enhancement based on a new architecture of wasserstein generative adversarial networks

S Ye, T Jiang, S Qin, W Zou… - 2018 11th International …, 2018 - ieeexplore.ieee.org

Most conventional speech enhancement methods work poorly at low SNRs. And the speech

enhancement method based on generative adversarial network (SEGAN) gets lower speech

quality though it has lots of parameters in its generator. To solve these problems, we …

Wasserstein generative recurrent adversarial networks for image generating

C Zhang, Y Feng, B Qiang… - 2018 24th International …, 2018 - ieeexplore.ieee.org

Most generative models are generating images at a time, but in fact, painting is usually done

iteratively and repeatedly. Generative Adversarial Networks (GAN) are well known for

generating images, however, it is hard to train stably. To tackle this problem, we propose a …

Motion-blind blur removal for CT images with Wasserstein generative adversarial networks

Y Lyu, W Jiang, Y Lin, L Voros, M Zhang… - … Congress on Image …, 2018 - ieeexplore.ieee.org

Advanced deblurring techniques for computed tomography (CT) images are necessary and

crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup

and treatment response assessment in radiation oncology. Currently, medical image …

2018

Discrete Wasserstein Generative Adversarial Networks (DWGAN)

R Fathony, N Goela - 2018 - openreview.net

Generating complex discrete distributions remains as one of the challenging problems in

machine learning. Existing techniques for generating complex distributions with high

degrees of freedom depend on standard generative models like Generative Adversarial …

The Wasserstein Distance and its Application to Generative Adversarial Networks

[PDF] univie.ac.at

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

Scene classification using hierarchical Wasserstein CNN

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

In multiclass classification, convolutional neural network (CNN) is generally coupled with the

cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a

ground truth class and ignores the interclass relationship. We argue that CNN can be …

2018 PDF

Barycentres dans l'espace de Wasserstein

www.math.u-bordeaux.fr › Le-Teich-barycenters_carlier

Barycentres dans l'espace de Wasserstein. Guillaume CARLIER a. Journées IOPS - Image, Optimisation, Probabilités et. Statistique. Réserve ornithologique du ...

[CITATION] Barycentres dans l'espace de Wasserstein

G CARLIER

2018

Propriétés statistiques du barycentre dans l'espace de Wasserstein

E Cazelles - 2018 - tel.archives-ouvertes.fr

Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de

probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension des outils

statistiques usuels sur cet espace muni de la distance de Wasserstein. Une première notion …

[PDF] Barycentres de Wasserstein pour les abstractions topologiques

<——2018—-— 2018———960—

[PDF] upmc.fr

J Tierny - edb.upmc.fr

Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui

permet en pratique d'introduire une mesure de bruit sur les structures topologiques, comme

les singularités (sphères de couleur) dans cet exemple de carte d'élévation. Cette mesure …

2018

Distance de Wasserstein d'une imagea une mesure quelconque

F de GOURNAY, L LEBRAT, J KHAN, P WEISS - smai.emath.fr

Mots-clés : Transport optimal, distance de Wasserstein, cellules de Laguerre Le calcul du transport

optimal entre deux mesures de probabilités i et ν a connu un spectaculaire développement durant

les derni`eres années. Il existe principalement 3 méthodes, les méthodes semi- discretes [1 …

2018

Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DF Fonseca Valero - repositorio.uniandes.edu.co

El presente texto tiene como finalidad analizar el volumen de cuentos El aprendiz de mago

y otros cuentos de miedo (1992) del escritor colombiano Evelio José Rosero Diago (1958),

teniendo en cuenta la forma como se consolidan los diversos matices de la violenta y …

[CITATION] Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DFF Valero - 2018 - Uniandes

2018

Problemas de clasificación :una perspectiva robusta con la ...

repositorio.uniandes.edu.co › handle

Problemas de clasificación :una perspectiva robusta con la métrica de Wasserstein. RIS Mendeley. URI: http://hdl.handle.net/1992/39523. Autor(es

[CITATION] Problemas de clasificación: una perspectiva robusta con la métrica de Wasserstein

JAA Melo - 2018 - Uniandes
[CITATION] Problemas de clasificación: una perspectiva robusta con la métrica de Wasserstein

JAA Melo - 2018 - Uniandes

2018

Propriétés statistiques du barycentre dans l'espace de Wasserstein

E Cazelles - 2018 - tel.archives-ouvertes.fr

Cette thèse se concentre sur l'analyse de données présentées sous forme de mesures de

probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension des outils

statistiques usuels sur cet espace muni de la distance de Wasserstein. Une première notion …

2018

Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - arXiv preprint arXiv:1805.07594, 2018 - arxiv.org

Embedding complex objects as vectors in low dimensional spaces is a longstanding

problem in machine learning. We propose in this work an extension of that approach, which

consists in embedding objects as elliptical probability distributions, namely distributions …

2018

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

Y Chen, HG Müller - arXiv preprint arXiv:1809.03498, 2018 - arxiv.org

Many studies have been conducted on flows of probability measures, often in terms of

gradient flows. We utilize a generalized notion of derivatives with respect to time to model

the instantaneous evolution of empirically observed one-dimensional distributions that vary …

2018

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - Journal of Statistical Computation …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

sets in the size of millions of entries. We consider the situation when the information on a

large univariate data set or sample needs to be preserved, stored or transferred. We suggest …

2018

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

Differential properties of sinkhorn approximation for learning with wasserstein distance

G Luise, A Rudi, M Pontil, C Ciliberto - arXiv preprint arXiv:1805.11897, 2018 - arxiv.org

Applications of optimal transport have recently gained remarkable attention thanks to the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version …

<——2018—-— 2018———970—

[PDF] aaai.org

Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

domain via utilizing the knowledge distilled from a source domain which has a different but

related data distribution. One solution to domain adaptation is to learn domain invariant …

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

Hashgan: Deep learning to hash with pair conditional wasserstein gan

Y Cao, B Liu, M Long, J Wang - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Deep learning to hash improves image retrieval performance by end-to-end representation

learning and hash coding from training data with pairwise similarity information. Subject to

the scarcity of similarity information that is often expensive to collect for many application …

CITATION] HashGAN: Deep Learning to Hash with Pair Conditional Wasserstein GAN [C]

C Yue, L Bin, L Mingsheng - IEEE/CVF Conference on Computer Vision & Pattern …, 2018

Wasserstein cnn: Learning invariant features for nir-vis face recognition

R He, X Wu, Z Sun, T Tan - IEEE transactions on pattern …, 2018 - ieeexplore.ieee.org

Heterogeneous face recognition (HFR) aims at matching facial images acquired from

different sensing modalities with mission-critical applications in forensics, security and

commercial sectors. However, HFR presents more challenging issues than traditional face …

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. In this context, an important question is the …

2018

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein …

Bayesian learning with wasserstein barycenters

J Backhoff-Veraguas, J Fontbona, G Rios… - arXiv preprint arXiv …, 2018 - arxiv.org

We introduce a novel paradigm for Bayesian learning based on optimal transport theory.

Namely, we propose to use the Wasserstein barycenter of the posterior law on models as a

predictive posterior, thus introducing an alternative to classical choices like the maximum a …

[PDF] Learning disentangled representations with wasserstein auto-encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

… 1 INTRODUCTION Wasserstein auto-encoders (WAEs) are a recently introduced

auto-encoder architecture with justifica- tion stemming from the theory of Optimal Transport

(Tolstikhin et al., 2018) … Page 3. Workshop track - ICLR 2018 (a) (b) (c) (d) Figure 2: Row …

Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

necessary. Computer aided diagnosis offers an objective score that is independent of …

[PDF] Multi-Level Metric Learning via Smoothed Wasserstein Distance.

J Xu, L Luo, C Deng, H Huang - IJCAI, 2018 - ijcai.org

Traditional metric learning methods aim to learn a single Mahalanobis distance matrix M,

which, however, is not discriminative enough to characterize the complex and

heterogeneous data. Besides, if the descriptors of the data are not strictly aligned …

<——2018—-— 2018———980—

Distributionally robust games: Wasserstein metric

J Gao, H Tembine - 2018 International Joint Conference on …, 2018 - ieeexplore.ieee.org

Deep generative models are powerful but difficult to train due to its instability, saturation

problem and high dimensional data distribution. This paper introduces a game theory

framework with Wasserstein metric to train generative models, in which the unknown data …

Unsupervised feature learning for outlier detection with stacked convolutional autoencoders, siamese networks and wasserstein autoencoders: application to epilepsy …

Z Alaverdyan, J Chai, C Lartizien - … Analysis and Multimodal Learning for …, 2018 - Springer

In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric

(T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist

(MRI negative). We cast this problem as an outlier detection problem and adapt the …

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

Learning to optimize via wasserstein deep inverse optimal control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's

true cost function from the observed temporal behavior. In contrast to traditional

phenomenological works that aim to learn a generative model to fit the behavioral data, we …

Learning and inference with Wasserstein metrics

CCA Frogner - 2018 - dspace.mit.edu

This thesis develops new approaches for three problems in machine learning, using tools

from the study of optimal transport (or Wasserstein) distances between probability

distributions. Optimal transport distances capture an intuitive notion of similarity between …

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

2018

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

Learning Joint Wasserstein Auto-Encoders for Joint Distribution Matching

J Cao, Y Guo, L Mo, P Zhao, J Huang, M Tan - 2018 - openreview.net

We study the joint distribution matching problem which aims at learning bidirectional

mappings to match the joint distribution of two domains. This problem occurs in

unsupervised image-to-image translation and video-to-video synthesis tasks, which …

2018

[PDF] joig.org

[PDF] Automatic liver segmentation using u-net with wasserstein gans

Y Enokiya, Y Iwamoto, YW Chen, XH Han - J. Image Graph., 2018 - joig.org

Automatic liver segmentation in CT images is an important step for computer-aided

diagnosis and computeraided hepatic surgery. Recently, though numerous methods based

on deep learning such as U-Net have been proposed for automatic liver segmentation, it is …

Using Wasserstein GAN to generate high quality adversarial examples

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various

machine learning tasks, in recent years, they are found to be vulnerable to so-called

adversarial examples Specifically, take x is an element of D on which a neural network has …

[PDF] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

This article introduces a new non-linear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so called displacement interpolations (aka Wasserstein …

<——2018—-— 2018———990—

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

… 4 × 1 4 2 × 1 4 3 × 1 2 1 2 3 4 5 6 7 8 9 10 µ = 1 4 1[1,2] + 1 4 1[3,4] + 1 2 1[9,10] µ = 1 2 1[5,7]

François Fleuret AMMI – Introduction to Deep Learning / 10.2. Wasserstein GAN 2 / 16 Page

10. An alternative choice is the “earth moving distance”, which intuitively is the minimum mass …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology

theory, and their main output is a descriptor called persistence diagram (PD), which encodes

the topology of a space at all scales in the form of a point cloud with multiplicities in the …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Γ-convergence of Entropy Regularized Wasserstein …

S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized

optimal transport (OT) problem to the non-regularized OT problem, as described in

[CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

Using Wasserstein GAN to generate high quality adversarial examples

www.ideals.illinois.edu › handle

May 25, 2018 — Using Wasserstein GAN to generate high quality adversarial examples ... ECE499-Sp2018-xiong.pdf (675kB) Restricted to U of Illinois ... have been proposed to create such adversarial examples x′, but many of them cannot ...

[CITATION] Using Wasserstein GAN to Generate Adversarial Examples

Z Xiong, P Moulin

Using Wasserstein GAN to generate high quality adversarial ...

www.ideals.illinois.edu › handle

by Z Xiong · 2018 — Using Wasserstein GAN to generate high quality adversarial examples ... ECE499-Sp2018-xiong.pdf (675kB) Restricted to U of Illinois ... have been proposed to create such adversarial examples x′, but many of them cannot ...

A note on reinforcement learning with Wasserstein distance ...

www.groundai.com › project › a-note-on-reinforcemen...

Feb 12, 2018 — In this note we describe an application of Wasserstein distance to ... distance regularisation, with applications to multipolicy learning.

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

Wasserstein Center 손실을 이용한 스케치 기반 3 차원 물체 검색

2018

[PDF] jics.or.kr

지명근， 전준철， 김남기 - 인터넷정보학회논문지, 2018 - dbpia.co.kr

스케치 기반 3 차원 물체 검색은 다양한 3 차원 물체를 사람이 손으로 그린 스케치를 질의

(query) 로 사용하여 물체를 편리하게 검색하는 방법이다. 본 논문에서는 스케치 기반 3 차원

물체 검색을 위해 스케치 CNN (Convolutional Neural Network) 과 Wasserstein CNN 모델에 …

Policy optimization as wasserstein gradient flows

[Korean Sketch-based 3-D object search using Wasserstein Center loss]

R Zhang, C Chen, C Li, L Carin - … Conference on Machine …, 2018 - proceedings.mlr.press

Policy optimization is a core component of reinforcement learning (RL), and most existing

RL methods directly optimize parameters of a policy based on maximizing the expected total

reward, or its surrogate. Though often achieving encouraging empirical success, its …

2018

Data-driven risk-averse stochastic optimization with Wasserstein metric

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

In this paper, we study a data-driven risk-averse stochastic optimization approach with

Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we

can successfully reformulate the risk-averse two-stage stochastic optimization problem with …

[HTML] Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - Mathematical Programming, 2018 - Springer

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

[PDF] dml.cz

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

V Kaňková, V Omelčenko - Kybernetika, 2018 - dml.cz

Optimization problems with stochastic dominance constraints are helpful to many real-life

applications. We can recall eg, problems of portfolio selection or problems connected with

energy production. The above mentioned constraints are very suitable because they …

<——2018—-— 2018———1000—

Non-local texture optimization with wasserstein regularization under convolutional neural network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

[PDF] uma.es

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

A Esteban-Pérez, JM Morales - 2018 - riuma.uma.es

We consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

Data-driven risk-averse stochastic optimization with Wasserstein metric

2018

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

In this paper, we study a data-driven risk-averse stochastic optimization approach with

Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we

can successfully reformulate the risk-averse two-stage stochastic optimization problem with …

[HTML] Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - Mathematical Programming, 2018 - Springer

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

2018

Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

We provide an exact deterministic reformulation for data-driven chance constrained

programs over Wasserstein balls. For individual chance constraints as well as joint chance

constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer …

[PDF] wiley.com

Data-driven affinely adjustable distributionally robust framework for unit commitment based on Wasserstein metric

W Hou, R Zhu, H Wei, H TranHoang - IET Generation, Transmission & …, 2018 - IET

This study proposes a data-driven distributionally robust framework for unit commitment

based on Wasserstein metric considering the wind power generation forecasting errors. The

objective of the constructed model is to minimise the expected operating cost, including the …

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

2018

[PDF] uma.es

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

A Esteban-Pérez, JM Morales - 2018 - riuma.uma.es

We consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

<——2018—-— 2018———1010—

[Submitted on 21 Jul 2018 (v1), last revised 26 Dec 2018 (this version, v3)] ... metric-driven Bayesian inversion with applications to signal processing ... Thirdly, in the particular case of signal processing problems, while a normal ... We apply the new framework to a class of signal processing ... (or arXiv:1807.09682v3 [math.

ITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018

Jul 4, 2018 — Data-Driven Distributionally Robust Chance-Constrained Optimization with Wasserstein Metric. Ran Ji (rji2 ***at*** gmu.edu) Miguel Lejeune ...

[CITATION] Data-driven distributionally robust chance-constrained programming with Wasserstein metric

R Ji, M Lejeune - Available at Optimization Online, 2018

Evaluating a stochastic parametrization for a fastslow system ...

2018 PDF

centaur.reading.ac.uk › npg-25-413-2018-2

Jun 19, 2018 — Open access. Vissio, G. and Lucarini, V. (2018) Evaluating a stochastic parametrization for a fastslow system using the Wasserstein distance. ... of interest as well as Wasserstein distance between the pro- jected measure of the ... and constructed by coupling the Lorenz 84 (Lorenz, 1984) model with the ...

CITATION] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Evaluating a stochastic parametrization for a fastslow system ...

2018 PDF

centaur.reading.ac.uk › npg-25-413-2018-2

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Towards high resolution video generation with progressive growing of sliced wasserstein gans

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

since the temporal dimension of videos introduces an extra challenge during the generation

process. Besides, due to the limitation of memory and training stability, the generation …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

2018

Constructing misfit function for full waveform inversion based on sliced Wasserstein distance

F Chen, D Peter - 80th EAGE Conference and Exhibition 2018, 2018 - earthdoc.org

It has been proven that full waveform inversion (FWI) based on optimal transport (OT) is

robust against noise and contains less local minima. The accurate solution to OT problem on

the real line (1D) is analytical with the selected distance function which can be effectively …

W-entropy formulas on super Ricci flowsand Langevin deformation on Wasserstein spaceover Riemannian manifolds

[PDF] Sliced Wasserstein Kernel for Persistence Diagrams M. CARRIÈRE M. CUTURI 2

S OUDOT - crest.science

Persistence diagrams play a key role in topological data analysis (TDA), in which they are

routinely used to describe topological properties of complicated shapes. persistence

diagrams enjoy strong stability properties and have proven their utility in various learning …

L Songzi, L Xiang-Dong - SCIENCE CHINA Mathematics, 2018 - engine.scichina.com

In this survey paper, we give an overview of our recent works on the study of the $ W $-

entropy for the heat equation associated with the Witten Laplacian onsuper-Ricci flows and

the Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired …

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function

is known to suffer from cycle-skipping issues that increase the risk of computing a local

rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to …

CITATION] Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion: Geophysics, 83

Y Yang, B Engquist, J Sun, BF Hamfeldt - R43–R62, 2018

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2018 - projecteuclid.org

We introduce a general theory for a consensus-based combination of estimations of

probability measures. Potential applications include parallelized or distributed sampling

schemes as well as variations on aggregation from resampling techniques like boosting or …

<——2018—-— 2018———1020—

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

distributions with a set of particles. In this paper we introduce a new particle-based

variational inference method based on the theory of semi-discrete optimal transport. Instead …

Application of auxiliary classifier wasserstein generative adversarial networks in wireless signal classification of illegal unmanned aerial vehicles

C Zhao, C Chen, Z He, Z Wu - Applied Sciences, 2018 - mdpi.com

Recently, many studies have reported on image synthesis based on Generative Adversarial

Networks (GAN). However, the use of GAN does not provide much attention on the signal

classification problem. In the context of using wireless signals to classify illegal Unmanned …

… feature learning for outlier detection with stacked convolutional autoencoders, siamese networks and wasserstein autoencoders: application to epilepsy detection

Z Alaverdyan, J Chai, C Lartizien - Deep Learning in Medical Image …, 2018 - Springer

In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric

(T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist

(MRI negative). We cast this problem as an outlier detection problem and adapt the …

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

2018

The Wasserstein Distance and its Application to Generative Adversarial Networks

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

Wasserstein metric-driven Bayesian inversion with ...

[Submitted on 21 Jul 2018 (v1), last revised 26 Dec 2018 (this version, v3)] ... Thirdly, in the particular case of signal processing problems, while a normal ... We apply the new framework to a class of signal processing problems, that is, the ...

Missing: wave ‎| Must include: wave

[CITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.0397

[PDF] oregonstate.edu

Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

J McClelland - 2018 - ir.library.oregonstate.edu

The UniFrac metric (Definitions 1.1. 13 and 1.1. 14) is a robust and well-used β-diversity

metric in metagenomics. Evans and Matsen demonstrated in [28], using the dual formulation

of the 1-Wasserstein metric (Definition 1.2. 4), that the UniFrac metric is the 1-Wasserstein …

<——2018—-— 2018———1030—

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

[PDF] imperial.ac.uk

[PDF] Bregman and Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond

GANR Wasserstein - wwwf.imperial.ac.uk

Page 1. Bregman Divergence Function Generative Adversarial Networks (GANs) Wasserstein

Divergence and GANs Relaxed Wasserstein Empirical Results Conclusions Bregman and

Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond Xin Guo …

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space

of Wasserstein in the framework of mean field control problems. The main motivation for this

study is given by the control of multi-agent systems, where the number of the agents is so …

6, 2018

Cited by 1 Related artic

Gradient flows of time-dependent functionals in metric spaces ...

WGAN and WGAN-GP - Statistician's Deeplearning

by LCF Ferreira · 2018 · Cited by 6 — We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. ... In order to obtain strong convergence, a careful analysis is done by using a type of \lambda -convexity that changes as the time evolves

kionkim.github.io › 2018/07/26 › WGAN_3

Jul 26, 2018 — The main idea of WGAN is that neural network can be used for finding accurate Wasserstein distanc

2018

Anomaly detection with Wasserstein GAN

I Haloui, JS Gupta, V Feuillard - arXiv preprint arXiv:1812.02463, 2018 - arxiv.org

Generative adversarial networks are a class of generative algorithms that have been widely

used to produce state-of-the-art samples. In this paper, we investigate GAN to perform

anomaly detection on time series dataset. In order to achieve this goal, a bibliography is …

… feature learning for outlier detection with stacked convolutional autoencoders, siamese networks and wasserstein autoencoders: application to epilepsy detection

Z Alaverdyan, J Chai, C Lartizien - Deep Learning in Medical Image …, 2018 - Springer

In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric

(T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist

(MRI negative). We cast this problem as an outlier detection problem and adapt the …

Geometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

J Li, F Zhang - Journal of Computational and Graphical …, 2018 - amstat.tandfonline.com

An ensemble of forecasts generated by different model simulations provides rich information

for meteorologists about impending weather such as precipitating clouds. One major form of

forecasts presents cloud images created by multiple ensemble members. Common features …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

Saliency detection based on aggregated Wasserstein distance

F Sun, W Li - Journal of Electronic Imaging, 2018 - spiedigitallibrary.org

This paper proposes a saliency detection method based on the aggregated Wasserstein

distance. A multidimensional Gaussian mixture model is used to model the superpixels,

whereby the color information of different color spaces is combined. To overcome the lack of …

<——2018—-— 2018———1040—

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PEC de Raynal, N Frikha - arXiv preprint arXiv:1811.06904, 2018 - arxiv.org

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Odd orthogonal matrices and the non-injectivity of the Vaserstein symbol

DR Rao, S Kolte - Journal of Algebra, 2018 - Elsevier

RA Rao–W. van der Kallen showed that the Vaserstein symbol V Γ (SR 3) from the orbit

space of unimodular rows of length three over the coordinate ring of the real three sphere

SR 3 modulo elementary action to the elementary symplectic Witt group WE (Γ (SR 3)) is not …

Calculating Wasserstein's distance between an empirical ...

distribution and a combination of normal distributions

Jan 4, 2018 — Let ξ be a random variable (with real value) with support Ξ=R and ξ1,…,ξN be a sample of ξ. We consider the empirical probability ˆPN:=1NN∑i=1 ...

Generative modeling using the sliced wasserstein distance

I Deshpande, Z Zhang… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Abstract Generative Adversarial Nets (GANs) are very successful at modeling distributions

from given samples, even in the high-dimensional case. However, their formulation is also

known to be hard to optimize and often not stable. While this is particularly true for early GAN …

Generative Modeling Using the Sliced Wasserstein Distance

AG Schwing - CVPR, 2018 - openreview.net

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given

samples, even in the high-dimensional case. However, their formulation is also known to be

hard to optimize and often not stable. While this is particularly true for early GAN …

2018 [HTML] springer.com

[HTML] Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - Mathematical Programming, 2018 - Springer

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

2018

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

Visual feature attribution using wasserstein gans

CF Baumgartner, LM Koch… - Proceedings of the …, 2018 - openaccess.thecvf.com

Attributing the pixels of an input image to a certain category is an important and well-studied

problem in computer vision, with applications ranging from weakly supervised localisation to

understanding hidden effects in the data. In recent years, approaches based on interpreting …

[PDF] Robust Hypothesis Testing Using Wasserstein Uncertainty Sets.

R Gao, L Xie, Y Xie, H Xu - NeurIPS, 2018 - papers.nips.cc

We develop a novel computationally efficient and general framework for robust hypothesis

testing. The new framework features a new way to construct uncertainty sets under the null

and the alternative distributions, which are sets centered around the empirical distribution …

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - arXiv preprint arXiv:1805.07594, 2018 - arxiv.org

Embedding complex objects as vectors in low dimensional spaces is a longstanding

problem in machine learning. We propose in this work an extension of that approach, which

consists in embedding objects as elliptical probability distributions, namely distributions …

<——2018—-— 2018———1050—

Scene classification using hierarchical Wasserstein CNN

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

In multiclass classification, convolutional neural network (CNN) is generally coupled with the

cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a

ground truth class and ignores the interclass relationship. We argue that CNN can be …

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

machine learning and computer vision. Such an image can be generated at pixel level by

learning from a large collection of images. Learning to generate colorful cartoon images …

[PDF] sjtu.edu.cn

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Generalization error bounds using Wasserstein distances

AT Lopez, V Jog - 2018 IEEE Information Theory Workshop …, 2018 - ieeexplore.ieee.org

Generalization error of a learning algorithm characterizes the gap between an algorithm's

performance on test data versus performance on training data. In recent work, Xu &

Raginsky [1] showed that generalization error may be upper-bounded using the mutual …

Cited by 13 Related articles

Image labeling based on graphical models using wasserstein messages and geometric assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete

graphical models. By utilizing local Wasserstein distances for coupling assignment

measures across edges of the underlying graph, a given discrete objective function is …

2018

[PDF] copernicus.org

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modeling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs

G Auricchio, F Bassetti, S Gualandi… - arXiv preprint arXiv …, 2018 - arxiv.org

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance

between a pair of $ d $-dimensional histograms having $ n $ bins each. We prove that this

problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+ 1) $-partite …

Lp-WGAN: Using Lp-norm normalization to stabilize Wasserstein generative adversarial networks

C Zhou, J Zhang, J Liu - Knowledge-Based Systems, 2018 - Elsevier

Wasserstein generative adversarial networks (Wasserstein GANs, WGAN) improve the

performance of GANs significantly by imposing the Lipschitz constraints on the critic, which

is implemented by weight clipping. In this work, we argue that weight clipping could result in …

<——2018—-— 2018———1060—

[PDF] joig.org

[PDF] Automatic liver segmentation using u-net with wasserstein gans

Y Enokiya, Y Iwamoto, YW Chen, XH Han - J. Image Graph., 2018 - joig.org

Automatic liver segmentation in CT images is an important step for computer-aided

diagnosis and computeraided hepatic surgery. Recently, though numerous methods based

on deep learning such as U-Net have been proposed for automatic liver segmentation, it is …

Cross-lingual document retrieval using regularized Wasserstein distance

G Balikas, C Laclau, I Redko, MR Amini - European Conference on …, 2018 - Springer

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

Cross-Lingual Document Retrieval Using Regularized Wasserstein Distance

MR Amini - Advances in Information Retrieval: 40th European …, 2018 - books.google.com

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

One-dimensional data augmentation using a Wasserstein generative adversarial network with supervised signal

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains;

however, there is still some difficulties in training the network, which are mainly caused by

mode collapse, vanishing gradient of generator and indirect assessment criteria of …

[HTML] nature.com

[HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with

asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian

dynamics and the collective motion of living organisms. In this study, we found that particles …

Sparse-view CT reconstruction using wasserstein GANs

F Thaler, K Hammernik, C Payer, M Urschler… - … workshop on machine …, 2018 - Springer

We propose a 2D computed tomography (CT) slice image reconstruction method from a

limited number of projection images using Wasserstein generative adversarial networks

(wGAN). Our wGAN optimizes the 2D CT image reconstruction by utilizing an adversarial …

2018

Topological data assimilation using Wasserstein distance

L Li, A Vidard, FX Le Dimet, J Ma - Inverse Problems, 2018 - iopscience.iop.org

This work combines a level-set approach and the optimal transport-based Wasserstein

distance in a data assimilation framework. The primary motivation of this work is to reduce

assimilation artifacts resulting from the position and observation error in the tracking and …

Image inpainting using wasserstein generative adversarial network

P Hua, X Liu, M Liu, L Dong, M Hui… - Optics and Photonics …, 2018 - spiedigitallibrary.org

Recent advances in convolution neural networks have shown promising results for the

challenging task of filling large missing regions in an image with semantically plausible and

context aware details. These learning-based methods are significantly more effective in …

[PDF] eg.org

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

H Farooq, Y Chen, T Georgiou, C Lenglet - Computational Diffusion MRI, 2018 - Springer

Several studies have used structural connectivity information to parcellate brain areas like

the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult

to achieve using conventional MRI techniques. They typically employ diffusion MRI (dMRI) …

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

Diagnosis of Schizophrenia Disorder Using Wasserstein Based Active Contour and Texture Features

<——2018—-— 2018———1070—

M Latha, G Kavitha - Computational Signal Processing and Analysis, 2018 - Springer

Magnetic resonance (MR) brain images have a significant role in diagnosis of many

neuropsychiatric disorders such as Schizophrenia (SZ). In this work, Wasserstein-based

active contour and the texture features such as Hu moments and gray-level co-occurrence …

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

Sketch-based 3D object retrieval using Wasserstein Center Loss

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using

human-drawn sketches as query. In this paper, we propose a new method of using Sketch

CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search …

Using Wasserstein GAN to generate high quality adversarial examples

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various

machine learning tasks, in recent years, they are found to be vulnerable to so-called

adversarial examples Specifically, take x is an element of D on which a neural network has …

[PDF] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018 - imo.universite-paris-saclay.fr

We study the numerical implementation of a minimizing movement scheme using the 1-

Wasserstein distance introduced in [1]. We implement this scheme using two different primal

dual algorithm: a Augmented Lagrangian technique with the ADMM algorithm and the …

2018

Using Wasserstein GAN to generate high quality adversarial ...

https://www.ideals.illinois.edu › handle

by Z Xiong · 2018 — In this thesis, we propose a new algorithm to generate adversarial examples based on Generative Adversarial Networks (GANs), specifically, a ...

You visited this page on 3/21/21.

[CITATION] Using Wasserstein GAN to Generate Adversarial Examples

Z Xiong, P Moulin

2018 [PDF] inria.fr

Topological data assimilation using Wasserstein distance

L Li, A Vidard, FX Le Dimet, J Ma - Inverse Problems, 2018 - iopscience.iop.org

… is the utilization of the Wasserstein measure to misfit the discrepancy … Wasserstein metric

instead of the Euclidean measure, two novel methods called original and splitting topological …

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein …

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

T Vayer, L Chapel, R Flamary, R Tavenard… - arXiv preprint arXiv …, 2018 - arxiv.org

Optimal transport theory has recently found many applications in machine learning thanks to

its capacity for comparing various machine learning objects considered as distributions. The

Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the …

[CITATION] … Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty. Fused gromov-wasserstein distance for structured objects: theoretical foundations and …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

<——2018—-— 2018———1080—

Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

necessary. Computer aided diagnosis offers an objective score that is independent of …

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

Unsupervised feature learning for outlier detection with stacked convolutional autoencoders, siamese networks and wasserstein autoencoders: application to epilepsy …

Z Alaverdyan, J Chai, C Lartizien - Deep Learning in Medical Image …, 2018 - Springer

In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric

(T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist

(MRI negative). We cast this problem as an outlier detection problem and adapt the …

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - Unknown Journal, 2018 - experts.umn.edu

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

2018

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - Journal of Statistical Computation …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

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A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

Generative Adversarial Networks (GANs) are a very powerful framework for generative

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M Sommerfeld, A Munk - 2018 - pubag.nal.usda.gov

The Wasserstein distance is an attractive tool for data analysis but statistical inference is

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All 7 versions

[PDF] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

This article introduces a new non-linear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

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W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

<——2018—-— 2018———1090—

2018

Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

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related data distribution. One solution to domain adaptation is to learn domain invariant …

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function

is known to suffer from cycle-skipping issues that increase the risk of computing a local

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[PDF] aaai.org

Semi-supervised biomedical translation with cycle wasserstein regression GANs

M McDermott, T Yan, T Naumann, N Hunt… - Proceedings of the …, 2018 - ojs.aaai.org

The biomedical field offers many learning tasks that share unique challenges: large amounts

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MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

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Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

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2018

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org

This paper is concerned by the study of barycenters for random probability measures in the

Wasserstein space. Using a duality argument, we give a precise characterization of the

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Y Chen, TT Georgiou, A Tannenbaum - Emerging applications of control …, 2018 - Springer

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined

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I Malkiel, S Ahn, V Taviani, A Menini, L Wolf… - arXiv preprint arXiv …, 2019 - arxiv.org

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L Mi, W Zhang, Y Wang - CoRR, 2018 - public.asu.edu

We raise the problem of regularizing Wasserstein means and propose several terms tailored

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Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

<——2018—-— 2018———1100—

[PDF] theses.fr

E Cazelles - 2018 - theses.fr

Résumé Cette thèse se concentre sur l'analyse de données présentées sous forme de

mesures de probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension

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[PDF] bayesiandeeplearning.org

[PDF] Semi-Supervised Pairing via Basis-Sharing Wasserstein Matching Auto-Encoder

Z Liu, YHH Tsai, M Yamada, R Salakhutdinov - bayesiandeeplearning.org

Semi-supervised pairing, learning explicit pairing relation between unlabeled input and

target distribution in an otherwise semisupervised setting, has recently attracted lots of

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2018

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M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

This article introduces a new non-linear dictionary learning method for histograms in the

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[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology

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S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized

optimal transport (OT) problem to the non-regularized OT problem, as described in

[CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

Wasserstein-distance-based Gaussian mixture reduction

A Assa, KN Plataniotis - IEEE Signal Processing Letters, 2018 - ieeexplore.ieee.org

Gaussian mixtures (GMs) are widely used in signal processing applications to capture the

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GM components in such applications, Gaussian mixture reduction (GMR) approaches are …

2018

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M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

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C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

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Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been

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2018

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W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

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MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

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<——2018—-— 2018———1110—

[PDF] siam.org

Image labeling based on graphical models using wasserstein messages and geometric assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete

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C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Beyond their benign uses, the small Unmanned Aerial Vehicles (UAVs) are expected to take

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Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

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naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

Speech enhancement based on a new architecture of wasserstein generative adversarial networks

S Ye, T Jiang, S Qin, W Zou… - 2018 11th International …, 2018 - ieeexplore.ieee.org

Most conventional speech enhancement methods work poorly at low SNRs. And the speech

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quality though it has lots of parameters in its generator. To solve these problems, we …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

2018

Single image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network

and Wasserstein generative adversarial nets is proposed aiming at generating a photo-

realistic image with finer texture details. Specifically, we construct a framework consisting of …

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

DT Zhou, J Chen, H Wu, DH Yang, LY Qiu - arXiv preprint arXiv …, 2018 - arxiv.org

In our previous work [Chen el al., J. Comput. Phys., 373 (2018)], the quadratic Wasserstein

metric is successfully applied to the earthquake location problem. The actual earthquake

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G Cai, Q Lin, N Chen - International Conference on Security with Intelligent …, 2018 - Springer

Text sentiment analysis is mainly to detect the sentiment polarity implicit in text data. Most

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in text sentiment analysis. The key of cross-domain text sentiment analysis is how to extract …

Geometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

J Li, F Zhang - Journal of Computational and Graphical …, 2018 - amstat.tandfonline.com

An ensemble of forecasts generated by different model simulations provides rich information

for meteorologists about impending weather such as precipitating clouds. One major form of

forecasts presents cloud images created by multiple ensemble members. Common features …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

<——2018—-— 2018———1120—

Generative model based on minimizing exact empirical wasserstein distance

A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

Generative Adversarial Networks (GANs) are a very powerful framework for generative

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unstable. Wasserstein GAN (WGAN) is a promising framework to deal with the instability …

Diagnosis of Schizophrenia Disorder Using Wasserstein Based Active Contour and Texture Features

M Latha, G Kavitha - Computational Signal Processing and Analysis, 2018 - Springer

Magnetic resonance (MR) brain images have a significant role in diagnosis of many

neuropsychiatric disorders such as Schizophrenia (SZ). In this work, Wasserstein-based

active contour and the texture features such as Hu moments and gray-level co-occurrence …

Saliency detection based on aggregated Wasserstein distance

F Sun, W Li - Journal of Electronic Imaging, 2018 - spiedigitallibrary.org

This paper proposes a saliency detection method based on the aggregated Wasserstein

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whereby the color information of different color spaces is combined. To overcome the lack of …

Constructing misfit function for full waveform inversion based on sliced Wasserstein distance

F Chen, D Peter - 80th EAGE Conference and Exhibition 2018, 2018 - earthdoc.org

It has been proven that full waveform inversion (FWI) based on optimal transport (OT) is

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the real line (1D) is analytical with the selected distance function which can be effectively …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

2018

[PDF] Regularized Wasserstein Means Based on Variational Transportation

L Mi, W Zhang, Y Wang - CoRR, 2018 - public.asu.edu

We raise the problem of regularizing Wasserstein means and propose several terms tailored

to tackle different problems. Our formulation is based on the variational transportation to

distribute a sparse discrete measure into the target domain without mass splitting. The …

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

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R Zhang, Y Chen, S Bian, D Gao - Global Intelligence Industry …, 2018 - spiedigitallibrary.org

In view of the complexity and variability of bathymetric data, the paper introduces a new

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Sketch-based 3D object retrieval using Wasserstein Center Loss

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using

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[PDF] crest.science

[PDF] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY… - crest.science

This article introduces a new non-linear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so called displacement interpolations (aka Wasserstein …

<——2018—-— 2018———1130—

Sketch-based 3D object retrieval using Wasserstein Center Loss

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using

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CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search …

2018

Underwater Object Detection and Effective Classification Using Sparse Representation Vasershtein Metric

www.jardcs.org › backissues › abstract

Underwater Object Detection and Effective Classification Using Sparse Representation Vasershtein Metric. N. Poornachandra Rao, R. Obulakonda Reddy and ...
2018

[CITATION] Underwater Object Detection and Effective Classification Using Sparse Representation Vasershtein Metric

N Poornach - 2018 - jardcs.org

Identification and several issues for the categorization of objects in camera images needs to

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Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

We provide an exact deterministic reformulation for data-driven chance constrained

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[PDF] ucla.edu

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Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - math.ucla.edu

We study the Wasserstein natural gradient in parametric statistical models with continuous

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density space to parameter space, under which the parameter space become a Riemannian …

Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

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2018

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

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variational inference method based on the theory of semi-discrete optimal transport. Instead …

[PDF] unil.ch

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - Journal of Statistical Computation …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

sets in the size of millions of entries. We consider the situation when the information on a

large univariate data set or sample needs to be preserved, stored or transferred. We suggest …

[PDF] WASSERSTEIN NATURAL GRADIENT IN STATISTICAL MANIFOLDS WITH CONTINUOUS SAMPLE SPACE

Y Chen, W LI - arXiv preprint arXiv:1805.08380, 2018 - researchgate.net

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample spaces. Our approach is to pull back the L2-Wasserstein metric tensor in the

probability density space to a parameter space, equipping the latter with a positive definite …

Discrete Wasserstein Generative Adversarial Networks (DWGAN)

R Fathony, N Goela - 2018 - openreview.net

Generating complex discrete distributions remains as one of the challenging problems in

machine learning. Existing techniques for generating complex distributions with high

degrees of freedom depend on standard generative models like Generative Adversarial …

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

<——2018—-— 2018———1140—

2018 arXiv

Strongly Polynomial 2-Approximations of Discrete Wasserstein Barycenters

Steffen Borgwardt

Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals. They arise in applications from economics to statistics. In many applications, data is given as a set of probability measures with finite support. The discrete barycenters that arise in this setting exhibit favorable properties: All barycenters have finite support, and there always is one with a provably sparse support. Further, each barycenter allows a non-mass splitting optimal transport to each of the marginals.

It is open whether the computation of a discrete barycenter is possible in polynomial time. The best known algorithms are based on linear programming, but the sizes of these programs scale exponentially. In this paper, we prove that there is a strongly polynomial, tight 2-approximation, based on restricting the possible support of the approximate barycenter to the support of the measures. The resulting measure is sparse, but its optimal transport will generally split mass. We then exhibit an algorithm to recover the non-mass split property in strongly polynomial time. Finally, we present an iterative scheme that alternates between these two computations. It terminates with a 2-approximation that has a sparse support and does not split mass at the same time. We conclude with some practical computations.

Subjects:	Optimization and Control (math.OC)
MSC classes:	90B80, 90C05, 90C46, 90C90
Cite as:	arXiv:1704.05491 [math.OC]
	(or arXiv:1704.05491v2 [math.OC] for this version)

Submission history

From: Steffen Borgwardt [view email]

[v1] Tue, 18 Apr 2017 18:38:15 UTC (141 KB)

[v2] Fri, 30 Mar 2018 23:49:13 UTC (143 KB)

[v3] Tue, 23 Oct 2018 21:09:25 UTC (137 KB)

[v4] Mon, 1 Jul 2019 19:57:18 UTC (293 KB)

[v5] Mon, 9 Sep 2019 21:02:56 UTC (295 KB)

[v6] Wed, 22 Apr 2020 21:31:25 UTC (303 KB)

Data-Driven Distributionally Robust Chance-Constrained ...http://www.optimization-online.org › 2018/07
http://www.optimization-online.org › 2018/07
Jul 4, 2018 — Abstract: We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity ...

[CITATION] Data-driven distributionally robust chance-constrained programming with Wasserstein metric

R Ji, M Lejeune - Available at Optimization Online, 2018

2018 May

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Probabilistic generation of natural language sentences is an important task in NLP. Existing models such as variational autoencoders (VAE) for sequence ...

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Gromov-Wasserstein alignment of word embedding spaces

D Alvarez-Melis, TS Jaakkola - arXiv preprint arXiv:1809.00013, 2018 - arxiv.org

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from

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D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

Network embedding, aiming to embed a network into a low dimensional vector space while

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Embedding complex objects as vectors in low dimensional spaces is a longstanding

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H Xu, W Wang, W Liu, L Carin - arXiv preprint arXiv:1809.04705, 2018 - arxiv.org

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Variational autoencoders~(VAEs) have shown a promise in data-driven conversation

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Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

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C Sun, H Yan, X Qiu, X Huang - arXiv preprint arXiv:1808.07016, 2018 - arxiv.org

Compared with word embedding based on point representation, distribution-based word

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D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

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Stochastic wasserstein autoencoder for probabilistic sentence generation

H Bahuleyan, L Mou, H Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

The variational autoencoder (VAE) imposes a probabilistic distribution (typically Gaussian)

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posterior and prior. In NLP, VAEs are extremely difficult to train due to the problem of KL …

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

Probabilistic Natural Language Generation with Wasserstein ...

www.researchgate.net › publication › 325965500_Probab...

Probabilistic generation of natural language sentences is an important task in NLP. Existing models such as variational autoencoders (VAE) for sequence ...

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[CITATION] Probabilistic natural language generation with wasserstein autoencoders

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Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

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[HTML] deepai.org

[HTML] Equivalence between wasserstein and value-aware model-based reinforcement learning

K Asadi, E Cater, D Misra, ML Littman - FAIM Workshop on Prediction …, 2018 - deepai.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. Recently Farahmand et al.(2017) proposed …

Cited by 10 Related articles All 2 versions
[2018 CITATION] Equivalence Between Wasserstein and Value-Aware Model-based Reinforcement Learning. ArXiv e-prints (June 2018)

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint cs.LG/1806.01265, 2018

2018

Wasserstein riemannian geometry of positive definite matrices

L Malago, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Lp-WGAN: Using Lp-norm normalization to stabilize Wasserstein generative adversarial networks

C Zhou, J Zhang, J Liu - Knowledge-Based Systems, 2018 - Elsevier

Wasserstein generative adversarial networks (Wasserstein GANs, WGAN) improve the

performance of GANs significantly by imposing the Lipschitz constraints on the critic, which

is implemented by weight clipping. In this work, we argue that weight clipping could result in …

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

Model risk measurement under wasserstein distance

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018 - arxiv.org

The paper proposes a new approach to model risk measurement based on the Wasserstein

distance between two probability measures. It formulates the theoretical motivation resulting

from the interpretation of fictitious adversary of robust risk management. The proposed …

[CITATION] Model risk measurement under Wasserstein distance. arXiv

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

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Generative model based on minimizing exact empirical wasserstein distance

A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

Generative Adversarial Networks (GANs) are a very powerful framework for generative

modeling. However, they are often hard to train, and learning of GANs often becomes

unstable. Wasserstein GAN (WGAN) is a promising framework to deal with the instability …

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

Supplement to “Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance.”

[PDF] Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

ESG Model - openreview.net

In this paper we study generative modeling via autoencoders while using the elegant

geometric properties of the optimal transport (OT) problem and the Wasserstein distances.

We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that …

[CITATION] Sliced-wasserstein autoencoder: an embarrassingly simple generative model. arXiv e-prints

S Kolouri, PE Pope, CE Martin, GK Rohde - 2018

J Weed, F Bach - 2018 - projecteuclid.org

We begin by giving an informal outline of the idea of the proof. Consider a partition {Qi} i∈ I of S, for some index set I. The measures µ and ν both induce measures on each set in the …

Supplement to “Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance.”

J Weed, F Bach - 2018 - projecteuclid.org

We begin by giving an informal outline of the idea of the proof. Consider a partition {Qi} i∈ I

of S, for some index set I. The measures µ and ν both induce measures on each set in the …

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

2018

Image labeling based on graphical models using wasserstein messages and geometric assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete

graphical models. By utilizing local Wasserstein distances for coupling assignment

measures across edges of the underlying graph, a given discrete objective function is …

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

Generative models with both discrete and continuous latent variables are highly motivated

by the structure of many real-world data sets. They present, however, subtleties in training

often manifesting in the discrete latent being under leveraged. In this paper, we show that …

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

This paper is focused on the statistical analysis of probability measures $\boldsymbol {\nu} _

{1},\ldots,\boldsymbol {\nu} _ {n} $ on ${\mathbb {R}} $ that can be viewed as independent

realizations of an underlying stochastic process. We consider the situation of practical …

One-dimensional data augmentation using a Wasserstein generative adversarial network with supervised signal

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains;

however, there is still some difficulties in training the network, which are mainly caused by

mode collapse, vanishing gradient of generator and indirect assessment criteria of …

2018

A Malliavin-Stein approach for multivariate approximations in ...

https://www.researchgate.net › publication › 322695156_...

A Malliavin-Stein approach for multivariate approximations in Wasserstein ... concerned with bounding their Wasserstein distance, deﬁned as follows:.

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

https://imsarchives.nus.edu.sg › files › christian

<——2018—-— 2018———1170—

2018 zzz 42

[CITATION] Wasserstein-1 in generative models

A Nowak - 2018

[CITATION] Wasserstein-1 in generative models

A Nowak - 2018

Related articles
[CITATION] Wasserstein-1 in generative models

A Nowak - 2018

2018 see 2017

https://imsarchives.nus.edu.sg › files › christianPD

Inference in generative models using the. Wasserstein distance. Christian P. Robert. (Paris Dauphine PSL & Warwick U.) joint work with E. Bernton (Harvard), ...

[CITATION] Inference in generative models using the Wasserstein distance

[CITATION] Inference in generative models using the Wasserstein distance

[HTML] Improved Wasserstein conditional generative adversarial network speech enhancement

S Qin, T Jiang - EURASIP Journal on Wireless Communications and …, 2018 - Springer

The speech enhancement based on the generative adversarial network has achieved

excellent results with large quantities of data, but performance in the low-data regime and

tasks like unseen data learning still lag behind. In this work, we model Wasserstein …

Distilled wasserstein learning for word embedding and topic modeling

H Xu, W Wang, W Liu, L Carin - arXiv preprint arXiv:1809.04705, 2018 - arxiv.org

We propose a novel Wasserstein method with a distillation mechanism, yielding joint

learning of word embeddings and topics. The proposed method is based on the fact that the

Euclidean distance between word embeddings may be employed as the underlying …

Hashgan: Deep learning to hash with pair conditional wasserstein gan

Y Cao, B Liu, M Long, J Wang - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Deep learning to hash improves image retrieval performance by end-to-end representation

learning and hash coding from training data with pairwise similarity information. Subject to

the scarcity of similarity information that is often expensive to collect for many application …

[CITATION] HashGAN: Deep Learning to Hash with Pair Conditional Wasserstein GAN [C]

C Yue, L Bin, L Mingsheng - IEEE/CVF Conference on Computer Vision & Pattern …, 2018

2018

Dialogwae: Multimodal response generation with conditional wasserstein auto-encoder

X Gu, K Cho, JW Ha, S Kim - arXiv preprint arXiv:1805.12352, 2018 - arxiv.org

Variational autoencoders~(VAEs) have shown a promise in data-driven conversation

modeling. However, most VAE conversation models match the approximate posterior

distribution over the latent variables to a simple prior such as standard normal distribution …

Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - arXiv preprint arXiv:1805.07594, 2018 - arxiv.org

Embedding complex objects as vectors in low dimensional spaces is a longstanding

problem in machine learning. We propose in this work an extension of that approach, which

consists in embedding objects as elliptical probability distributions, namely distributions …

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

machine learning and computer vision. Such an image can be generated at pixel level by

learning from a large collection of images. Learning to generate colorful cartoon images …

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Sparse-view CT reconstruction using wasserstein GANs

F Thaler, K Hammernik, C Payer, M Urschler… - … workshop on machine …, 2018 - Springer

We propose a 2D computed tomography (CT) slice image reconstruction method from a

limited number of projection images using Wasserstein generative adversarial networks

(wGAN). Our wGAN optimizes the 2D CT image reconstruction by utilizing an adversarial …

Learning to optimize via wasserstein deep inverse optimal control

<——2018—-— 2018———1180—

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's

true cost function from the observed temporal behavior. In contrast to traditional

phenomenological works that aim to learn a generative model to fit the behavioral data, we …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

A Fast Proximal Point Method for Computing Exact Wasserstein Distance

by Y Xie · 2018 · Cited by 54 — Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Furthermore, a new algorithm is proposed based on IPOT to obtain sharper Wasserstein barycenter. ..

[CITATION] A fast proximal point method for computing wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Improving the improved training of wasserstein gans: A consistency term and its dual effect

X Wei, B Gong, Z Liu, W Lu, L Wang - arXiv preprint arXiv:1803.01541, 2018 - arxiv.org

Despite being impactful on a variety of problems and applications, the generative

adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed

by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the …

Wasserstein distributionally robust Kalman filtering

S Shafieezadeh-Abadeh, VA Nguyen, D Kuhn… - arXiv preprint arXiv …, 2018 - arxiv.org

We study a distributionally robust mean square error estimation problem over a nonconvex

Wasserstein ambiguity set containing only normal distributions. We show that the optimal

estimator and the least favorable distribution form a Nash equilibrium. Despite the non …

A canonical barycenter via Wasserstein regularization

YH Kim, B Pass - SIAM Journal on Mathematical Analysis, 2018 - SIAM

We introduce a weak notion of barycenter of a probability measure μ on a metric measure

space (X,d,\bfm), with the metric d and reference measure \bfm. Under the assumption that

all optimal transport plans transporting \bfm to any probability measure ν on X are induced …

Non-local texture optimization with wasserstein regularization under convolutional neural network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

(PDF) Bobrovsky–Zakai-Type Bound for Periodic Stochastic Filtering ...

https://www.academia.edu › Bobrovsky_Zakai_Type_B...

Bobrovsky–Zakai-Type Bound for Periodic Stochastic Filtering.pdf. IEEE Signal Process. Lett., 2018. Eyal Nitzan. Joseph Tabrikian. Tirza Routtenberg.

<—2018—-— 2018———1190—

[HTML] Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

S Amari, R Karakida, M Oizumi - Information Geometry, 2018 - Springer

Two geometrical structures have been extensively studied for a manifold of probability

distributions. One is based on the Fisher information metric, which is invariant under

reversible transformations of random variables, while the other is based on the Wasserstein …

[HTML] nature.com

[HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with

asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian

dynamics and the collective motion of living organisms. In this study, we found that particles …

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

This paper is focused on the statistical analysis of probability measures $\boldsymbol {\nu} _

{1},\ldots,\boldsymbol {\nu} _ {n} $ on ${\mathbb {R}} $ that can be viewed as independent

realizations of an underlying stochastic process. We consider the situation of practical …

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - ALEA: Latin American Journal of Probability …, 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

2018

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as …

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

This paper is focused on the statistical analysis of probability measures $\boldsymbol {\nu} _

{1},\ldots,\boldsymbol {\nu} _ {n} $ on ${\mathbb {R}} $ that can be viewed as independent

realizations of an underlying stochastic process. We consider the situation of practical …

Model risk measurement under wasserstein distance

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018 - arxiv.org

The paper proposes a new approach to model risk measurement based on the Wasserstein

distance between two probability measures. It formulates the theoretical motivation resulting

from the interpretation of fictitious adversary of robust risk management. The proposed …

[CITATION] Model risk measurement under Wasserstein distance. arXiv

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018

[PDF] Wasserstein Proximal of GANs

A Tong Lin, W Li, S Osher, G Montúfar - 2018 - mis.mpg.de

We introduce a new method for training GANs by applying the Wasserstein-2 metric

proximal on the generators. This approach is based on the gradient operator induced by

optimal transport theory, which connects the geometry of the sample space and the …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

<——2018—-— 2018———1200—

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in

each of the following cases:(a) X and Y are geodesic spaces and Y is covered by X via a …

Type spaces and Wasserstein spaces

S Song - Journal of the Korean Mathematical Society, 2018 - koreascience.or.kr

Abstract Types (over parameters) in the theory of atomless random variable structures

correspond precisely to (conditional) distributions in probability theory. Moreover, the logic

(resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) …

Image inpainting using wasserstein generative adversarial network

P Hua, X Liu, M Liu, L Dong, M Hui… - Optics and Photonics …, 2018 - spiedigitallibrary.org

… We also use global and local Wasserstein discriminators that are jointly trained to distinguish real images from completed ones. We evaluate our approach on four datasets including …

A Fast Proximal Point Method for Computing Exact Wasserstein Distance

Y Xie, X Wang, R Wang, H Zha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

Wasserstein distance plays increasingly important roles in machine learning, stochastic

programming and image processing. Major efforts have been under way to address its high

computational complexity, some leading to approximate or regularized variations such as …

[CITATION] A fast proximal point method for computing wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

Model risk measurement under wasserstein distance

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018 - arxiv.org

The paper proposes a new approach to model risk measurement based on the Wasserstein

distance between two probability measures. It formulates the theoretical motivation resulting

from the interpretation of fictitious adversary of robust risk management. The proposed …

CITATION] Model risk measurement under Wasserstein distance. arXiv

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018

Accelerated discrete distribution clustering under wasserstein distance

[CITATION] Model risk measurement under Wasserstein distance. arXiv

Y Feng, E Schlögl - arXiv preprint arXiv:1809.03641, 2018

[PDF] googleapis.com

J Ye, J Li, JZ Wang - US Patent 10,013,477, 2018 - Google Patents

Computationally efficient accelerated D2-clustering algorithms are disclosed for clustering

discrete distributions under the Wasserstein distance with improved scalability. Three first-

order methods include subgradient descent method with re-parametrization, alternating …

Non-local texture optimization with wasserstein regularization under convolutional neural network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

Y Chen, HG Müller - arXiv preprint arXiv:1809.03498, 2018 - arxiv.org

Many studies have been conducted on flows of probability measures, often in terms of

gradient flows. We utilize a generalized notion of derivatives with respect to time to model

the instantaneous evolution of empirically observed one-dimensional distributions that vary …

[PDF] ON WASSERSTEIN ISOMETRIES OF PROBABILITY MEASURES ON UNIT SPHERES

D VIROSZTEK - arXiv preprint arXiv:1802.03305, 2018 - researchgate.net

We consider the space of all Borel probability measures on the unit sphere of a Euclidean

space endowed with the Wasserstein metric Wp for arbitrary p≥ 1. Our goal is to describe

the isometry group of this metric space. We make some progress in the direction of a Banach …

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under wasserstein distance

Y Han, J Jiao, T Weissman - Conference On Learning …, 2018 - proceedings.mlr.press

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for

symmetric functional estimation and distribution estimation under Wasserstein distance. We

construct an efficiently computable estimator that achieves the minimax rates in estimating …

<——2018—-— 2018———1210—

Generalization error bounds using Wasserstein distances

AT Lopez, V Jog - 2018 IEEE Information Theory Workshop …, 2018 - ieeexplore.ieee.org

Generalization error of a learning algorithm characterizes the gap between an algorithm's

performance on test data versus performance on training data. In recent work, Xu &

Raginsky [1] showed that generalization error may be upper-bounded using the mutual …

Cited by 13 Related articles

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Non-local texture optimization with wasserstein regularization under convolutional neural network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS

G Degottex, M Gales - 2018 IEEE Spoken Language …, 2018 - ieeexplore.ieee.org

Generative networks can create an artificial spectrum based on its conditional distribution

estimate instead of predicting only the mean value, as the Least Square (LS) solution does.

This is promising since the LS predictor is known to oversmooth features leading to muffling …

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a

data distribution and sample distribution. Recent studies have proposed stabilizing the

training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

Image labeling based on graphical models using wasserstein messages and geometric assignment

2018

[PDF] siam.org

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete

graphical models. By utilizing local Wasserstein distances for coupling assignment

measures across edges of the underlying graph, a given discrete objective function is …

Speech enhancement based on a new architecture of wasserstein generative adversarial networks

S Ye, T Jiang, S Qin, W Zou… - 2018 11th International …, 2018 - ieeexplore.ieee.org

Most conventional speech enhancement methods work poorly at low SNRs. And the speech

enhancement method based on generative adversarial network (SEGAN) gets lower speech

quality though it has lots of parameters in its generator. To solve these problems, we …

mage labeling based on graphical models using wasserstein messages and geometric assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete

graphical models. By utilizing local Wasserstein distances for coupling assignment

measures across edges of the underlying graph, a given discrete objective function is …

<——2018—-— 2018———1220—

Dialogwae: Multimodal response generation with conditional wasserstein auto-encoder

X Gu, K Cho, JW Ha, S Kim - arXiv preprint arXiv:1805.12352, 2018 - arxiv.org

Variational autoencoders~(VAEs) have shown a promise in data-driven conversation

modeling. However, most VAE conversation models match the approximate posterior

distribution over the latent variables to a simple prior such as standard normal distribution …

Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator

VA Nguyen, D Kuhn, PM Esfahani - arXiv preprint arXiv:1805.07194, 2018 - arxiv.org

We introduce a distributionally robust maximum likelihood estimation model with a

Wasserstein ambiguity set to infer the inverse covariance matrix of a $ p $-dimensional

Gaussian random vector from $ n $ independent samples. The proposed model minimizes …

2018

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

Differential properties of sinkhorn approximation for learning with wasserstein distance

G Luise, A Rudi, M Pontil, C Ciliberto - arXiv preprint arXiv:1805.11897, 2018 - arxiv.org

Applications of optimal transport have recently gained remarkable attention thanks to the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version …

Gromov-Wasserstein alignment of word embedding spaces

D Alvarez-Melis, TS Jaakkola - arXiv preprint arXiv:1809.00013, 2018 - arxiv.org

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from

machine translation to transfer learning. Recently, purely unsupervised methods operating

on monolingual embeddings have become effective alignment tools. Current state-of-the-art …

2018

A two-step computation of the exact gan wasserstein distance

H Liu, GU Xianfeng, D Samaras - … Conference on Machine …, 2018 - proceedings.mlr.press

In this paper, we propose a two-step method to compute the Wasserstein distance in

Wasserstein Generative Adversarial Networks (WGANs): 1) The convex part of our objective

can be solved by linear programming; 2) The non-convex residual can be approximated by …

Wasserstein Riemannian geometry of Gaussian densities

L Malagò, L Montrucchio, G Pistone - Information Geometry, 2018 - Springer

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Cited by 26 Related articles

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function

is known to suffer from cycle-skipping issues that increase the risk of computing a local

rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to …

Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - arXiv preprint arXiv:1805.07594, 2018 - arxiv.org

Embedding complex objects as vectors in low dimensional spaces is a longstanding

problem in machine learning. We propose in this work an extension of that approach, which

consists in embedding objects as elliptical probability distributions, namely distributions …

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

We propose in this paper a construction of a diffusion process on the space $\mathcal P_2

(\mathbb R) $ of probability measures with a second-order moment. This process was

introduced in several papers by Konarovskyi (see eg [12]) and consists of the limit as $ N …

<——2018—-— 2018———1230—

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

This paper is concerned with the statistical analysis of datasets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the principal component analysis (PCA) of histograms with …

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

Towards high resolution video generation with progressive growing of sliced wasserstein gans

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

since the temporal dimension of videos introduces an extra challenge during the generation

process. Besides, due to the limitation of memory and training stability, the generation …

Cited by 22 Related articles

Towards High Resolution Video Generation with Progressive ...

paperswithcode.com › paper › towards-high-resolution-vi...

Furthermore, we introduce a sliced version of Wasserstein GAN (SWGAN) loss to improve the distribution learning on the video data of ...

Papers With Code · cantabilewq ·

Towards High Resolution Video Generation with Progressive Growing of Sliced Wasserstein GANs

Oct 4, 2018

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org

This paper is concerned by the study of barycenters for random probability measures in the

Wasserstein space. Using a duality argument, we give a precise characterization of the

population barycenter for various parametric classes of random probability measures with …

Classification of small UAVs based on auxiliary classifier wasserstein GANs

C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Beyond their benign uses, the small Unmanned Aerial Vehicles (UAVs) are expected to take

the major role in future smart cities that have attracted the attention of the public and

authorities. Therefore, detecting, tracking and classifying the type of UAVs is important for …

2018

On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order

one between a pair of two-dimensional histograms. Recent works in Computer Vision and

Machine Learning have shown the benefits of measuring Wasserstein distances of order …

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

J Bigot, R Gouet, T Klein, A Lopez - Electronic journal of …, 2018 - projecteuclid.org

This paper is focused on the statistical analysis of probability measures $\boldsymbol {\nu} _

{1},\ldots,\boldsymbol {\nu} _ {n} $ on ${\mathbb {R}} $ that can be viewed as independent

realizations of an underlying stochastic process. We consider the situation of practical …

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Q Qin, JP Hobert - arXiv preprint arXiv:1810.08826, 2018 - arxiv.org

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

We present upper bounds for the Wasserstein distance of order $ p $ between the marginals

of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the

convolution structure, we further derive upper bounds for the total variation distance …

Propagation of chaos, Wasserstein gradient flows and toric Kähler–Einstein metrics

RJ Berman, M Önnheim - Analysis & PDE, 2018 - msp.org

Motivated by a probabilistic approach to Kähler–Einstein metrics we consider a general

nonequilibrium statistical mechanics model in Euclidean space consisting of the stochastic

gradient flow of a given (possibly singular) quasiconvex N-particle interaction energy. We …

<——2018—-— 2018———1240—

Application of auxiliary classifier wasserstein generative adversarial networks in wireless signal classification of illegal unmanned aerial vehicles

C Zhao, C Chen, Z He, Z Wu - Applied Sciences, 2018 - mdpi.com

Recently, many studies have reported on image synthesis based on Generative Adversarial

Networks (GAN). However, the use of GAN does not provide much attention on the signal

classification problem. In the context of using wireless signals to classify illegal Unmanned …

Wasserstein geometry of quantum states and optimal transport of matrix-valued measures

Y Chen, TT Georgiou, A Tannenbaum - … applications of control and systems …, 2018 - Springer

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined

on the space of scalar probability densities, to the space of Hermitian matrices and of matrix-

valued distributions, as well as some extensions of the theory to vector-valued distributions …

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - Unknown Journal, 2018 - experts.umn.edu

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

2018

Evolution of the Wasserstein distance between the marginals of two Markov processes

A Alfonsi, J Corbetta, B Jourdain - Bernoulli, 2018 - projecteuclid.org

In this paper, we are interested in the time derivative of the Wasserstein distance between

the marginals of two Markov processes. As recalled in the introduction, the Kantorovich

duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the …

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - … of Statistical Computation and …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

sets in the size of millions of entries. We consider the situation when the information on a

large univariate data set or sample needs to be preserved, stored or transferred. We suggest …

[HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with

asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian

dynamics and the collective motion of living organisms. In this study, we found that particles …

-Wasserstein distances of tracial -algebras and their disintegration problem

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with

multiplication operators arising as the logarithmic mean under a functional calculus …

Bayes and maximum likelihood for L 1 -Wasserstein deconvolution of Laplace mixtures

C Scricciolo - Statistical Methods & Applications, 2018 - Springer

We consider the problem of recovering a distribution function on the real line from

observations additively contaminated with errors following the standard Laplace distribution.

Assuming that the latent distribution is completely unknown leads to a nonparametric …

<——2018—-— 2018———1250—

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

[PDF] Wasserstein Proximal of GANs

A Tong Lin, W Li, S Osher, G Montúfar - 2018 - mis.mpg.de

We introduce a new method for training GANs by applying the Wasserstein-2 metric

proximal on the generators. This approach is based on the gradient operator induced by

optimal transport theory, which connects the geometry of the sample space and the …

Wasserstein Gradients for the Temporal Evolution of Probability Distributions

Y Chen, HG Müller - arXiv preprint arXiv:1809.03498, 2018 - arxiv.org

Many studies have been conducted on flows of probability measures, often in terms of

gradient flows. We utilize a generalized notion of derivatives with respect to time to model

the instantaneous evolution of empirically observed one-dimensional distributions that vary …

Lifted and geometric differentiability of the squared quadratic Wasserstein distance

A Alfonsi, B Jourdain - 2018 - hal.archives-ouvertes.fr

In this paper, we remark that any optimal coupling for the quadratic Wasserstein distance

W22 (μ, ν) between two probability measures μ and ν with finite second order moments on

Rd is the composition of a martingale coupling with an optimal transport map T. We check …

A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS

G Degottex, M Gales - 2018 IEEE Spoken Language …, 2018 - ieeexplore.ieee.org

Generative networks can create an artificial spectrum based on its conditional distribution

estimate instead of predicting only the mean value, as the Least Square (LS) solution does.

This is promising since the LS predictor is known to oversmooth features leading to muffling …

2018

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a

data distribution and sample distribution. Recent studies have proposed stabilizing the

training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so …

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

magnetic resonance images of the brain, represented as densities on a voxel grid. We aim

<——2018—-— 2018———1260—

[PDF] ON WASSERSTEIN ISOMETRIES OF PROBABILITY MEASURES ON UNIT SPHERES

D VIROSZTEK - arXiv preprint arXiv:1802.03305, 2018 - researchgate.net

We consider the space of all Borel probability measures on the unit sphere of a Euclidean

space endowed with the Wasserstein metric Wp for arbitrary p≥ 1. Our goal is to describe

the isometry group of this metric space. We make some progress in the direction of a Banach …

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

Résumé Cette thèse se concentre sur l'analyse de données présentées sous forme de

mesures de probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension

des outils statistiques usuels sur cet espace muni de la distance de Wasserstein. Une …

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

Evaluating a stochastic parametrization for a fast–slow system ...

https://pure.mpg.de › rest › file_3277792 › content

PDF

by G Vissio · 2018 · Cited by 8 — ... fast–slow system using the Wasserstein distance ... G. Vissio and V. Lucarini: Evaluating a stochastic parametrization for a fast–slow system for a system ... sio and Lucarini (2018), for more complex couplings the stochastic ...

[CITATION] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Evaluating a stochastic parametrization for a fast–slow ... - NPG

https://npg.copernicus.org › articles › 2018

by G Vissio · 2018 · Cited by 8 — https://doi.org/10.5194/npg-25-413-2018 ... Research article | 19 Jun 2018. Evaluating a stochastic parametrization for a fast–slow system using the ... well as Wasserstein distance between the projected measure of the original system on the ...

Missing: Coupling ‎| Must include: Coupling

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. In this context, an important question is the …

2018

Decentralize and randomize: Faster algorithm for Wasserstein barycenters

P Dvurechensky, D Dvinskikh, A Gasnikov… - arXiv preprint arXiv …, 2018 - arxiv.org

We study the decentralized distributed computation of discrete approximations for the

regularized Wasserstein barycenter of a finite set of continuous probability measures

distributedly stored over a network. We assume there is a network of agents/machines …

Distilled wasserstein learning for word embedding and topic modeling

H Xu, W Wang, W Liu, L Carin - arXiv preprint arXiv:1809.04705, 2018 - arxiv.org

We propose a novel Wasserstein method with a distillation mechanism, yielding joint

learning of word embeddings and topics. The proposed method is based on the fact that the

Euclidean distance between word embeddings may be employed as the underlying …

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - … and Software for Big …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

Lifted Wasserstein matcher for fast and robust topology tracking

M Soler, M Plainchault, B Conche… - … Large Data Analysis and …, 2018 - ieeexplore.ieee.org

This paper presents a robust and efficient method for tracking topological features in time-

varying scalar data. Structures are tracked based on the optimal matching between

persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on …

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under wasserstein distance

Y Han, J Jiao, T Weissman - Conference On Learning …, 2018 - proceedings.mlr.press

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for

symmetric functional estimation and distribution estimation under Wasserstein distance. We

construct an efficiently computable estimator that achieves the minimax rates in estimating …

<—–2018—–—ƒ2018———1270—

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PEC de Raynal, N Frikha - arXiv preprint arXiv:1811.06904, 2018 - arxiv.org

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

T Vayer, L Chapel, R Flamary, R Tavenard… - arXiv preprint arXiv …, 2018 - arxiv.org

Optimal transport theory has recently found many applications in machine learning thanks to

its capacity for comparing various machine learning objects considered as distributions. The

Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the …

Wasserstein distance and the distributionally robust TSP

JG Carlsson, M Behroozi, K Mihic - Operations Research, 2018 - pubsonline.informs.org

Recent research on the robust and stochastic traveling salesman problem and the vehicle

routing problem has used many different approaches for describing the region of ambiguity

including taking convex combinations of observed demand vectors or imposing constraints …

[CITATION] … Flamary, Romain Tavenard, and Nicolas Courty. Fused gromov-wasserstein distance for structured objects: theoretical foundations and mathematical …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

[HTML] Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

S Amari, R Karakida, M Oizumi - Information Geometry, 2018 - Springer

Two geometrical structures have been extensively studied for a manifold of probability

distributions. One is based on the Fisher information metric, which is invariant under

reversible transformations of random variables, while the other is based on the Wasserstein …

Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

necessary. Computer aided diagnosis offers an objective score that is independent of …

2018

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE Power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

Wasserstein auto-encoders: Latent dimensionality and random encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

OpenReview is created by the Information Extraction and Synthesis Laboratory, College of Information

and Computer Science, University of Massachusetts Amherst. We gratefully acknowledge the

support of the OpenReview sponsors: Google, Facebook, NSF, the University of Massachusetts …

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in

each of the following cases:(a) X and Y are geodesic spaces and Y is covered by X via a …

<——2018—-— 2018———1280—

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - … on Computer and …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - … Conference on Progress in Informatics and …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

H Farooq, Y Chen, T Georgiou, C Lenglet - Computational Diffusion MRI, 2018 - Springer

Several studies have used structural connectivity information to parcellate brain areas like

the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult

to achieve using conventional MRI techniques. They typically employ diffusion MRI (dMRI) …

Learning and inference with Wasserstein metrics

CCA Frogner - 2018 - dspace.mit.edu

This thesis develops new approaches for three problems in machine learning, using tools

from the study of optimal transport (or Wasserstein) distances between probability

distributions. Optimal transport distances capture an intuitive notion of similarity between …

[PDF] oregonstate.edu

The Wasserstein Distance and its Application to Generative Adversarial Networks

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

2018

Graph clustering and the nuclear Wasserstein metric

D Roux Uribe - 2018 - repositorio.uniandes.edu.co

INTRODUCTION: one of the most relevant situations in public health in Colombia is child

stunting and in parallel, the social effects caused by armed conflict. Currently, it is unknown if

exposure to armed conflict is related to child stunting. OBJECTIVES: identify if significant …

[PDF] Wasserstein Adversarial Mixture for Deep Generative Modeling and Clustering

W Harchaoui, PA Mattei, A Almansa, C Bouveyron - harchaoui.org

Unsupervised learning, and in particular clustering, is probably the most central problem in

learning theory nowadays. This work focuses on the clustering of complex data by

introducing a deep generative approach for both modeling and clustering. The proposed …

[PDF] Bregman and Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond

[PDF] imperial.ac.uk

GANR Wasserstein - wwwf.imperial.ac.uk

Page 1. Bregman Divergence Function Generative Adversarial Networks (GANs) Wasserstein

Divergence and GANs Relaxed Wasserstein Empirical Results Conclusions Bregman and

Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond Xin Guo …

[PDF] uma.es

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

A Esteban-Pérez, JM Morales - 2018 - riuma.uma.es

We consider optimization problems where the information on the uncertain parameters

reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of

probability distributions centered at the empirical distribution is constructed. The goal is to …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

[PDF] osu.edu

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology

theory, and their main output is a descriptor called persistence diagram (PD), which encodes

the topology of a space at all scales in the form of a point cloud with multiplicities in the …

<——2018—-— 2018———1290—

Wasserstein distance for generalized persistence modules ...

https://open.library.ubc.ca › collections › items

Aug 7, 2018 — Wasserstein distance for generalized persistence modules and abelian categories Scott, Jonathan 2018-08-07T13:02. mp4. 00:00 00:00 ...

[CITATION] Wasserstein distance for generalized persistence modules and abelian categories

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018

Cited by 5 Related articles

Wasserstein distance for generalized persistence modules ...

https://open.library.ubc.ca › collections › items

Aug 7, 2018 — Wasserstein distance for generalized persistence modules and abelian categories Scott, Jonathan 2018-08-07T13:02. mp4. 00:00 00:00 ...

[CITATION] … Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty. Fused gromov-wasserstein distance for structured objects: theoretical foundations and …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

Cited by 5 Related articles

1611.00092v2] The Wasserstein distance between stationary ...

128.84.21.199 › abs

[Submitted on 1 Nov 2016 (v1), revised 18 May 2018 (this version, v2), latest version ... We also study the case of two stationary measures associated to different ...

CITATION] The Wasserstein distance between stationary measures

I Cipriano - arXiv preprint arXiv:1611.00092, 2018

Optimal Transport on Discrete Domains

See 2016

arXiv.org > math > arXiv:1611.00092

[v2] Fri, 18 May 2018 21:48:09 UTC (223 KB)

[v3] Fri, 27 Jul 2018 03:29:15 UTC (223 KB)

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2018

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by J Solomon · 2018 · Cited by 28 — lems, the optimal transport (or Monge–Kantorovich) problem involves the matching of probability ... OC] 1 May 2018 ... This amount of work is known as the 1-Wasserstein distance in optimal transport; in one dimension,.

[CITATION] Optimal transport and wasserstein distance

L Wasserman - 2018

Equivalence Between Wasserstein and Value-Aware Loss for ...

Generative modeling using the sliced wasserstein distance

by K Asadi · 2018 · Cited by 12 — Learning a generative model is a key component of model-based reinforcement learning. Though learning a good model in the tabular setting is ...

Missing: e- ‎prints ‎(June

I Deshpande, Z Zhang… - … the IEEE conference on …, 2018 - openaccess.thecvf.com

Abstract Generative Adversarial Nets (GANs) are very successful at modeling distributions

from given samples, even in the high-dimensional case. However, their formulation is also

known to be hard to optimize and often not stable. While this is particularly true for early GAN …

Generative Modeling Using the Sliced Wasserstein Distance

AG Schwing - CVPR, 2018 - openreview.net

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given

samples, even in the high-dimensional case. However, their formulation is also known to be

hard to optimize and often not stable. While this is particularly true for early GAN …

2018 [HTML] springer.com

[HTML] Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - Mathematical Programming, 2018 - Springer

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

The quadratic Wasserstein metric for earthquake location

J Chen, Y Chen, H Wu, D Yang - Journal of Computational Physics, 2018 - Elsevier

Abstract In Engquist et al.(2016)[8], the Wasserstein metric was successfully introduced to

the full waveform inversion. We apply this method to the earthquake location problem. For

this problem, the seismic stations are far from each other. Thus, the trace by trace …

<——2018——— 2018———1300—

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Wasserstein distance and the distributionally robust TSP

JG Carlsson, M Behroozi, K Mihic - Operations Research, 2018 - pubsonline.informs.org

Recent research on the robust and stochastic traveling salesman problem and the vehicle

routing problem has used many different approaches for describing the region of ambiguity

including taking convex combinations of observed demand vectors or imposing constraints …

Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator

VA Nguyen, D Kuhn, PM Esfahani - arXiv preprint arXiv:1805.07194, 2018 - arxiv.org

We introduce a distributionally robust maximum likelihood estimation model with a

Wasserstein ambiguity set to infer the inverse covariance matrix of a $ p $-dimensional

Gaussian random vector from $ n $ independent samples. The proposed model minimizes …

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2018 - projecteuclid.org

We introduce a general theory for a consensus-based combination of estimations of

probability measures. Potential applications include parallelized or distributed sampling

schemes as well as variations on aggregation from resampling techniques like boosting or …

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modeling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

Cited by 8 Re

2018

[PDF] Accelerated first-order methods on the wasserstein space for bayesian inference

C Liu, J Zhuo, P Cheng, R Zhang, J Zhu, L Carin - stat, 2018 - researchgate.net

We consider doing Bayesian inference by minimizing the KL divergence on the 2-

Wasserstein space P2. By exploring the Riemannian structure of P2, we develop two

inference methods by simulating the gradient flow on P2 via updating particles, and an …

[PDF] dagstuhl.de

The wasserstein distance as a dissimilarity measure for mass spectra with application to spectral deconvolution

S Majewski, MA Ciach, M Startek… - … on Algorithms in …, 2018 - drops.dagstuhl.de

We propose a new approach for the comparison of mass spectra using a metric known in the

computer science under the name of Earth Mover's Distance and in mathematics as the

Wasserstein distance. We argue that this approach allows for natural and robust solutions to …

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

DT Zhou, J Chen, H Wu, DH Yang, LY Qiu - arXiv preprint arXiv …, 2018 - arxiv.org

In our previous work [Chen el al., J. Comput. Phys., 373 (2018)], the quadratic Wasserstein

metric is successfully applied to the earthquake location problem. The actual earthquake

hypocenter can be accurately recovered starting from initial values very far from the true …

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

<——2018—-— 2018———1310—

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

Gradient flows for frame potentials on the Wasserstein space

C Wickman, K Okoudjou - arXiv preprint arXiv:1808.09319, 2018 - arxiv.org

In this paper we bring together some of the key ideas and methods of two very lively fields of

mathematical research, frame theory and optimal transport, using the methods of the second

to answer questions posed in the first. In particular, we construct gradient flows in the …

On the Wasserstein distance between mutually singular measures

G Buttazzo, G Carlier, M Laborde - Advances in Calculus of …, 2018 - degruyter.com

We study the Wasserstein distance between two measures μ, ν which are mutually singular.

In particular, we are interested in minimization problems of the form W⁢(μ, 𝒜)= inf⁡{W⁢(μ,

ν): ν∈ 𝒜}, where μ is a given probability and 𝒜 is contained in the class μ⊥ of probabilities …

Convergence in the Wasserstein Distance

R Douc, E Moulines, P Priouret, P Soulier - Markov Chains, 2018 - Springer

In the previous chapters, we obtained rates of convergence in the total variation distance of

the iterates P^ n of an irreducible positive Markov kernel P to its unique invariant measure π

for π-almost every x ∈ X and for all x ∈ X if the kernel P is irreducible and positive Harris …

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

2018

On the minimizing movement with the 1-Wasserstein distance

M Agueh, G Carlier, N Igbida - ESAIM: Control, Optimisation and …, 2018 - esaim-cocv.org

We consider a class of doubly nonlinear constrained evolution equations which may be

viewed as a nonlinear extension of the growing sandpile model of [L. Prigozhin, Eur. J. Appl.

Math. 7 (1996) 225–235.]. We prove existence of weak solutions for quite irregular sources …

The Wasserstein Distance and its Application to Generative Adversarial Networks

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

Graph clustering and the nuclear Wasserstein metric

D Roux Uribe - 2018 - repositorio.uniandes.edu.co

INTRODUCTION: one of the most relevant situations in public health in Colombia is child

stunting and in parallel, the social effects caused by armed conflict. Currently, it is unknown if

exposure to armed conflict is related to child stunting. OBJECTIVES: identify if significant …

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - ALEA: Latin American Journal of Probability …, 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

[PDF] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018 - imo.universite-paris-saclay.fr

We study the numerical implementation of a minimizing movement scheme using the 1-

Wasserstein distance introduced in [1]. We implement this scheme using two different primal

dual algorithm: a Augmented Lagrangian technique with the ADMM algorithm and the …

<——2018—-— 2018———1320—

Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

domain via utilizing the knowledge distilled from a source domain which has a different but

related data distribution. One solution to domain adaptation is to learn domain invariant …

Wasserstein divergence for gans

J Wu, Z Huang, J Thoma, D Acharya… - Proceedings of the …, 2018 - openaccess.thecvf.com

In many domains of computer vision, generative adversarial networks (GANs) have

achieved great success, among which the family of Wasserstein GANs (WGANs) is

considered to be state-of-the-art due to the theoretical contributions and competitive …

[CITATION] Wasserstein divergence for gans

W Jiqing, H Zhiwu, T Janine, A Dinesh, VG Luc - ECCV, 2018

Perturbation theory for Markov chains via Wasserstein distance

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

Wasserstein cnn: Learning invariant features for nir-vis face recognition

R He, X Wu, Z Sun, T Tan - IEEE transactions on pattern …, 2018 - ieeexplore.ieee.org

Heterogeneous face recognition (HFR) aims at matching facial images acquired from

different sensing modalities with mission-critical applications in forensics, security and

commercial sectors. However, HFR presents more challenging issues than traditional face …

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

2018

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Stochastic wasserstein autoencoder for probabilistic sentence generation

H Bahuleyan, L Mou, H Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

The variational autoencoder (VAE) imposes a probabilistic distribution (typically Gaussian)

on the latent space and penalizes the Kullback--Leibler (KL) divergence between the

posterior and prior. In NLP, VAEs are extremely difficult to train due to the problem of KL …

Computing Wasserstein distance for persistence diagrams on a quantum computer

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to

provide a concise description of a filtered topological space. What makes them even more

useful in practice is that they come with a notion of a metric, the Wasserstein distance …

[PDF] wiley.com

Data-driven affinely adjustable distributionally robust framework for unit commitment based on Wasserstein metric

W Hou, R Zhu, H Wei, H TranHoang - IET Generation, Transmission & …, 2018 - IET

This study proposes a data-driven distributionally robust framework for unit commitment

based on Wasserstein metric considering the wind power generation forecasting errors. The

objective of the constructed model is to minimise the expected operating cost, including the …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

[PDF] Wasserstein coresets for Lipschitz costs

S Claici, J Solomon - stat, 2018 - people.csail.mit.edu

Sparsification is becoming more and more relevant with the proliferation of huge data sets.

Coresets are a principled way to construct representative weighted subsets of a data set that

have matching performance with the full data set for specific problems. However, coreset …

<——2018—-— 2018———1330—

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

The exponential contraction in $ L^ 1$-Wasserstein distance and exponential convergence

in $ L^ q $-Wasserstein distance ($ q\geq 1$) are considered for stochastic differential

equations with irregular drift. When the irregular drift drift is locally bounded, the exponential …

Motion-blind blur removal for CT images with Wasserstein generative adversarial networks

Y Lyu, W Jiang, Y Lin, L Voros, M Zhang… - … Congress on Image …, 2018 - ieeexplore.ieee.org

Advanced deblurring techniques for computed tomography (CT) images are necessary and

crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup

and treatment response assessment in radiation oncology. Currently, medical image …

Wasserstein generative recurrent adversarial networks for image generating

C Zhang, Y Feng, B Qiang… - 2018 24th International …, 2018 - ieeexplore.ieee.org

Most generative models are generating images at a time, but in fact, painting is usually done

iteratively and repeatedly. Generative Adversarial Networks (GAN) are well known for

generating images, however, it is hard to train stably. To tackle this problem, we propose a …

Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

An algebraic Wasserstein distance for generalized persistence modules

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018 - arxiv.org

The Wasserstein distances are a family of $ L^ p $ distances, with $1\leq p\leq\infty $, for

persistence diagrams. We define Wasserstein distances for persistence modules, the

algebraic counterpart to persistence diagrams, and prove the following isometry theorem …

2018

[HTML] Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

J Tugaut - Comptes Rendus Mathematique, 2018 - Elsevier

It is well-known (see Bolley et al.[3]) that there exists a contraction in Wasserstein distance

between the solution to the granular media equation and its unique steady state, provided

that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is …

Constructing misfit function for full waveform inversion based on sliced Wasserstein distance

F Chen, D Peter - 80th EAGE Conference and Exhibition 2018, 2018 - earthdoc.org

It has been proven that full waveform inversion (FWI) based on optimal transport (OT) is

robust against noise and contains less local minima. The accurate solution to OT problem on

the real line (1D) is analytical with the selected distance function which can be effectively …

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

Learning Joint Wasserstein Auto-Encoders for Joint Distribution Matching

J Cao, Y Guo, L Mo, P Zhao, J Huang, M Tan - 2018 - openreview.net

We study the joint distribution matching problem which aims at learning bidirectional

mappings to match the joint distribution of two domains. This problem occurs in

unsupervised image-to-image translation and video-to-video synthesis tasks, which …

<——2018—-— 2018———1340—

2018 see 2016 [HTML] springer.com

[HTML] Wasserstein discriminant analysis

R Flamary, M Cuturi, N Courty, A Rakotomamonjy - Machine Learning, 2018 - Springer

… For $\lambda \ge 0$, the regularized Wasserstein distance we adopt in this paper between

\(… fixed point iteration designed to compute Wasserstein barycenters, we propose in this …

Inference for empirical Wasserstein distances on finite spaces Series B Statistical methodology

M Sommerfeld, A Munk - 2018 - pubag.nal.usda.gov

The Wasserstein distance is an attractive tool for data analysis but statistical inference is

hindered by the lack of distributional limits. To overcome this obstacle, for probability

measures supported on finitely many points, we derive the asymptotic distribution of …

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

A Fast Proximal Point Method for Computing Exact Wasserstein Distance

Y Xie, X Wang, R Wang, H Zha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

Wasserstein distance plays increasingly important roles in machine learning, stochastic

programming and image processing. Major efforts have been under way to address its high

computational complexity, some leading to approximate or regularized variations such as …

[CITATION] A fast proximal point method for computing wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

PDF] researchgate.net

[PDF] Wasserstein distance measure machines

A Rakotomamonjy, A Traore, M Berar… - arXiv preprint arXiv …, 2018 - researchgate.net

… we focus our analysis on Wasserstein distances which come … , for some problems, the Wasserstein distance satisfies these … for empirical distributions with Wasserstein distance as a …

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

2018

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition

[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

Gaussian word embedding with a wasserstein distance loss

C Sun, H Yan, X Qiu, X Huang - arXiv preprint arXiv:1808.07016, 2018 - arxiv.org

Compared with word embedding based on point representation, distribution-based word

embedding shows more flexibility in expressing uncertainty and therefore embeds richer

semantic information when representing words. The Wasserstein distance provides a …

Computing Wasserstein distance for persistence diagrams on a quantum computer

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to

provide a concise description of a filtered topological space. What makes them even more

useful in practice is that they come with a notion of a metric, the Wasserstein distance …

A canonical barycenter via Wasserstein regularization

YH Kim, B Pass - SIAM Journal on Mathematical Analysis, 2018 - SIAM

We introduce a weak notion of barycenter of a probability measure μ on a metric measure

space (X,d,\bfm), with the metric d and reference measure \bfm. Under the assumption that

all optimal transport plans transporting \bfm to any probability measure ν on X are induced …

One-dimensional data augmentation using a Wasserstein generative adversarial network with supervised signal

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains;

however, there is still some difficulties in training the network, which are mainly caused by

mode collapse, vanishing gradient of generator and indirect assessment criteria of …

<-––2018—––—2018———1350—

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

[PDF] eg.org

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

[HTML] Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

J Tugaut - Comptes Rendus Mathematique, 2018 - Elsevier

It is well-known (see Bolley et al.[3]) that there exists a contraction in Wasserstein distance

between the solution to the granular media equation and its unique steady state, provided

that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is …

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

A Fast Proximal Point Method for Computing Exact ...

[CITATION] A fast proximal point method for Wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

A Fast Proximal Point Method for Computing Exact ... - arXiv

by Y Xie · 2018 · Cited by 54 — In this paper, we propose a new framework, Inexact Proximal point method for Optim

[CITATION] A fast proximal point method for computing wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

A Malliavin-Stein approach for multivariate approximations in ...

2018

https://www.semanticscholar.org › paper › A-Malliavin-St...

Stein's method has been widely used for probability approximations. However ... approximations with near optimal error bounds on the Wasserstein distance. ... A Malliavin-Stein approach for multivariate approximations in Wasserstein distance ... Mathematics, Computer Science; ArXiv. 2018. 10. PDF. Alert. Research

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

[PDF] A Central Limit Theorem for Wasserstein type distances between two different laws

2018

P Berthet, JC Fort, T Klein - researchgate.net

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs

between two distinct continuous distributions F and G on R. The estimator is based on the

order statistics of (possibly dependent) samples of F resp. G. We prove the consistency and …

[CITATION] A central limit theorem for Wasserstein type distances between two different real distributions

P Berthet, JC Fort, T Klein - Ann. Inst. Henri Poincaré Probab. Stat., hal-01526879, 2018

A note on reinforcement learning with Wasserstein distance ...

https://www.groundai.com › project › a-note-on-reinfor...

Feb 12, 2018 — A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning. Mohammed Amin Abdullah ...

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

[PDF] Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - jmlr.org

Divide-and-conquer based methods for Bayesian inference provide a general approach for

tractable posterior inference when the sample size is large. These methods divide the data

into smaller subsets, sample from the posterior distribution of parameters in parallel on all …

[PDF] shichuan.org

Deep variational network embedding in wasserstein space

D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

Network embedding, aiming to embed a network into a low dimensional vector space while

preserving the inherent structural properties of the network, has attracted considerable

attentions recently. Most of the existing embedding methods embed nodes as point vectors …

<——2018—-— 2018———1360—

Minimax distribution estimation in Wasserstein distance

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

The Wasserstein metric is an important measure of distance between probability

distributions, with applications in machine learning, statistics, probability theory, and data

analysis. This paper provides upper and lower bounds on statistical minimax rates for the …

Hashgan: Deep learning to hash with pair conditional wasserstein gan

Y Cao, B Liu, M Long, J Wang - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Deep learning to hash improves image retrieval performance by end-to-end representation

learning and hash coding from training data with pairwise similarity information. Subject to

the scarcity of similarity information that is often expensive to collect for many application …

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Y Yang, B Engquist, J Sun, BF Hamfeldt - Geophysics, 2018 - library.seg.org

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function

is known to suffer from cycle-skipping issues that increase the risk of computing a local

rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to …

[CITATION] Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion: Geophysics, 83

Y Yang, B Engquist, J Sun, BF Hamfeldt - R43–R62, 2018

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

2018

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PEC de Raynal, N Frikha - arXiv preprint arXiv:1811.06904, 2018 - arxiv.org

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

This paper is concerned with the statistical analysis of datasets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the principal component analysis (PCA) of histograms with …

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

[PDF] ucla.edu

[PDF] Natural gradient in Wasserstein statistical manifold

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - math.ucla.edu

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample space. Our approach is to pull back the L2-Wasserstein metric tensor in probability

density space to parameter space, under which the parameter space become a Riemannian …

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2018 - projecteuclid.org

We introduce a general theory for a consensus-based combination of estimations of

probability measures. Potential applications include parallelized or distributed sampling

schemes as well as variations on aggregation from resampling techniques like boosting or …

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org

This paper is concerned by the study of barycenters for random probability measures in the

Wasserstein space. Using a duality argument, we give a precise characterization of the

population barycenter for various parametric classes of random probability measures with …

<——2018—-— 2018———1370—

Lp-WGAN: Using Lp-norm normalization to stabilize Wasserstein generative adversarial networks

C Zhou, J Zhang, J Liu - Knowledge-Based Systems, 2018 - Elsevier

Wasserstein generative adversarial networks (Wasserstein GANs, WGAN) improve the

performance of GANs significantly by imposing the Lipschitz constraints on the critic, which

is implemented by weight clipping. In this work, we argue that weight clipping could result in …

Wasserstein GAN and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a WaveNet vocoder

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

[PDF] dagstuhl.de

The wasserstein distance as a dissimilarity measure for mass spectra with application to spectral deconvolution

S Majewski, MA Ciach, M Startek… - … on Algorithms in …, 2018 - drops.dagstuhl.de

We propose a new approach for the comparison of mass spectra using a metric known in the

computer science under the name of Earth Mover's Distance and in mathematics as the

Wasserstein distance. We argue that this approach allows for natural and robust solutions to …

Application of auxiliary classifier wasserstein generative adversarial networks in wireless signal classification of illegal unmanned aerial vehicles

C Zhao, C Chen, Z He, Z Wu - Applied Sciences, 2018 - mdpi.com

Recently, many studies have reported on image synthesis based on Generative Adversarial

Networks (GAN). However, the use of GAN does not provide much attention on the signal

classification problem. In the context of using wireless signals to classify illegal Unmanned …

Extremal flows in Wasserstein space

G Conforti, M Pavon - Journal of Mathematical Physics, 2018 - aip.scitation.org

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein

space. We show that the flows associated with the Schrödinger bridge with general prior,

with optimal mass transport, and with the Madelung fluid can all be characterized as …

2018

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

distributions with a set of particles. In this paper we introduce a new particle-based

variational inference method based on the theory of semi-discrete optimal transport. Instead …

Exponential convergence in Wasserstein distance for diffusion semigroups with irregular drifts

SQ Zhang - arXiv preprint arXiv:1812.10190, 2018 - arxiv.org

The exponential contraction in $ L^ 1$-Wasserstein distance and exponential convergence

in $ L^ q $-Wasserstein distance ($ q\geq 1$) are considered for stochastic differential

equations with irregular drift. When the irregular drift drift is locally bounded, the exponential …

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

We consider a sequence of identically independently distributed random samples from an

absolutely continuous probability measure in one dimension with unbounded density. We

establish a new rate of convergence of the $\infty-$ Wasserstein distance between the …

Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm

Q Qin, JP Hobert - Unknown Journal, 2018 - experts.umn.edu

Over the last 25 years, techniques based on drift and minorization (d&m) have been

mainstays in the convergence analysis of MCMC algorithms. However, results presented

herein suggest that d&m may be less useful in the emerging area of convergence complexity …

Non-local texture optimization with wasserstein regularization under convolutional neural network

<——2018—-— 2018———1380—

[HTML] nature.com

[HTML] Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

R Ishiwata, R Kinukawa, Y Sugiyama - Scientific reports, 2018 - nature.com

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with

asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian

dynamics and the collective motion of living organisms. In this study, we found that particles …

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

MA Abdullah, A Pacchiano, M Draief - arXiv preprint arXiv:1802.03976, 2018 - arxiv.org

We describe an application of Wasserstein distance to Reinforcement Learning. The

Wasserstein distance in question is between the distribution of mappings of trajectories of a

policy into some metric space, and some other fixed distribution (which may, for example …

[CITATION] A note on reinforcement learning with Wasserstein distance regularisation, with applications to multipolicy learning.

MA Abdullah, A Pacchiano, M Draief - CoRR, abs/1802.03976, 2018

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

2018

Learning to optimize via wasserstein deep inverse optimal control

[PDF] What is optimized in Wasserstein GANs?

T Pinetz, D Soukup, T Pock - … of the 23rd Computer Vision Winter …, 2018 - researchgate.net

Wasserstein Generative Adversarial Networks (GANs) work by approximating the

Wasserstein distance using large Neural Networks (NNs) with specific architectures,

hyperparameter and regularization techniques. We show that those networks severely …

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's

true cost function from the observed temporal behavior. In contrast to traditional

phenomenological works that aim to learn a generative model to fit the behavioral data, we …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances

J Tong, X Jin, Z Zhang - Potential Analysis, 2018 - Springer

In this paper, we consider the ergodicity for stochastic differential equations driven by

symmetric α-stable processes with Markovian switching in Wasserstein distances. Some

sufficient conditions for the exponential ergodicity are presented by using the theory of M …

Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus

H Dietert, J Evans, T Holding - Kinetic & Related Models, 2018 - aimsciences.org

We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the

stochastic differential equation, we show contraction and therefore exponential convergence

in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a …

<——2018—-— 2018———1390—

[PDF] WASSERSTEIN NATURAL GRADIENT IN STATISTICAL MANIFOLDS WITH CONTINUOUS SAMPLE SPACE

Y Chen, W LI - arXiv preprint arXiv:1805.08380, 2018 - researchgate.net

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample spaces. Our approach is to pull back the L2-Wasserstein metric tensor in the

probability density space to a parameter space, equipping the latter with a positive definite …

[HTML] Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

J Tugaut - Comptes Rendus Mathematique, 2018 - Elsevier

It is well-known (see Bolley et al.[3]) that there exists a contraction in Wasserstein distance

between the solution to the granular media equation and its unique steady state, provided

that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is …

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

Convergence in the Wasserstein Distance

R Douc, E Moulines, P Priouret, P Soulier - Markov Chains, 2018 - Springer

In the previous chapters, we obtained rates of convergence in the total variation distance of

the iterates P^ n of an irreducible positive Markov kernel P to its unique invariant measure π

for π-almost every x ∈ X and for all x ∈ X if the kernel P is irreducible and positive Harris …

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - d-nb.info

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible

to describe the dynamics of matter without resorting to a notion of space, in particular to a …

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

2018

[PDF] hse.ru

AG Bronevich, IN Rozenberg - International Conference on Belief …, 2018 - Springer

The aim of this paper is to show that the Kantorovich problem, well known in models of

economics and very intensively studied in probability theory in recent years, can be viewed

as the basis of some constructions in the theory of belief functions. We demonstrate this by …

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

Résumé Cette thèse se concentre sur l'analyse de données présentées sous forme de

mesures de probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension

des outils statistiques usuels sur cet espace muni de la distance de Wasserstein. Une …

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

The Wasserstein Distance and its Application to Generative Adversarial Networks

AF Leuchtenberger - 2018 - othes.univie.ac.at

In the last years neural networks had a great revival. Today they are a popular topic in

computer science, but also in mathematics. When they appeared in 1940-1960 and later in

1980-1990 neither the computational capacity of the hardware nor the amount of data was …

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space

of Wasserstein in the framework of mean field control problems. The main motivation for this

study is given by the control of multi-agent systems, where the number of the agents is so …

<——2018—-— 2018———1400—

[PDF] imperial.ac.uk

[PDF] Bregman and Wasserstein, with Applications to Generative Adversarial Networks (GANs) and beyond

GANR Wasserstein - wwwf.imperial.ac.uk

… 5 / 50 Page 20. Bregman Divergence Function Generative Adversarial Networks (GANs)

Wasserstein Divergence and GANs Relaxed Wasserstein Empirical Results Conclusions Answer:

Bregman Loss Fucntions Dφ(x,y) (Banerjee, G. and Wang (2005)) Sufficient arg min Y ∈G …

Using Wasserstein GAN to generate high quality adversarial examples

Z Xiong - 2018 - ideals.illinois.edu

Although Deep Neural Networks (DNNs) have state-of-the-art performance in various

machine learning tasks, in recent years, they are found to be vulnerable to so-called

adversarial examples Specifically, take x is an element of D on which a neural network has …

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein

barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in

the probability simplex. Our method simultaneously estimates such atoms and, for each

datapoint, the vector of weights that can optimally reconstruct it as an optimal transport …

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein

barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in

the probability simplex. Our method simultaneously estimates such atoms and, for each

datapoint, the vector of weights that can optimally reconstruct it as an optimal transport …

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein

barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in

the probability simplex. Our method simultaneously estimates such atoms and, for each

datapoint, the vector of weights that can optimally reconstruct it as an optimal transport …

[CITATION] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY…

2018

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - ALEA: Latin American Journal of Probability …, 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

[PDF] AMMI–Introduction to Deep Learning 10.2. Wasserstein GAN

F Fleuret - fleuret.org

… (Arjovsky et al., 2017) François Fleuret AMMI – Introduction to Deep Learning / 10.2.

Wasserstein GAN 14 / 16 Page 27. However, as Arjovsky et al. wrote: “Weight clipping is

a clearly terrible way to enforce a Lipschitz constraint. If the clipping parameter is large, then …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Report on” Sliced Wasserstein Distance for Persistence …

X Zha - people.math.osu.edu

The tools developed in Topological data analysis are built upon persistence homology

theory, and their main output is a descriptor called persistence diagram (PD), which encodes

the topology of a space at all scales in the form of a point cloud with multiplicities in the …

[PDF] Report for CSE 5339 2018—(OTMLSA) Optimal Transport in Machine Learning and Shape Analysis Γ-convergence of Entropy Regularized Wasserstein …

S Chowdhury - people.math.osu.edu

In this paper, we are interested in the convergence of the solution to the entropy-regularized

optimal transport (OT) problem to the non-regularized OT problem, as described in

[CDPS17]. All these results will be in the case of Euclidean space … We write PpR mq to denote …

iReport for CSE 5339 2018—(OTMLSA) Optimal Transport

Solving Approximate Wasserstein GANs to Stationarity

https://www.groundai.com › project › solving-approximat...

Feb 22, 2018 — Generative Adversarial Networks (GANs) are one of the most practical strategies to learn data distributions. A popular GAN formulation is based ...

[CITATION] Solving approximate Wasserstein GANs to stationarity

M Sanjabi, J Ba, M Razaviyayn, JD Lee - arXiv preprint arXiv:1802.08249, 2018

Wasserstein metric-driven Bayesian inversion with ...

CITATION] Solving approximate Wasserstein GANs to stationarity

M Sanjabi, J Ba, M Razaviyayn, JD Lee - arXiv preprint arXiv:1802.08249, 2018

M Motamed · 2018 · Cited by 8 — [Submitted on 21 Jul 2018 (v1), last revised 26 Dec 2018 (this version, v3)] ... Thirdly, in the particular case of signal processing problems, while a normal ... We apply the new framework to a class of signal processing problems, that is, the ...

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[CITATION] Wasserstein metric-driven Bayesian inversion with application to wave propagation problems

M Motamed, D Appelo - arXiv preprint arXiv:1807.09682, 2018

Multivariate approximations in Wasserstein distance by Stein's ...

<—2018—-— 2018———1410—

bX Fang · 2018 · Cited by 22 — [Submitted on 24 Jan 2018 (v1), last revised 14 Aug 2018 (this version, v2)] ... in Malliavin calculus to control the derivatives of the Stein equation ... Combined with Stein's exchangeable pair approach, we obtain a general theorem for multivariate approximations with near optimal error bounds on the Wasserstein distance.

[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

Multivariate approximations in Wasserstein distance by Stein's ...

by X Fang · 2018 · Cited by 22 — [Submitted on 24 Jan 2018 (v1), last revised 14 Aug 2018 (this version, v2)] ... in Malliavin calculus to control the derivatives of the Stein equation ... Combined with Stein's exchangeable pair approach, we obtain a general theorem for multivariate approximations with near optimal error bounds on the Wasserstein distance.

You visited this page on 3/27

[CITATION] A Malliavin-Stein approach for multivariate approximations in Wasserstein distance

X Fang, QM Shao, L Xu - Arxiv preprint, 2018

[HTML] Quasineutral limit for Vlasov–Poisson via Wasserstein stability estimates in higher dimension

2018 see 2017 [HTML] sciencedirect.com

D Han-Kwan, M Iacobelli - Journal of Differential Equations, 2017 - Elsevier

… In our case the Wasserstein space P 2 ( M ) is the space of probability measures which have a finite moment of order 2 and it will always be equipped with the quadratic Wasserstein …

Hashgan: Deep learning to hash with pair conditional wasserstein gan

Y Cao, B Liu, M Long, J Wang - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Deep learning to hash improves image retrieval performance by end-to-end representation

learning and hash coding from training data with pairwise similarity information. Subject to

the scarcity of similarity information that is often expensive to collect for many application

domains, existing deep learning to hash methods may overfit the training data and result in

substantial loss of retrieval quality. This paper presents HashGAN, a novel architecture for

deep learning to hash, which learns compact binary hash codes from both real images and …

[CITATION] HashGAN: Deep Learning to Hash with Pair Conditional Wasserstein GAN [C]

C Yue, L Bin, L Mingsheng - IEEE/CVF Conference on Computer Vision & Pattern …, 2018

Wasserstein stability of the entropy power inequality for log-concave random vectors

TA Courtade, M Fathi… - 2017 IEEE International …, 2017 - ieeexplore.ieee.org

… in the quadratic Wasserstein distance. Further, if one … Wasserstein distance. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein …

2018

Using Wasserstein GAN to generate high quality adversarial ...

https://www.ideals.illinois.edu › handle

[CITATION] Using Wasserstein GAN to Generate Adversarial Examples

Z Xiong, P Moulin

Evaluating a Parametrization of the Coupling in a Fast-Slow ...

https://npg.copernicus.org › npg-2018-16 › npg-...

PDF

by G Vissio — Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance. Gabriele Vissio1,2 and Valerio Lucarini2,3,4. 1International ...

[CITATION] Evaluating a Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

… In order to evaluate how much such measures differ, we resort to consid- ering their Wasserstein

distance (Villani, 2009) … www.nonlin-processes-geophys.net/25/413/2018/ Page 7. G. Vissio and

V. Lucarini: Evaluating a stochastic parametrization for a fast–slow system 419 …

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

… Abstract: We present upper bounds for the Wasserstein distance of order p between the marginals of Lévy processes, including Gaussian0 approximations for jumps of infinite activity. …

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as …

<——2018—-— 2018———1420—

Sliced-wasserstein autoencoder: An embarrassingly simple generative model

S Kolouri, PE Pope, CE Martin, GK Rohde - arXiv preprint arXiv …, 2018 - arxiv.org

In this paper we study generative modeling via autoencoders while using the elegant

geometric properties of the optimal transport (OT) problem and the Wasserstein distances.

We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that …

[CITATION] Sliced-wasserstein autoencoder: an embarrassingly simple generative model. arXiv e-prints

S Kolouri, PE Pope, CE Martin, GK Rohde - 2018

[PDF] Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

ESG Model - openreview.net

In this paper we study generative modeling via autoencoders while using the elegant

geometric properties of the optimal transport (OT) problem and the Wasserstein distances.

We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that …

Semantic image inpainting through improved wasserstein generative adversarial networks

P Vitoria, J Sintes, C Ballester - arXiv preprint arXiv:1812.01071, 2018 - arxiv.org

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image.

In this work we tackle this problem not only by using the available visual data but also by

incorporating image semantics through the use of generative models. Our contribution is …

T Pinetz, D Soukup, T Pock - … of the 23rd Computer Vision Winter …, 2018 - researchgate.net

Wasserstein Generative Adversarial Networks (GANs) work by approximating the

Wasserstein distance using large Neural Networks (NNs) with specific architectures,

hyperparameter and regularization techniques. We show that those networks severely …

An algebraic Wasserstein distance for generalized persistence modules

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018 - arxiv.org

The Wasserstein distances are a family of $ L^ p $ distances, with $1\leq p\leq\infty $, for

persistence diagrams. We define Wasserstein distances for persistence modules, the

algebraic counterpart to persistence diagrams, and prove the following isometry theorem …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

[PDF] Multi-Level Metric Learning via Smoothed Wasserstein Distance.

J Xu, L Luo, C Deng, H Huang - IJCAI, 2018 - ijcai.org

Traditional metric learning methods aim to learn a single Mahalanobis distance matrix M,

which, however, is not discriminative enough to characterize the complex and

heterogeneous data. Besides, if the descriptors of the data are not strictly aligned …

A canonical barycenter via Wasserstein regularization

YH Kim, B Pass - SIAM Journal on Mathematical Analysis, 2018 - SIAM

We introduce a weak notion of barycenter of a probability measure μ on a metric measure

space (X,d,\bfm), with the metric d and reference measure \bfm. Under the assumption that

all optimal transport plans transporting \bfm to any probability measure ν on X are induced …

Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

J Evans - arXiv preprint arXiv:1810.01324, 2018 - arxiv.org

We study the kinetic Fokker-Planck equation on the whole space with a confining potential.

We show quantitative rates of exponential convergence to equilibrium in a well chosen

Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by …

Learning to optimize via wasserstein deep inverse optimal control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's

true cost function from the observed temporal behavior. In contrast to traditional

phenomenological works that aim to learn a generative model to fit the behavioral data, we …

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv preprint arXiv:1809.05990, 2018 - arxiv.org

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

<——2018—-— 2018———1430—

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a

data distribution and sample distribution. Recent studies have proposed stabilizing the

training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

[PDF] bayesiandeeplearning.org

[PDF] Semi-Supervised Pairing via Basis-Sharing Wasserstein Matching Auto-Encoder

Z Liu, YHH Tsai, M Yamada, R Salakhutdinov - bayesiandeeplearning.org

Semi-supervised pairing, learning explicit pairing relation between unlabeled input and

target distribution in an otherwise semisupervised setting, has recently attracted lots of

attention [16, 12], since data labeling is often time-consuming and requires lots of human …

A Fast Proximal Point Method for Computing Exact ...

[CITATION] A fast proximal point method for computing wasserstein distance

Y Xie, X Wang, R Wang, H Zha - arXiv preprint arXiv:1802.04307, 2018

roblemas de clasificación: Una perspectiva robusta con la ...

https://repositorio.uniandes.edu.co › bitstream › handle

by JA Acosta Melo — Equivalencia problemas cónicos con problema principal 14. 3.4. ... proporciona un planteamiento equivalente y su justificación para hacer el problema robus- ... problemas de clasificación con regresión logıstica y máquinas de soporte vectorial. ... 2018. [4] D. W. Hosmer and S. Lemeshow. Applied logistic regression. 2000.

[CITATION] Problemas de clasificación: una perspectiva robusta con la métrica de Wasserstein

JAA Melo - 2018 - Uniandes

2018

Minimax distribution estimation in Wasserstein distance

S Singh, B Póczos - arXiv preprint arXiv:1802.08855, 2018 - arxiv.org

The Wasserstein metric is an important measure of distance between probability

distributions, with applications in machine learning, statistics, probability theory, and data

analysis. This paper provides upper and lower bounds on statistical minimax rates for the …

[PDF] Regularized Wasserstein Means Based on Variational Transportation

L Mi, W Zhang, Y Wang - CoRR, 2018 - public.asu.edu

We raise the problem of regularizing Wasserstein means and propose several terms tailored

to tackle different problems. Our formulation is based on the variational transportation to

distribute a sparse discrete measure into the target domain without mass splitting. The …

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

2018 [PDF] arxiv.org

An algebraic Wasserstein distance for generalized persistence modules

P Bubenik, J Scott, D Stanley - arXiv preprint arXiv:1809.09654, 2018 - arxiv.org

… We define Wasserstein distances for persistence modules, the algebraic counterpart to …

Since our algebraic Wasserstein distances do not require computing a persistence diagram, they …

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges

in the numerical modeling of geophysical fluids. We consider here the simple yet

paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a …

<——2018—-— 2018———14340—

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DF Fonseca Valero - repositorio.uniandes.edu.co

El presente texto tiene como finalidad analizar el volumen de cuentos El aprendiz de mago

y otros cuentos de miedo (1992) del escritor colombiano Evelio José Rosero Diago (1958),

teniendo en cuenta la forma como se consolidan los diversos matices de la violenta y …

[CITATION] Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DFF Valero - 2018 - Uniandes

Wasserstein riemannian geometry of positive definite matrices

L Malago, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Wasserstein geometry of quantum states and optimal transport of matrix-valued measures

Y Chen, TT Georgiou, A Tannenbaum - Emerging applications of control …, 2018 - Springer

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined

on the space of scalar probability densities, to the space of Hermitian matrices and of matrix-

valued distributions, as well as some extensions of the theory to vector-valued distributions …

Towards high resolution video generation with progressive growing of sliced wasserstein gans

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

since the temporal dimension of videos introduces an extra challenge during the generation

process. Besides, due to the limitation of memory and training stability, the generation …

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

T Vayer, L Chapel, R Flamary, R Tavenard… - arXiv preprint arXiv …, 2018 - arxiv.org

Optimal transport theory has recently found many applications in machine learning thanks to

its capacity for comparing various machine learning objects considered as distributions. The

Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the …

[CITATION] Laetita Chapel, Rémi Flamary, Romain Tavenard, and Nicolas Courty. Fused gromov-wasserstein distance for structured objects: theoretical foundations …

T Vayer - arXiv preprint arXiv:1811.02834, 2018

Classification of small UAVs based on auxiliary classifier wasserstein GANs

C Zhao, C Chen, Z Cai, M Shi, X Du… - 2018 IEEE Global …, 2018 - ieeexplore.ieee.org

Beyond their benign uses, the small Unmanned Aerial Vehicles (UAVs) are expected to take

the major role in future smart cities that have attracted the attention of the public and

authorities. Therefore, detecting, tracking and classifying the type of UAVs is important for …

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

Cross-domain text sentiment classification based on Wasserstein distance

G Cai, Q Lin, N Chen - International Conference on Security with Intelligent …, 2018 - Springer

Text sentiment analysis is mainly to detect the sentiment polarity implicit in text data. Most

existing supervised learning algorithms are difficult to solve the domain adaptation problem

in text sentiment analysis. The key of cross-domain text sentiment analysis is how to extract …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

<——2018—-— 2018———1450—

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

We provide an exact deterministic reformulation for data-driven chance constrained

programs over Wasserstein balls. For individual chance constraints as well as joint chance

constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer …

Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In the presence of

VRE uncertainties, this paper discusses a distributionally robust chance constrained …

Motion-blind blur removal for CT images with Wasserstein generative adversarial networks

Y Lyu, W Jiang, Y Lin, L Voros, M Zhang… - … Congress on Image …, 2018 - ieeexplore.ieee.org

Advanced deblurring techniques for computed tomography (CT) images are necessary and

crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup

and treatment response assessment in radiation oncology. Currently, medical image …

Sparse-view CT reconstruction using wasserstein GANs

F Thaler, K Hammernik, C Payer, M Urschler… - … workshop on machine …, 2018 - Springer

We propose a 2D computed tomography (CT) slice image reconstruction method from a

limited number of projection images using Wasserstein generative adversarial networks

(wGAN). Our wGAN optimizes the 2D CT image reconstruction by utilizing an adversarial …

2018

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

2018

Diagnosis of Schizophrenia Disorder Using Wasserstein Based Active Contour and Texture Features

M Latha, G Kavitha - Computational Signal Processing and Analysis, 2018 - Springer

Magnetic resonance (MR) brain images have a significant role in diagnosis of many

neuropsychiatric disorders such as Schizophrenia (SZ). In this work, Wasserstein-based

active contour and the texture features such as Hu moments and gray-level co-occurrence …

Cross-domain text sentiment classification based on Wasserstein distance

[PDF] joig.org

[PDF] Automatic liver segmentation using u-net with wasserstein gans

Y Enokiya, Y Iwamoto, YW Chen, XH Han - J. Image Graph., 2018 - joig.org

Automatic liver segmentation in CT images is an important step for computer-aided

diagnosis and computeraided hepatic surgery. Recently, though numerous methods based

on deep learning such as U-Net have been proposed for automatic liver segmentation, it is …

G Cai, Q Lin, N Chen - International Conference on Security with Intelligent …, 2018 - Springer

Text sentiment analysis is mainly to detect the sentiment polarity implicit in text data. Most

existing supervised learning algorithms are difficult to solve the domain adaptation problem

in text sentiment analysis. The key of cross-domain text sentiment analysis is how to extract …

Wasserstein 거리를 이용한 feature selection에 대한 학술자료

2018

Analysis of survivability for combatants during offensive … - ‎Kim - Cited by 5 62

[CITATION] Wasserstein 거리를 이용한 feature selection

지종호， 신현정 - 한국정보과학회 학술발표논문집, 2018 - dbpia.co.kr

요 약그래프기반 준지도학습 (graph based semi-supervised learning) 은 그래프를 어떻게

만드냐에 따라 성능이 달라진다. 특히, 그래프의 엣지는 레코드 간 유사도로 생성되는데

유사도가 어떻게 정의되는가는 준지도학습의 성능에 상당한 영향을 미친다. 일반적으로 가장 …

[Korean Feature selection using Wasserstein distance]

<––2018——2018———1460—

Wasserstein distance guided representation learning for domain adaptation

J Shen, Y Qu, W Zhang, Y Yu - Proceedings of the AAAI Conference on …, 2018 - ojs.aaai.org

Abstract Domain adaptation aims at generalizing a high-performance learner on a target

domain via utilizing the knowledge distilled from a source domain which has a different but

related data distribution. One solution to domain adaptation is to learn domain invariant …

elated data distribution. One solution to domain adaptation is to learn domain invariant …

2018 see 2016

[CITATION] A multivariate CLT in Wasserstein distance with near optimal convergence rate

A Zhai - Probab. Theory Related Fields, 2018

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

Semantic image inpainting through improved wasserstein generative adversarial networks

P Vitoria, J Sintes, C Ballester - arXiv preprint arXiv:1812.01071, 2018 - arxiv.org

Image inpainting is the task of filling-in missing regions of a damaged or incomplete image.

In this work we tackle this problem not only by using the available visual data but also by

incorporating image semantics through the use of generative models. Our contribution is …

Perturbation theory for Markov chains via Wasserstein distance

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

In this survey paper, we give an overview of our recent works on the study of the W-entropy

for the heat equation associated with the Witten Laplacian on super-Ricci flows and the

Langevin deformation on the Wasserstein space over Riemannian manifolds. Inspired by …

2018

Single image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network

and Wasserstein generative adversarial nets is proposed aiming at generating a photo-

realistic image with finer texture details. Specifically, we construct a framework consisting of …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

Face super-resolution has attracted much attention in recent years. Many algorithms have

been proposed. However, these approaches only perform well under the condition that the

input is noiseless or has small noise. These existing approaches think the measure of …

2018

Single image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network

and Wasserstein generative adversarial nets is proposed aiming at generating a photo-

realistic image with finer texture details. Specifically, we construct a framework consisting of …

2018

[PDF] WASSERSTEIN NATURAL GRADIENT IN STATISTICAL MANIFOLDS WITH CONTINUOUS SAMPLE SPACE

Y Chen, W LI - arXiv preprint arXiv:1805.08380, 2018 - researchgate.net

We study the Wasserstein natural gradient in parametric statistical models with continuous

sample spaces. Our approach is to pull back the L2-Wasserstein metric tensor in the

probability density space to a parameter space, equipping the latter with a positive definite …

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. In this context, an important question is the …

<——2018—-— 2018———1470—

Computing Wasserstein distance for persistence diagrams on a quantum computer

JJ Berwald, JM Gottlieb, E Munch - arXiv preprint arXiv:1809.06433, 2018 - arxiv.org

Persistence diagrams are a useful tool from topological data analysis which can be used to

provide a concise description of a filtered topological space. What makes them even more

useful in practice is that they come with a notion of a metric, the Wasserstein distance …

T Pinetz, D Soukup, T Pock - … of the 23rd Computer Vision Winter …, 2018 - researchgate.net

Wasserstein Generative Adversarial Networks (GANs) work by approximating the

Wasserstein distance using large Neural Networks (NNs) with specific architectures,

hyperparameter and regularization techniques. We show that those networks severely …

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation

H Wu, PC Ma, Y Lv, M Ihme - 2018 AIAA Aerospace Sciences Meeting, 2018 - arc.aiaa.org

The objective of this work is to address the need for assessing the quality of large-eddy

simulations with particular application to turbulent reacting flows. Such assessments include

the consideration of resolution requirements and the quantitative evaluation of the accuracy …

2018

Single image super-resolution based on wasserstein GANs

F Wu, B Wang, D Cui, L Li - 2018 37th Chinese Control …, 2018 - ieeexplore.ieee.org

In this paper, a novel single image super-resolution method unifying deep residual network

and Wasserstein generative adversarial nets is proposed aiming at generating a photo-

realistic image with finer texture details. Specifically, we construct a framework consisting of …

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

2018 [PDF] eg.org

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

2018 [PDF] eg.org

[PDF] Light Field Synthesis from a Single Image using Improved Wasserstein Generative Adversarial Network.

L Ruan, B Chen, ML Lam - Eurographics (Posters), 2018 - diglib.eg.org

We present a deep learning-based method to synthesize a 4D light field from a single 2D

RGB image. We consider the light field synthesis problem equivalent to image super-

resolution, and solve it by using the improved Wasserstein Generative Adversarial Network …

2018

Saliency detection based on aggregated Wasserstein distance

F Sun, W Li - Journal of Electronic Imaging, 2018 - spiedigitallibrary.org

This paper proposes a saliency detection method based on the aggregated Wasserstein distance. A multidimensional Gaussian mixture model is used to model the superpixels, …

Save Cite Cited by 1 Related articles All 2 versions

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

Cross-lingual document retrieval using regularized Wasserstein distance

G Balikas, C Laclau, I Redko, MR Amini - … on Information Retrieval, 2018 - Springer

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

Cross-Lingual Document Retrieval Using Regularized Wasserstein Distance

MR Amini - Advances in Information Retrieval: 40th European …, 2018 - books.google.com

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

Sketch-based 3D object retrieval using Wasserstein Center Loss

M Ji, J Chun, N Kim - Journal of Internet Computing and Services, 2018 - koreascience.or.kr

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using

human-drawn sketches as query. In this paper, we propose a new method of using Sketch

CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search …

<——2018—-— 2018———1480—

Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks

Y Liu, Z Qin, T Wan, Z Luo - Neurocomputing, 2018 - Elsevier

Recently, realistic image generation using deep neural networks has become a hot topic in

machine learning and computer vision. Such an image can be generated at pixel level by

learning from a large collection of images. Learning to generate colorful cartoon images …

Differential properties of sinkhorn approximation for learning with wasserstein distance

G Luise, A Rudi, M Pontil, C Ciliberto - arXiv preprint arXiv:1805.11897, 2018 - arxiv.org

Applications of optimal transport have recently gained remarkable attention thanks to the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version …

Piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

P Arbenz, W Guevara-Alarcón - Journal of Statistical Computation …, 2018 - Taylor & Francis

Big data applications and Monte Carlo simulation results can nowadays easily contain data

sets in the size of millions of entries. We consider the situation when the information on a

large univariate data set or sample needs to be preserved, stored or transferred. We suggest …

Cited by 2 Related

[PDF] Wasserstein coresets for Lipschitz costs

S Claici, J Solomon - stat, 2018 - people.csail.mit.edu

Sparsification is becoming more and more relevant with the proliferation of huge data sets.

Coresets are a principled way to construct representative weighted subsets of a data set that

have matching performance with the full data set for specific problems. However, coreset …

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

V Perchet, M Quincampoix - arXiv preprint arXiv:1811.04575, 2018 - arxiv.org

Studying continuous time counterpart of some discrete time dynamics is now a standard and

fruitful technique, as some properties hold in both setups. In game theory, this is usually

done by considering differential games on Euclidean spaces. This allows to infer properties …

2018

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

One-dimensional data augmentation using a Wasserstein generative adversarial network with supervised signal

H Lou, Z Qi, J Li - 2018 Chinese Control And Decision …, 2018 - ieeexplore.ieee.org

In recent years, Generative Adversarial Network (GAN) is widely applied in many domains;

however, there is still some difficulties in training the network, which are mainly caused by

mode collapse, vanishing gradient of generator and indirect assessment criteria of …

Sliced-wasserstein autoencoder: An embarrassingly simple generative model

S Kolouri, PE Pope, CE Martin, GK Rohde - arXiv preprint arXiv …, 2018 - arxiv.org

In this paper we study generative modeling via autoencoders while using the elegant

geometric properties of the optimal transport (OT) problem and the Wasserstein distances.

We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that …

ITATION] Sliced-wasserstein autoencoder: an embarrassingly simple generative model. arXiv e-prints

S Kolouri, PE Pope, CE Martin, GK Rohde - 2018

[PDF] Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

ESG Model - openreview.net

In this paper we study generative modeling via autoencoders while using the elegant

geometric properties of the optimal transport (OT) problem and the Wasserstein distances.

We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that …

Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GAN

C Kim, S Park, HJ Hwang - arXiv preprint arXiv:1810.02528, 2018 - arxiv.org

Wasserstein GAN (WGAN) is a model that minimizes the Wasserstein distance between a

data distribution and sample distribution. Recent studies have proposed stabilizing the

training process for the WGAN and implementing the Lipschitz constraint. In this study, we …

<——2018—-— 2018———1490—

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

Supplement to “Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance.”

J Weed, F Bach - 2018 - projecteuclid.org

We begin by giving an informal outline of the idea of the proof. Consider a partition {Qi} i∈ I

of S, for some index set I. The measures µ and ν both induce measures on each set in the

partition. We will transport µ to ν by first moving mass between sets in this partition, and then …

[PDF] rit.edu

[BOOK] A Comparative Assessment of the Impact of Various Norms on Wasserstein Generative Adversarial Networks

C Ramesh - 2018 - search.proquest.com

Abstract Generative Adversarial Networks (GANs) provide a fascinating new paradigm in

machine learning and artificial intelligence, especially in the context of unsupervised

learning. GANs are quickly becoming a state of the art tool, used in various applications …

Lifted Wasserstein matcher for fast and robust topology tracking

M Soler, M Plainchault, B Conche… - 2018 IEEE 8th …, 2018 - ieeexplore.ieee.org

This paper presents a robust and efficient method for tracking topological features in time-

varying scalar data. Structures are tracked based on the optimal matching between

persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on …

Convergence rates of the front tracking method for conservation laws in the Wasserstein distances

S Solem - SIAM Journal on Numerical Analysis, 2018 - SIAM

We prove that front tracking approximations to scalar conservation laws with convex fluxes

converge at a rate of Δx^2 in the 1-Wasserstein distance W_1. Assuming positive initial data,

we also show that the approximations converge at a rate of Δx in the ∞-Wasserstein …

2018

year 2018

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space

of Wasserstein in the framework of mean field control problems. The main motivation for this

study is given by the control of multi-agent systems, where the number of the agents is so …

2018

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PEC de Raynal, N Frikha - arXiv preprint arXiv:1811.06904, 2018 - arxiv.org

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under

mild assumptions on the coefficients as well as classical solutions for a class of associated …

2018

Perturbation theory for Markov chains via Wasserstein distance

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

2018 [PDF] nips.cc

[PDF] Robust Hypothesis Testing Using Wasserstein Uncertainty Sets.

R Gao, L Xie, Y Xie, H Xu - NeurIPS, 2018 - papers.nips.cc

We develop a novel computationally efficient and general framework for robust hypothesis

testing. The new framework features a new way to construct uncertainty sets under the null

and the alternative distributions, which are sets centered around the empirical distribution …

year 2018

Some aspects of differential inclusions in Wasserstein space and applications

A Marigonda - ENCONTRO DE MATEMATICA EM MEMORIA DE … - inmvg.uevora.pt

In this talk we will present some recent results on differential inclusions theory in the space

of Wasserstein in the framework of mean field control problems. The main motivation for this

study is given by the control of multi-agent systems, where the number of the agents is so …

<——2018—-— 2018———1500—

The quadratic Wasserstein metric for earthquake location

J Chen, Y Chen, H Wu, D Yang - Journal of Computational Physics, 2018 - Elsevier

Abstract In Engquist et al.(2016)[8], the Wasserstein metric was successfully introduced to

the full waveform inversion. We apply this method to the earthquake location problem. For

this problem, the seismic stations are far from each other. Thus, the trace by trace …

2018

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2018 - projecteuclid.org

We introduce a general theory for a consensus-based combination of estimations of

probability measures. Potential applications include parallelized or distributed sampling

schemes as well as variations on aggregation from resampling techniques like boosting or …

Semi-supervised biomedical translation with cycle wasserstein regression GANs

M McDermott, T Yan, T Naumann, N Hunt… - Proceedings of the …, 2018 - ojs.aaai.org

The biomedical field offers many learning tasks that share unique challenges: large amounts

of unpaired data, and a high cost to generate labels. In this work, we develop a method to

address these issues with semi-supervised learning in regression tasks (eg, translation from …

2018

Sliced wasserstein distance for learning gaussian mixture models

S Kolouri, GK Rohde… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Gaussian mixture models (GMM) are powerful parametric tools with many applications in

machine learning and computer vision. Expectation maximization (EM) is the most popular

algorithm for estimating the GMM parameters. However, EM guarantees only convergence …

2018

Wasserstein-distance-based Gaussian mixture reduction

A Assa, KN Plataniotis - IEEE Signal Processing Letters, 2018 - ieeexplore.ieee.org

Gaussian mixtures (GMs) are widely used in signal processing applications to capture the

multimodal behavior of dynamic systems. Due to an exponential increase in the number of

GM components in such applications, Gaussian mixture reduction (GMR) approaches are …

[CITATION] … Filtering............ E. Nitzan, T. Routtenberg, and J. Tabrikian 1460 Wasserstein-Distance-Based Gaussian Mixture Reduction............................. A. Assa and …

S Khanna, CR Murthy, L Hu, J Zhang, X Wang, S Wang… - ieeexplore.ieee.org

LETTERS Digital and Multirate Signal Processing Recovery of the Starting Times of Delayed

Signals . . . . . . . . . . . . . . . . . . . . . . . . LC Perotti, D. Vrinceanu, and D. Bessis … An Optimal-Dimensionality

Sampling for Spin-s Functions on the Sphere …

[CITATION] … Stochastic Filtering............ E. Nitzan, T. Routtenberg, and J. Tabrikian 1460 Wasserstein-Distance-Based Gaussian Mixture Reduction............................. A …

S Khanna, CR Murthy, L Hu, J Zhang, X Wang, S Wang… - ieeexplore.ieee.org

LETTERS Digital and Multirate Signal Processing Recovery of the Starting Times of Delayed

Signals . . . . . . . . . . . . . . . . . . . . . . . . LC Perotti, D. Vrinceanu, and D. Bessis … An Optimal-Dimensionality

Sampling for Spin-s Functions on the Sphere

2018

A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

Generative models with both discrete and continuous latent variables are highly motivated

by the structure of many real-world data sets. They present, however, subtleties in training

often manifesting in the discrete latent being under leveraged. In this paper, we show that …

2018 [PDF] cam.ac.uk

G Degottex, M Gales - 2018 IEEE Spoken Language …, 2018 - ieeexplore.ieee.org

Generative networks can create an artificial spectrum based on its conditional distribution

estimate instead of predicting only the mean value, as the Least Square (LS) solution does.

This is promising since the LS predictor is known to oversmooth features leading to muffling …

2018 [PDF] archives-ouvertes.fr

Wasserstein Adversarial Mixture Clustering

W Harchaoui, A Almansa, PA Mattei, C Bouveyron - 2018 - hal.archives-ouvertes.fr

Clustering complex data is a key element of unsupervised learning which is still a

challenging problem. In this work, we introduce a deep approach for unsupervised

clustering based on a latent mixture living in a low-dimensional space. We achieve this …

Diagnosis of Schizophrenia Disorder Using Wasserstein Based Active Contour and Texture Features

M Latha, G Kavitha - Computational Signal Processing and Analysis, 2018 - Springer

Magnetic resonance (MR) brain images have a significant role in diagnosis of many

neuropsychiatric disorders such as Schizophrenia (SZ). In this work, Wasserstein-based

active contour and the texture features such as Hu moments and gray-level co-occurrence …

2018 [PDF] wiley.com

A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow

D Matthes, C Cances, F Nabet - PAMM, 2019 - Wiley Online Library

Existence of solutions to a non‐local Cahn‐Hilliard model with degenerate mobility is

considered. The PDE is written as a gradient flow with respect to the L2‐Wasserstein metric …

[CITATION] A degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

<——2018—-— 2018———1510—

Policy optimization as wasserstein gradient flows

R Zhang, C Chen, C Li, L Carin - … Conference on Machine …, 2018 - proceedings.mlr.press

Policy optimization is a core component of reinforcement learning (RL), and most existing

RL methods directly optimize parameters of a policy based on maximizing the expected total

reward, or its surrogate. Though often achieving encouraging empirical success, its …

2018 [PDF] dagstuhl.de

The wasserstein distance as a dissimilarity measure for mass spectra with application to spectral deconvolution

S Majewski, MA Ciach, M Startek… - … on Algorithms in …, 2018 - drops.dagstuhl.de

We propose a new approach for the comparison of mass spectra using a metric known in the

computer science under the name of Earth Mover's Distance and in mathematics as the

Wasserstein distance. We argue that this approach allows for natural and robust solutions to …

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation

H Wu, PC Ma, Y Lv, M Ihme - 2018 AIAA Aerospace Sciences Meeting, 2018 - arc.aiaa.org

The objective of this work is to address the need for assessing the quality of large-eddy

simulations with particular application to turbulent reacting flows. Such assessments include

the consideration of resolution requirements and the quantitative evaluation of the accuracy …

2018 [PDF] uni-muenster.de

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

magnetic resonance images of the brain, represented as densities on a voxel grid. We aim

to use the Wasserstein distance for dimensionality reduction of MR images by using it as a …

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

2018

Graph Classification with Gromov-Wasserstein Distance via ...

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

기관이 구독 중인 논문을 이용하실 수 있습니다. 회원님의 기관인증 상태 ... 지종호, 신현정 · 한국정보과학회 학술발표논문집 · 한국정보과학회; 2018. 2. Wasserstein ...

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as …

2018

Semi-supervised biomedical translation with cycle wasserstein regression GANs

M McDermott, T Yan, T Naumann, N Hunt… - Proceedings of the …, 2018 - ojs.aaai.org

The biomedical field offers many learning tasks that share unique challenges: large amounts

of unpaired data, and a high cost to generate labels. In this work, we develop a method to

address these issues with semi-supervised learning in regression tasks (eg, translation from …

2018

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

distributions with a set of particles. In this paper we introduce a new particle-based

variational inference method based on the theory of semi-discrete optimal transport. Instead …

On the computation of Kantorovich-Wasserstein distances between 2D-histograms by uncapacitated minimum cost flows

F Bassetti, S Gualandi, M Veneroni - arXiv preprint arXiv:1804.00445, 2018 - arxiv.org

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order

one between a pair of two-dimensional histograms. Recent works in Computer Vision and

Machine Learning have shown the benefits of measuring Wasserstein distances of order …

<——2018—-— 2018———1520—

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

We present upper bounds for the Wasserstein distance of order $ p $ between the marginals

of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the

convolution structure, we further derive upper bounds for the total variation distance …

Evolution of the Wasserstein distance between the marginals of two Markov processes

A Alfonsi, J Corbetta, B Jourdain - Bernoulli, 2018 - projecteuclid.org

In this paper, we are interested in the time derivative of the Wasserstein distance between

the marginals of two Markov processes. As recalled in the introduction, the Kantorovich

duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the …

2018

[PDF] Robust Hypothesis Testing Using Wasserstein Uncertainty Sets.

R Gao, L Xie, Y Xie, H Xu - NeurIPS, 2018 - papers.nips.cc

We develop a novel computationally efficient and general framework for robust hypothesis

testing. The new framework features a new way to construct uncertainty sets under the null

and the alternative distributions, which are sets centered around the empirical distribution …

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

We present upper bounds for the Wasserstein distance of order $ p $ between the marginals

of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the

convolution structure, we further derive upper bounds for the total variation distance …

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions

towards addressing these issues. But we found in practice that gradient penalty WGANs (GP …

2018

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - IEEE transactions on …, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

2018 [PDF] inria.fr

Topological data assimilation using Wasserstein distance

L Li, A Vidard, FX Le Dimet, J Ma - Inverse Problems, 2018 - iopscience.iop.org

This work combines a level-set approach and the optimal transport-based Wasserstein

distance in a data assimilation framework. The primary motivation of this work is to reduce

assimilation artifacts resulting from the position and observation error in the tracking and …

2018

Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss

Q Yang, P Yan, Y Zhang, H Yu, Y Shi… - … on medical imaging, 2018 - ieeexplore.ieee.org

The continuous development and extensive use of computed tomography (CT) in medical

practice has raised a public concern over the associated radiation dose to the patient.

Reducing the radiation dose may lead to increased noise and artifacts, which can adversely …

The Wasserstein-Fisher-Rao metric for waveform based earthquake location

DT Zhou, J Chen, H Wu, DH Yang, LY Qiu - arXiv preprint arXiv …, 2018 - arxiv.org

In our previous work [Chen el al., J. Comput. Phys., 373 (2018)], the quadratic Wasserstein

metric is successfully applied to the earthquake location problem. The actual earthquake

hypocenter can be accurately recovered starting from initial values very far from the true …

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under wasserstein distance

Y Han, J Jiao, T Weissman - Conference On Learning …, 2018 - proceedings.mlr.press

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for

symmetric functional estimation and distribution estimation under Wasserstein distance. We

construct an efficiently computable estimator that achieves the minimax rates in estimating …

<——2018—-— 2018———1530—

2018 [PDF] mlr.press

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under wasserstein distance

Y Han, J Jiao, T Weissman - Conference On Learning …, 2018 - proceedings.mlr.press

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for

symmetric functional estimation and distribution estimation under Wasserstein distance. We

construct an efficiently computable estimator that achieves the minimax rates in estimating …

year 2018

[PDF] bayesiandeeplearning.org

[PDF] Semi-Supervised Pairing via Basis-Sharing Wasserstein Matching Auto-Encoder

Z Liu, YHH Tsai, M Yamada, R Salakhutdinov - bayesiandeeplearning.org

Semi-supervised pairing, learning explicit pairing relation between unlabeled input and

target distribution in an otherwise semisupervised setting, has recently attracted lots of

attention [16, 12], since data labeling is often time-consuming and requires lots of human …

2018 [PDF] archives-ouvertes.fr

Large Deviations for a matching problem related to the -Wasserstein distance

J Trashorras - ALEA: Latin American Journal of Probability …, 2018 - hal.archives-ouvertes.fr

Let $(E, d) $ be a compact metric space, $ X=(X_1,\dots, X_n,\dots) $ and $ Y=(Y_1,\dots,

Y_n,\dots) $ two independent sequences of independent $ E $-valued random variables

and $(L^ X_n) _ {n\geq 1} $ and $(L^ Y_n) _ {n\geq 1} $ the associated sequences of …

Scene classification using hierarchical Wasserstein CNN

2018

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

In multiclass classification, convolutional neural network (CNN) is generally coupled with the

cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a

ground truth class and ignores the interclass relationship. We argue that CNN can be …

2018

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

2018

Motion-blind blur removal for CT images with Wasserstein generative adversarial networks

Y Lyu, W Jiang, Y Lin, L Voros, M Zhang… - … Congress on Image …, 2018 - ieeexplore.ieee.org

Advanced deblurring techniques for computed tomography (CT) images are necessary and

crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup

and treatment response assessment in radiation oncology. Currently, medical image …

Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

2018 [PDF] arxiv.org

M Zhang, Q Ma, C Wen, H Chen, D Liu, X Gu… - arXiv preprint arXiv …, 2018 - arxiv.org

Lung nodules are commonly detected in screening for patients with a risk for lung cancer.

Though the status of large nodules can be easily diagnosed by fine needle biopsy or

bronchoscopy, small nodules are often difficult to classify on computed tomography (CT) …

Cross-lingual document retrieval using regularized Wasserstein distance

G Balikas, C Laclau, I Redko, MR Amini - European Conference on …, 2018 - Springer

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

Cross-Lingual Document Retrieval Using Regularized Wasserstein Distance

MR Amini - Advances in Information Retrieval: 40th European …, 2018 - books.google.com

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word

Mover's Distance was proposed to measure the divergence between text passages. In this …

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. In this context, an important question is the …

2018 [PDF] arxiv.org

Differential properties of sinkhorn approximation for learning with wasserstein distance

G Luise, A Rudi, M Pontil, C Ciliberto - arXiv preprint arXiv:1805.11897, 2018 - arxiv.org

Applications of optimal transport have recently gained remarkable attention thanks to the

computational advantages of entropic regularization. However, in most situations the

Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version …

<——2018—-— 2018———1540—

2018

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

This paper is concerned with the statistical analysis of datasets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the principal component analysis (PCA) of histograms with …

Statistical properties of barycenters in the Wasserstein space and fast algorithms for optimal transport of measures

E Cazelles - 2018 - theses.fr

Résumé Cette thèse se concentre sur l'analyse de données présentées sous forme de

mesures de probabilité sur R^ d. L'objectif est alors de fournir une meilleure compréhension

des outils statistiques usuels sur cet espace muni de la distance de Wasserstein. Une …

LEARNING WASSERSTEIN EMBEDDINGS - OpenReview

2018

https://openreview.net › pdf

https://openreview.net › pdfPDF

by N Courty · 2018 · Cited by 34 — This choice is motivated by the fact that the Wasserstein metric operates on probability distributions. 3.2 WASSERSTEIN DATA MINING IN THE EMBEDDED SPACE. Once ...

2018

[HTML] Wasserstein discriminant analysis

R Flamary, M Cuturi, N Courty, A Rakotomamonjy - Machine Learning, 2018 - Springer

Wasserstein discriminant analysis (WDA) is a new supervised linear dimensionality

reduction algorithm. Following the blueprint of classical Fisher Discriminant Analysis, WDA

selects the projection matrix that maximizes the ratio of the dispersion of projected points …

[CITATION] A., Rakotomamonjy. Wasserstein discriminant analysis

R Flamary, M Cuturi, N Courty - arXiv preprint arXiv:1608.08063, 2016

Inference for empirical Wasserstein distances on finite spaces Series B Statistical methodology

M Sommerfeld, A Munk - 2018 - pubag.nal.usda.gov

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of …

2018

2018 [PDF] arxiv.org

Improving the improved training of wasserstein gans: A consistency term and its dual effect

X Wei, B Gong, Z Liu, W Lu, L Wang - arXiv preprint arXiv:1803.01541, 2018 - arxiv.org

Despite being impactful on a variety of problems and applications, the generative

adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed

by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the …

2018 [PDF] arxiv.org

Dialogwae: Multimodal response generation with conditional wasserstein auto-encoder

X Gu, K Cho, JW Ha, S Kim - arXiv preprint arXiv:1805.12352, 2018 - arxiv.org

Variational autoencoders~(VAEs) have shown a promise in data-driven conversation

modeling. However, most VAE conversation models match the approximate posterior

distribution over the latent variables to a simple prior such as standard normal distribution …

2018 [PDF] mlr.press

çƒ√functional estimation and distribution estimation under wasserstein distance

Y Han, J Jiao, T Weissman - Conference On Learning …, 2018 - proceedings.mlr.press

Abstract We present\emph {Local Moment Matching (LMM)}, a unified methodology for

symmetric functional estimation and distribution estimation under Wasserstein distance. We

construct an efficiently computable estimator that achieves the minimax rates in estimating …

2018 [PDF] arxiv.org

Towards high resolution video generation with progressive growing of sliced wasserstein gans

D Acharya, Z Huang, DP Paudel, L Van Gool - arXiv preprint arXiv …, 2018 - arxiv.org

The extension of image generation to video generation turns out to be a very difficult task,

since the temporal dimension of videos introduces an extra challenge during the generation

process. Besides, due to the limitation of memory and training stability, the generation …

Non-local texture optimization with wasserstein regularization under convolutional neural network

J Li, Y Xiang, J Hou, D Xu - IEEE Transactions on Multimedia, 2018 - ieeexplore.ieee.org

Example-based texture synthesis aims to generate a new texture from an exemplar texture

and has long been drawing attention in the fields of computer graphics, computer vision, and

image processing. Nevertheless, synthesizing structured textures remains a challenging …

<——2018—-— 2018———1550—

2018 [PDF] eg.org

Diagnosis of Schizophrenia Disorder Using Wasserstein Based Active Contour and Texture Features

M Latha, G Kavitha - Computational Signal Processing and Analysis, 2018 - Springer

Magnetic resonance (MR) brain images have a significant role in diagnosis of many

neuropsychiatric disorders such as Schizophrenia (SZ). In this work, Wasserstein-based

active contour and the texture features such as Hu moments and gray-level co-occurrence …

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

2018

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

This paper is concerned with the statistical analysis of datasets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we

consider the issue of computing the principal component analysis (PCA) of histograms with …

2018

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

2018 [PDF] arxiv.org

Wasserstein Soft Label Propagation on Hypergraphs: Algorithm and Generalization Error Bounds

T Gao, S Asoodeh, Y Huang, J Evans - arXiv preprint arXiv:1809.01833, 2018 - arxiv.org

Inspired by recent interests of developing machine learning and data mining algorithms on

hypergraphs, we investigate in this paper the semi-supervised learning algorithm of

propagating" soft labels"(eg probability distributions, class membership scores) over …

Perturbation theory for Markov chains via Wasserstein distance

2018 [PDF] arxiv.org

D Rudolf, N Schweizer - Bernoulli, 2018 - projecteuclid.org

Perturbation theory for Markov chains addresses the question of how small differences in the

transition probabilities of Markov chains are reflected in differences between their

distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step …

2018

2018 [PDF] arxiv.org

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

2018 [PDF] arxiv.org

Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

We provide an exact deterministic reformulation for data-driven chance constrained

programs over Wasserstein balls. For individual chance constraints as well as joint chance

constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer …

[HTML] Wasserstein barycenters over Riemannian manifolds

YH Kim, B Pass - Advances in Mathematics, 2017 - Elsevier

We study barycenters in the space of probability measures on a Riemannian manifold,

equipped with the Wasserstein metric. Under reasonable assumptions, we establish

absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on Wasserstein …

Distributed computation of Wasserstein barycenters over networks

CA Uribe, D Dvinskikh, P Dvurechensky… - … IEEE Conference on …, 2018 - ieeexplore.ieee.org

We propose a new class-optimal algorithm for the distributed computation of Wasserstein

Barycenters over networks. Assuming that each node in a graph has a probability

distribution, we prove that every node reaches the barycenter of all distributions held in the …

2018 see 2017 Full View

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu… - IET Generation …, 2018 - ieeexplore.ieee.org

In order to address the wind power uncertainty in the security constrained economic

dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve

and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

<——2018—-— 2018———1560—

[PDF] oregonstate.edu

Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

J McClelland - 2018 - ir.library.oregonstate.edu

Microbial ecology has been transformed by metagenomics, the study of the genetic in-

formation in entire communities of organisms. In the following we develop metagenomic

tools arising from the classic Wasserstein metric as applied to questions regarding the …

2018

WGAN model method based on depth convolution nerve network 14 citations*

Zhou Zhiheng ,Li Lijun Convolution Network modelView More (9+)

The invention discloses a WGAN model method based on a depth convolution nerve network, and belongs to the deep learning nerve network field; the method comprises the following steps: S1, forming a Wasserstein generative confrontation network WGAN model; S2, forming a discriminator with the depth co... View Full Abstract

2018

WGAN method based on text generation 12 citations*

Zhou Zhiheng ,Li Lijun Deep learning Test dataView More (9+)

The invention, which belongs to the field of the deep learning neural network, discloses a WGAN method based on text generation. The method comprises the following steps: S1, constructing a Wasserstein generative WGAN model; S2, preparing a text data set for training; S3, coding the test data by usi... View Full Abstract

2018

Fuzzy-detection seed set generation method and generator based on WGAN (Wasserstein GAN) model

5 citations*

Ji Shouling ,Lyu Chenyang ,Chen Jianhai ,Li Yuwei Generator (mathematics)Set (abstract data type)View More (8+)

The invention discloses a fuzzy-detection seed set generator based on a WGAN (Wasserstein GAN) model.

The generator includes: a training set acquisition module, which has a fuzzy-detection tool basedon a mutation algorithm, uses normal input as seeds to detect a plurality of programs with the same i... View Full Abstract

A Method to Accelerate the Training of WGAN

2018 INTERNATIONAL CONFERENCE ON INFORMATION SCIENCE AND CONTROL ENGINEERING

Qi Sun ¹,Wei Wang ²

¹ Chinese Academy of Sciences ,² Technol. & Eng. Center for space utilization, Beijing, ChinaDiscriminator Data modeling

View More (9+)

Generative adversarial network draw much attention in recent years because of its impressive results.

The idea of adversary was cleverly introduced to the training of the network. And the result was used in the value function to evaluate the quality of the network. During the adversarial process, th... View Full Abstract

2018

Image channel fusion method based on WGAN model

Robustness (computer science)

Zhou Zhiheng ,Li Lijun

Communication channel

View More (9+)

The invention discloses an image channel fusion method based on a WGAN model, and belongs to the fields of deep learning and neural networks. The method comprises the following steps: S1, constructingan original generative adversarial network (GAN) model; S2, constructing Wasserstein distance to use... View Full Abstract

2018 see 2015

Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

707 citations* for all

684 citations*

2018 MATHEMATICAL PROGRAMMING

Peyman Mohajerin Esfahani ¹,Daniel Kuhn ²

¹ Delft University of Technology ,² École Polytechnique Fédérale de Lausanne

Wasserstein Distance Guided Representation Learning for Domain Adaptation.

Stochastic programming

View More (8+)

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on... View Full Abstract
Cited by 711 Related articles All 17 versions

2018 see 2017

307 citations* for all

284 citations*

2018 NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE

Jian Shen ,Yanru Qu ,Weinan Zhang ,Yong Yu

Shanghai Jiao Tong University

Domain (software engineering)

Feature learning

View More (9+)

Gromov-Wasserstein Alignment of Word Embedding Spaces.

2018 ARXIV: COMPUTATION AND LANGUAGE

Unsupervised Alignment of Embeddings with Wasserstein Procrustes

103 citations* for all

81 citations*

2019 INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS

Edouard Grave ¹,Armand Joulin ¹,Quentin Berthet ²

¹ Facebook ,² University of Cambridge

Permutation matrix

Word (computer architecture)

View More (8+)

We consider the task of aligning two sets of points in high dimension, which has many applications i

n natural language processing and computer vision. As an example, it was recently shown that it is possible

to infer a bilingual lexicon, without supervised data, by aligning word embeddings trained o... View Full Abstract

Gromov-Wasserstein alignment of word embedding spaces
Cited by 172 Related articles All 6 versions

Unsupervised Alignment of Embeddings with Wasserstein Procrustes

Generative Modeling Using the Sliced Wasserstein Distance

2018 ARXIV: LEARNING

99 citations* for all

81 citations*

2018 COMPUTER VISION AND PATTERN RECOGNITION

Ishan Deshpande ¹,Ziyu Zhang ²,Alexander Schwing ¹

¹ University of Illinois at Urbana–Champaign ,² [Snap Inc., Los Angeles]

Stability (probability)

View More (9+)

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is particularly true for early GAN formulations, there has been sig... View Full Abstract

Generative modeling using the sliced wasserstein distance

I Deshpande, Z Zhang… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Abstract Generative Adversarial Nets (GANs) are very successful at modeling distributions

from given samples, even in the high-dimensional case. However, their formulation is also

known to be hard to optimize and often not stable. While this is particularly true for early GAN …

<——2018—-— 2018———1570—

Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation using Holistic Convolutional Networks

61 citations*

2017 ARXIV: COMPUTER VISION AND PATTERN RECOGNITION

Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation Using Holistic Convolutional Networks

13 citations*

2017 INTERNATIONAL MICCAI BRAINLESION WORKSHOP

Visual Feature Attribution Using Wasserstein GANs

70 citations*

2018 COMPUTER VISION AND PATTERN RECOGNITION

Christian F. Baumgartner ,Lisa M. Koch ,Kerem Can Tezcan ,Jia Xi Ang

ETH Zurich

Feature (computer vision)

Artificial neural network

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DialogWAE: Multimodal Response Generation with Conditional Wasserstein Auto-Encoder

75 citations* for all

54 citations*

2018 INTERNATIONAL CONFERENCE ON LEARNING REPRESENTATIONS

Xiaodong Gu ¹,Kyunghyun Cho ¹,Jung Woo Ha ²,Sunghun Kim ¹

¹ Hong Kong University of Science and Technology ,² NAVER

Latent variable

Posterior probability

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Variational autoencoders~(VAEs) have shown a promise in data-driven conversation modeling.

However, most VAE conversation models match the approximate posterior distribution over

the latent variables to a simple prior such as standard normal distribution, thereby restricting

the generated responses ... View Full Abstract

Approximate inference with Wasserstein gradient flows

2018 ARXIV: MACHINE LEARNING

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

135 citations* for all

94 citations*

2018 INTERNATIONAL CONFERENCE ON LEARNING REPRESENTATIONS

Xiang Wei ,Boqing Gong ¹,Zixia Liu ²,Wei Lu ³,Liqiang Wang ⁴

¹ Tencent ,² University of Wyoming ,³ Beijing Jiaotong University ,⁴ University of Central Florida

Lipschitz continuity

Term (time)

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Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by \cite{arjovsky2017towards}, who also propose an alternative direction to avoid the caveats in the minmax two-player training... View Full Abstract

Wasserstein Soft Label Propagation on Hypergraphs: Algorithm and Generalization Error Bounds

T Gao, S Asoodeh, Y Huang, J Evans - arXiv preprint arXiv:1809.01833, 2018 - arxiv.org

… We will see that in this case, hypergraph label propagation can be cast into a Wasserstein … With this notation, it becomes easy to write down the Euler-Lagrange equation of the …

2018

(PDF) Generalised Wasserstein Dice Score for Imbalanced ...

https://www.researchgate.net › ... › Segmentation

PDF | The Dice score is widely used for binary segmentation due to its ... for Imbalanced Multi-class Segmentation Using Holistic Convolutional Networks.

[CITATION] Generalised Wasserstein dice score for imbalanced multi-class segmentation using holistic convolutional networks. ArXiv170700478 Cs 10670: 64–76

L Fidon, W Li, LC Garcia-Peraza-Herrera, J Ekanayake… - 2018

Generative modeling using the sliced wasserstein distance

2018

2018 [PDF] thecvf.com

I Deshpande, Z Zhang… - Proceedings of the IEEE …, 2018 - openaccess.thecvf.com

Abstract Generative Adversarial Nets (GANs) are very successful at modeling distributions

from given samples, even in the high-dimensional case. However, their formulation is also

known to be hard to optimize and often not stable. While this is particularly true for early GAN …

2018 see 2017 [PDF] arxiv.org

Improving the improved training of wasserstein gans: A consistency term and its dual effect

X Wei, B Gong, Z Liu, W Lu, L Wang - arXiv preprint arXiv:1803.01541, 2018 - arxiv.org

Despite being impactful on a variety of problems and applications, the generative

adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed

by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the …

Distilled wasserstein learning for word embedding and topic modeling

H Xu, W Wang, W Liu, L Carin - arXiv preprint arXiv:1809.04705, 2018 - arxiv.org

We propose a novel Wasserstein method with a distillation mechanism, yielding joint

learning of word embeddings and topics. The proposed method is based on the fact that the

2018

Wasserstein stationary subspace analysis

S Kaltenstadler, S Nakajima, KR Müller… - IEEE Journal of …, 2018 - ieeexplore.ieee.org

Learning under nonstationarity can be achieved by decomposing the data into a subspace

that is stationary and a nonstationary one [stationary subspace analysis (SSA)]. While SSA

has been used in various applications, its robustness and computational efficiency have …

[CITATION] … York, Again: Another foreign bank with US aspirations, Schroders Plc, finds itself casting about for direction stateside, having held talks with Wasserstein …

E Copulsky - INVESTMENT DEALERS DIGEST, 1999

2018 [PDF] arxiv.org

Gromov-Wasserstein alignment of word embedding spaces

D Alvarez-Melis, TS Jaakkola - arXiv preprint arXiv:1809.00013, 2018 - arxiv.org

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from

machine translation to transfer learning. Recently, purely unsupervised methods operating

on monolingual embeddings have become effective alignment tools. Current state-of-the-art …

2018 [PDF] oregonstate.edu

Wasserstein β-Diversity Metrics over Graphs: Derivation, Efficient Computation and Applications

J McClelland - 2018 - ir.library.oregonstate.edu

Microbial ecology has been transformed by metagenomics, the study of the genetic in-

formation in entire communities of organisms. In the following we develop metagenomic

tools arising from the classic Wasserstein metric as applied to questions regarding the …

<——2018—-— 2018———1580—

2018 [PDF] arxiv.org

Anomaly detection with Wasserstein GAN

I Haloui, JS Gupta, V Feuillard - arXiv preprint arXiv:1812.02463, 2018 - arxiv.org

Generative adversarial networks are a class of generative algorithms that have been widely

used to produce state-of-the-art samples. In this paper, we investigate GAN to perform

anomaly detection on time series dataset. In order to achieve this goal, a bibliography is …

2018

A PAM method for computing Wasserstein barycenter with unknown supports in D2-clustering

Y Qian, S Pan - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

A Wasserstein barycenter is the centroid of a collection of discrete probability distributions

that minimizes the average of the $\ell_2 $-Wasserstein distance. This paper concerns with

the computation of a Wasserstein barycenter under the case where the support points are …

PDF] arxiv.org

W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

S Li, XD Li - Science China Mathematics, 2018 - Springer

… the potential flow of the incompressible Euler equation with damping on (M,g). More precisely, if we let u = Vf, then (ρ, u) satisfies the incompressible Euler equation with damping …

2018

Approximate inference with Wasserstein gradient flows

2018 ARXIV: MACHINE LEARNING

{ Euclidean, Metric, and Wasserstein } Gradient Flows: an overview

113 citations* for all

111 citations*

2017 BULLETIN OF MATHEMATICAL SCIENCES

Filippo Santambrogio

Université Paris-Saclay

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

Intrinsic metric

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January 2018

Jérémie Bigot, Raúl Gouet, Thierry Klein, Alfredo López

Electronic Journal of Statistics Vol. 12, Issue 2 (Jan 2018), pg(s) 2253-2289

KEYWORDS: barycenter of probability measures, density registration, Fréchet mean, Functional data analysis, Minimax optimality, phase and amplitude variability, smoothing, Wasserstein space

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

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2018

1 November 2018 see 2017

Pedro C. Álvarez-Esteban, Eustasio del Barrio, Juan A. Cuesta-Albertos, Carlos Matrán

Bernoulli Vol. 24, Issue 4A (Nov 2018), pg(s) 3147-3179

KEYWORDS: impartial trimming, parallelized inference, robust aggregation, trimmed barycenter, trimmed distributions, Wasserstein distance, wide consensus

Stochastic Wasserstein Barycenters

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2018 see 2017

17 citations*

2018 ARXIV: LEARNING

Stochastic wasserstein barycenters

S Claici, E Chien, J Solomon - International Conference on …, 2018 - proceedings.mlr.press

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of …

2018

Wasserstein Proximal of GANs

18 citations* for all

2018 INTERNATIONAL CONFERENCE ON GEOMETRIC SCIENCE OF INFORMATION

Alex Tong Lin ¹,Wuchen Li ²,Stanley J. Osher ¹,Guido Montúfar ^1,3

¹ University of California, Los Angeles ,² University of South Carolina ,³ Max Planck Society

Distributionally Robust Chance-Constrained Approximate AC-OPF With Wasserstein Metric

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We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant natural gradient by pulling back optimal transport structures from... View Full Abstract

2018 see 2017

2018 IEEE TRANSACTIONS ON POWER SYSTEMS

86 citations*

Chao Duan ¹,Wanliang Fang ¹,Lin Jiang ²,Li Yao ¹,Jun Liu ¹

¹ Xi'an Jiaotong University ,² University of Liverpool

View More (8+)

Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate ac-OPF. The power flow model employed ... View Full Abstract

EXCERPTS (29)

Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In the presence of

VRE uncertainties, this paper discusses a distributionally robust chance constrained …

2018

Statistical Aspects of Wasserstein Distances.

Inference for empirical Wasserstein distances on finite spaces

2018 ARXIV: METHODOLOGY

89 citations* for all

78 citations*

2018 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY

Max Sommerfeld ¹,Axel Munk ^1,2

¹ University of Göttingen ,² Max Planck Society

Statistical inference

Statistical hypothesis testing

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Summary The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the Cited Cited by 222 Related articles All 7 versions

<——2018—-— 2018———1590—

Precise simulation of electromagnetic calorimeter showers using a Wasserstein Generative Adversarial Network

2018 ARXIV: INSTRUMENTATION AND DETECTORS

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

61 citations* for all

60 citations*

2018 COMPUTING AND SOFTWARE FOR BIG SCIENCE

Martin Erdmann ,Lukas Geiger ,Jonas Glombitza ,David Schmidt

RWTH Aachen University

Detector

Particle detector

View More (8+)

We use adversarial network architectures together with the Wasserstein distance to generate or refine simulated detector data. The data reflect two-dimensional projections of spatially distributed signal patterns with a broad spectrum of applications. As an example, we use an observatory to detect c... View Full Abstract

2018

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks.

2018 ARXIV: INSTRUMENTATION AND METHODS FOR ASTROPHYSICS

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

19 citations* for all

Estimation of covariance matrices

2021 OPERATIONS RESEARCH

Viet Anh Nguyen ¹,Daniel Kuhn ²,Peyman Mohajerin Esfahani ³

¹ Stanford University ,² École Polytechnique Fédérale de Lausanne ,³ Delft University of Technology

Shrinkage estimator

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Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depen...

2018

Banach Wasserstein GAN

35 citations*

2018 ARXIV: COMPUTER VISION AND PATTERN RECOGNITION

On the Bures–Wasserstein distance between positive definite matrices

105 citations* for all

102 citations*

2018 EXPOSITIONES MATHEMATICAE

Rajendra Bhatia ¹,Tanvi Jain ²,Yongdo Lim ³

¹ Ashoka University ,² Indian Statistical Institute ,³ Sungkyunkwan University

Riemannian geometry

C Cited by 152 Related articles All 11 versions

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Abstract The metric d ( A , B ) = tr A + tr B − 2 tr ( A 1 ∕ 2 B A 1 ∕ 2 ) 1 ∕ 2 1 ∕ 2 on the manifold of n × n positive definite matrices arises in various optimisation problems, in quantum information and in the the... View Full Abstract

2018

Minimax Statistical Learning with Wasserstein distances

85 citations* for all

69 citations*

2018 NEURAL INFORMATION PROCESSING SYSTEMS

Jaeho Lee ,Maxim Raginsky

University of Illinois at Urbana–Champaign

Empirical risk minimization

Minimax

View More (9+)

2018

Stochastic Wasserstein Barycenters

17 citations*

2018 ARXIV: LEARNING

Deep Variational Network Embedding in Wasserstein Space

78 citations*

2018 KNOWLEDGE DISCOVERY AND DATA MINING

Dingyuan Zhu ,Peng Cui ,Daixin Wang ,Wenwu Zhu

Tsinghua University

Node (networking)

Embedding

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2018

Uncoupled isotonic regression via minimum Wasserstein deconvolution

9 citations*

2018 ARXIV: STATISTICS THEORY

Isotonic regression

Upper and lower bounds

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Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$. While this problem is well understood both statistically and com... View Full Abstract

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

PC Alvarez-Esteban, E del Barrio, JA Cuesta-Albertos… - Bernoulli, 2018 - projecteuclid.org

We introduce a general theory for a consensus-based combination of estimations of

probability measures. Potential applications include parallelized or distributed sampling

schemes as well as variations on aggregation from resampling techniques like boosting or …

2018 [PDF] arxiv.org

Wasserstein riemannian geometry of positive definite matrices

L Malago, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a

Riemannian distance. After reviewing the properties of the distance and the metric geodesic,

we present an explicit form of the Riemannian metrics on positive-definite matrices and …

Comparison between W2 distance and Ḣ− 1 norm, and localization of wasserstein distance

R Peyre - ESAIM: Control, Optimisation and Calculus of …, 2018 - esaim-cocv.org

It is well known that the quadratic Wasserstein distance W 2 (⋅,⋅) is formally equivalent, for

infinitesimally small perturbations, to some weighted H− 1 homogeneous Sobolev norm. In

this article I show that this equivalence can be integrated to get non-asymptotic comparison …

2018

Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning

MA Schmitz, M Heitz, N Bonneel, F Ngole… - SIAM Journal on Imaging …, 2018 - SIAM

This paper introduces a new nonlinear dictionary learning method for histograms in the

probability simplex. The method leverages optimal transport theory, in the sense that our aim

is to reconstruct histograms using so-called displacement interpolations (aka Wasserstein …

[CITATION] Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning MA

SCHMITZ

M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY…

<——2018—-— 2018———1600—

2018 [PDF] arxiv.org

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

2018 [PDF] psu.edu

Geometry-sensitive ensemble mean based on Wasserstein barycenters: Proof-of-concept on cloud simulations

J Li, F Zhang - Journal of Computational and Graphical Statistics, 2018 - Taylor & Francis

An ensemble of forecasts generated by different model simulations provides rich information

for meteorologists about impending weather such as precipitating clouds. One major form of

forecasts presents cloud images created by multiple ensemble members. Common features …

2018 [PDF] arxiv.org

Learning to optimize via wasserstein deep inverse optimal control

Y Wang, L Song, H Zha - arXiv preprint arXiv:1805.08395, 2018 - arxiv.org

We study the inverse optimal control problem in social sciences: we aim at learning a user's

true cost function from the observed temporal behavior. In contrast to traditional

phenomenological works that aim to learn a generative model to fit the behavioral data, we …

On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests

162 citations*

2017 ENTROPY

Aaditya Ramdas ,Nicolás García Trillos ,Marco Cuturi

Nonparametric statistics

Univariate

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2018 see 2016

Wasserstein Divergence for GANs

2017 ARXIV: COMPUTER VISION AND PATTERN RECOGNITION

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

2018 SIAM JOURNAL ON IMAGING SCIENCES

82 citations*

Morgan A. Schmitz ¹,Matthieu Heitz ²,Nicolas Bonneel ²,Fred Maurice Ngolè Mboula ³,David Coeurjolly ² see all 8 authors

¹ Institut de Recherches sur les lois Fondamentales de l'Univers,² Geometry Processing and Constrained Optimization,³ Laboratoire d'analyse des données et d'intelligence des systèmes

Smoothing

Regularization (mathematics)

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2018

2018 see 2017

Wasserstein Divergence for GANs

60 citations* for all

59 citations*

2018 EUROPEAN CONFERENCE ON COMPUTER VISION

Jiqing Wu ,Zhiwu Huang ,Janine Thoma ,Dinesh Acharya ,Luc Van Gool

ETH Zurich

Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

View More (6+)

707 citations* for all

684 citations*

2018 MATHEMATICAL PROGRAMMING

Peyman Mohajerin Esfahani ¹,Daniel Kuhn ²

¹ Delft University of Technology ,² École Polytechnique Fédérale de Lausanne

Wasserstein Geometry of Quantum States and Optimal Transport of Matrix-Valued Measures

Stochastic programming

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2018

12 citations*

2018

Yongxin Chen ¹,Tryphon T. Georgiou ²,Allen Tannenbaum ³

¹ Iowa State University ,² University of California ,³ Stony Brook University

Hermitian matrix

Quantum state

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2018

Wasserstein Riemannian geometry of Gaussian densities

27 citations*

2018 INFORMATION GEOMETRY

Luigi Malagò ¹,Luigi Montrucchio ²,Giovanni Pistone ²

¹ Romanian Institute of Science and Technology, RIST, Cluj-Napoca, Romania,² Collegio Carlo Alberto

Riemannian geometry

Information geometry

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The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we present an explicit form of the Riemannian metrics on positive-definite matrices and compute its tensor form with respect to... View Full Abstract

2018

Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

2018

Hamza Farooq ¹,Yongxin Chen ²,Tryphon Georgiou ³,Christophe Lenglet ¹

¹ University of Minnesota ,² Memorial Sloan Kettering Cancer Center ,³ University of California, Irvine

Human Connectome Project

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Several studies have used structural connectivity information to parcellate brain areas like the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult to achieve using conventional MRI techniques. They typically employ diffusion MRI (dMRI) tractography and compare... View Full Abstract

<——2018—-— 2018———1610—

Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls

GA Hanasusanto, D Kuhn - Operations Research, 2018 - pubsonline.informs.org

Adaptive robust optimization problems are usually solved approximately by restricting the

adaptive decisions to simple parametric decision rules. However, the corresponding

approximation error can be substantial. In this paper we show that two-stage robust and …

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

We propose in this paper a construction of a diffusion process on the space $\mathcal P_2

(\mathbb R) $ of probability measures with a second-order moment. This process was

introduced in several papers by Konarovskyi (see eg [12]) and consists of the limit as $ N …

2018

On isometric embeddings of Wasserstein spaces--the discrete case

G Pál Gehér, T Titkos, D Virosztek - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

The aim of this short paper is to offer a complete characterization of all (not necessarily

surjective) isometric embeddings of the Wasserstein space $\mathcal {W} _p (\mathcal {X})

$, where $\mathcal {X} $ is a countable discrete metric space and $0< p<\infty $ is any …

Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks

M Erdmann, L Geiger, J Glombitza… - Computing and Software …, 2018 - Springer

We use adversarial network architectures together with the Wasserstein distance to

generate or refine simulated detector data. The data reflect two-dimensional projections of

spatially distributed signal patterns with a broad spectrum of applications. As an example …

2018

Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

H Farooq, Y Chen, T Georgiou, C Lenglet - Computational Diffusion MRI, 2018 - Springer

Several studies have used structural connectivity information to parcellate brain areas like

the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult

to achieve using conventional MRI techniques. They typically employ diffusion MRI (dMRI) …

2018

Sparse-view CT reconstruction using wasserstein GANs

F Thaler, K Hammernik, C Payer, M Urschler… - … image reconstruction, 2018 - Springer

We propose a 2D computed tomography (CT) slice image reconstruction method from a

limited number of projection images using Wasserstein generative adversarial networks

(wGAN). Our wGAN optimizes the 2D CT image reconstruction by utilizing an adversarial …

2018

Scene classification using hierarchical Wasserstein CNN

Y Liu, CY Suen, Y Liu, L Ding - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

In multiclass classification, convolutional neural network (CNN) is generally coupled with the

cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a

ground truth class and ignores the interclass relationship. We argue that CNN can be …

2018

Scene classification by coupling convolutional neural networks with Wasserstein distance

Y Liu, Y Liu, L Ding - IEEE Geoscience and Remote Sensing …, 2018 - ieeexplore.ieee.org

The traditional convolutional neural networks (CNNs) coupled with cross-entropy loss ignore

interclass relationship, and hence output unreasonable predictions from a holistic

perspective. We address this issue by integrating CNNs with Wasserstein distance (WD) …

2018 [PDF] sjtu.edu.cn

EEG data augmentation for emotion recognition using a conditional Wasserstein GAN

Y Luo, BL Lu - 2018 40th Annual International Conference of …, 2018 - ieeexplore.ieee.org

Due to the lack of electroencephalography (EEG) data, it is hard to build an emotion

recognition model with high accuracy from EEG signals using machine learning approach.

Inspired by generative adversarial networks (GANs), we introduce a Conditional …

[CITATION] EEG Data Augmentation for Emotion Recognition Using a Conditional Wasserstein GAN.[J]

L Yun, L Bao-Liang - … proceedings:... Annual International Conference of the …, 2018

Wasserstein gan and waveform loss-based acoustic model training for multi-speaker text-to-speech synthesis systems using a wavenet vocoder

2018 [PDF] ieee.org

Y Zhao, S Takaki, HT Luong, J Yamagishi… - IEEE …, 2018 - ieeexplore.ieee.org

WaveNet, which learns directly from speech waveform samples, has been used as an

alternative to vocoders and achieved very high-quality synthetic speech in terms of both

naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems …

<——2018—-— 2018———1620—

2018 [PDF] tse-fr.eu

[PDF] Lifted and geometric differentiability of the squared quadratic Wasserstein distance

A Alfonsi, B Jourdain - arXiv preprint arXiv:1811.07787, 2018 - tse-fr.eu

In this paper, we remark that any optimal coupling for the quadratic Wasserstein distance W2

2 (µ, ν) between two probability measures µ and ν with finite second order moments on Rd is

the composition of a martingale coupling with an optimal transport map T. We check the …

Wasserstein stationary subspace analysis

2018 [PDF] jmlr.org

[PDF] Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - jmlr.org

Divide-and-conquer based methods for Bayesian inference provide a general approach for

tractable posterior inference when the sample size is large. These methods divide the data

into smaller subsets, sample from the posterior distribution of parameters in parallel on all …

S Kaltenstadler, S Nakajima, KR Müller… - IEEE Journal of …, 2018 - ieeexplore.ieee.org

Learning under nonstationarity can be achieved by decomposing the data into a subspace

that is stationary and a nonstationary one [stationary subspace analysis (SSA)]. While SSA

has been used in various applications, its robustness and computational efficiency have …

2018

Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approach

21 citations*

2018 ARXIV: OPTIMIZATION AND CONTROL

node2coords: Graph Representation Learning with Wasserstein Barycenters

2 citations* for all

2021 IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS

Effrosyni Simou ,Dorina Thanou ,Pascal Frossard

École Polytechnique Fédérale de Lausanne

Graph (abstract data type)

Node (networking)

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In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods learn representations that cannot be interpreted in a straightforward way and that are relatively unstable to perturbations of the graph... View Full Abstract

2018

Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces

2018 ARXIV: STATISTICS THEORY

Wasserstein Index Generation Model: Automatic generation of time-series index with application to Economic Policy Uncertainty

1 citations* for all

New York University Wasserstein Index Generation Model: Automatic Generation of Time-series Index with Application to Economic Policy

2020 ECONOMICS LETTERS

Fangzhou Xie

Index (economics)

Series (mathematics)

View More (3+)

Abstract I propose a novel method, the Wasserstein Index Generation model (WIG), to generate a public sentiment index automatically. To test the model’s effectiveness, an application to generate Economic Policy Uncertainty (EPU) index is showcased.

2018

Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces

2018 ARXIV: STATISTICS THEORY

Wasserstein Index Generation Model: Automatic generation of time-series index with application to Economic Policy Uncertainty

1 citations* for all

New York University Wasserstein Index Generation Model: Automatic Generation of Time-series Index with Application to Economic Policy

2020 ECONOMICS LETTERS

Fangzhou Xie

Index (economics)

Series (mathematics)

View More (3+)

2018

The Gromov-Wasserstein distance between networks and stable network invariants

2018 ARXIV: DISCRETE MATHEMATICS

Gromov-Wasserstein Factorization Models for Graph Clustering

10 citations* for all

2020 NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE

Hongtengl Xu

Duke University

Clustering coefficient

Factorization

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We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters... View Full Abstract

2018

Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration

2018 ARXIV: METHODOLOGY

On the Wasserstein distance between classical sequences and the Lebesgue measure

7 citations* for all

6 citations*

2020 TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Louis Brown ,Stefan Steinerberger

Yale University

Nabla symbol

Lebesgue measure

View More (8+)

We discuss the classical problem of measuring the regularity of distribution of sets of $N$ points in $\mathbb{T}^d$. A recent line of investigation is to study the cost ($=$ mass $\times$ distance) necessary to move Dirac measures placed in these points to the uniform distribution. We show that Kro... View Full Abstract

2018 [PDF] arxiv.org

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

Learning a generative model is a key component of model-based reinforcement learning.

Though learning a good model in the tabular setting is a simple task, learning a useful

model in the approximate setting is challenging. In this context, an important question is the …

2018 [PDF] nips.cc

[PDF] Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - … of the 32nd International Conference on …, 2018 - papers.nips.cc

Embedding complex objects as vectors in low dimensional spaces is a longstanding

problem in machine learning. We propose in this work an extension of that approach, which

consists in embedding objects as elliptical probability distributions, namely distributions …

2018 [PDF] mlr.press

Policy optimization as wasserstein gradient flows

R Zhang, C Chen, C Li, L Carin - … Conference on Machine …, 2018 - proceedings.mlr.press

Policy optimization is a core component of reinforcement learning (RL), and most existing

RL methods directly optimize parameters of a policy based on maximizing the expected total

reward, or its surrogate. Though often achieving encouraging empirical success, its …

<——2018—-— 2018———1630—

2018 [PDF] psu.edu

Geometry-sensitive ensemble mean based on Wasserstein barycenters: Proof-of-concept on cloud simulations

J Li, F Zhang - Journal of Computational and Graphical Statistics, 2018 - Taylor & Francis

An ensemble of forecasts generated by different model simulations provides rich information

for meteorologists about impending weather such as precipitating clouds. One major form of

forecasts presents cloud images created by multiple ensemble members. Common features …

2018 [PDF] openreview.net

Diffusing Policies: Towards Wasserstein Policy Gradient Flows

PH Richemond, B Maginnis - 2018 - openreview.net

Policy gradients methods often achieve better performance when the change in policy is

limited to a small Kullback-Leibler divergence. We derive policy gradients where the change

in policy is limited to a small Wasserstein distance (or trust region). This is done in the …

2018 [PDF] thecvf.com

Visual feature attribution using wasserstein gans

CF Baumgartner, LM Koch… - Proceedings of the …, 2018 - openaccess.thecvf.com

Attributing the pixels of an input image to a certain category is an important and well-studied

problem in computer vision, with applications ranging from weakly supervised localisation to

understanding hidden effects in the data. In recent years, approaches based on interpreting …

Unsupervised feature extraction in hyperspectral images based on wasserstein generative adversarial network

M Zhang, M Gong, Y Mao, J Li… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Feature extraction (FE) is a crucial research area in hyperspectral image (HSI) processing.

Recently, due to the powerful ability of deep learning (DL) to extract spatial and spectral

features, DL-based FE methods have shown great potentials for HSI processing. However …

2018

Unsupervised feature learning for outlier detection with stacked convolutional autoencoders, siamese networks and wasserstein autoencoders: application to epilepsy …

Z Alaverdyan, J Chai, C Lartizien - Deep Learning in Medical Image …, 2018 - Springer

In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric

(T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist

(MRI negative). We cast this problem as an outlier detection problem and adapt the …

2018

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

Mutual information based feature selection algorithms measure feature relevance by

comparing mutual information between features and class labels, however those features do

not necessarily lead to good feature selection and classification accuracy. For each feature …

2018

Regularizing Feature Distribution Using Sliced Wasserstein Distance for Semi-supervised Learning

J Kim, C Lee, J Kim - International Conference on Multi-disciplinary Trends …, 2018 - Springer

We propose a novel consistency based regularization method for semi-supervised image

classification, called feature distribution matching (FDM), which is designed to induce

smoothness of feature space by reducing sliced Wasserstein distance between feature …

year 2018

[PDF] Supplementary Material for: Visual Feature Attribution using Wasserstein GANs

CF Baumgartner, LM Koch, KC Tezcan, JX Ang - openaccess.thecvf.com

In this section we describe the exact network architectures used for the 3D VA-GAN. We

present the critic and map generator functions as Python-inspired pseudo code, which we

found easier to interpret than a graphical representation. The layer parameters are specified …

Wasserstein 거리를 이용한 feature selection - 한국정보과학회 ...

2018

... 인터넷정보학회논문지 · 한국인터넷정보학회; 2018. Wasserstein 생산적 적대 신경망과 구조적 유사지수를 이용한 저선량 컴퓨터 단층촬영 영상 잡음 제거 기법.

[CITATION] Wasserstein 거리를 이용한 feature selection

지종호， 신현정 - 한국정보과학회 학술발표논문집, 2018 - dbpia.co.kr

요 약그래프기반 준지도학습 (graph based semi-supervised learning) 은 그래프를 어떻게

만드냐에 따라 성능이 달라진다. 특히, 그래프의 엣지는 레코드 간 유사도로 생성되는데

유사도가 어떻게 정의되는가는 준지도학습의 성능에 상당한 영향을 미친다. 일반적으로 가장 …

Wasserstein cnn: Learning invariant features for nir-vis face recognition

2018

R He, X Wu, Z Sun, T Tan - IEEE transactions on pattern …, 2018 - ieeexplore.ieee.org

Heterogeneous face recognition (HFR) aims at matching facial images acquired from

different sensing modalities with mission-critical applications in forensics, security and

commercial sectors. However, HFR presents more challenging issues than traditional face …

Cross-lingual document retrieval using regularized Wasserstein distance

G Balikas, C Laclau, I Redko, MR Amini - European Conference on …, 2018 - Springer

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word …

Cite Cited by 12 Related articles All 5 versions

Cross-Lingual Document Retrieval Using Regularized Wasserstein Distance

MR Amini - Advances in Information Retrieval: 40th European …, 2018 - books.google.com

Many information retrieval algorithms rely on the notion of a good distance that allows to

efficiently compare objects of different nature. Recently, a new promising metric called Word …

Cite Related articles

<——2018—-— 2018———1640—

2018 [PDF] uni-muenster.de

[PDF] The Entropy-Regularized Wasserstein Distance as a Metric for Machine Learning Based Post-Processing of Structural MR Images of the Brain

J Braunsmann - 2018 - uni-muenster.de

This thesis treats the Wasserstein distance and its applicability as a metric between

magnetic resonance images of the brain, represented as densities on a voxel grid. We aim …

Cite Cited by 1 Related articles All 2 versions

[PDF] Regularized Wasserstein Means Based on Variational Transportation

L Mi, W Zhang, Y Wang - CoRR, 2018 - researchgate.net

We raise the problem of regularizing Wasserstein means and propose several terms tailored

to tackle different problems. Our formulation is based on the variational transportation to …

Cite Related articles All 2 versions

2018

Wasserstein variational inference

L Ambrogioni, U Güçlü, Y Güçlütürk, M Hinne… - arXiv preprint arXiv …, 2018 - arxiv.org

This paper introduces Wasserstein variational inference, a new form of approximate

Bayesian inference based on optimal transport theory. Wasserstein variational inference …

2018 [PDF] shichuan.org

Deep variational network embedding in wasserstein space

D Zhu, P Cui, D Wang, W Zhu - Proceedings of the 24th ACM SIGKDD …, 2018 - dl.acm.org

Network embedding, aiming to embed a network into a low dimensional vector space while

preserving the inherent structural properties of the network, has attracted considerable …

2018 [PDF] thecvf.com

Variational wasserstein clustering

L Mi, W Zhang, X Gu, Y Wang - Proceedings of the …, 2018 - openaccess.thecvf.com

We propose a new clustering method based on optimal transportation. We discuss the

connection between optimal transportation and k-means clustering, solve optimal …

2018 [PDF] arxiv.org

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

L Ambrogioni, U Guclu, M van Gerven - arXiv preprint arXiv:1811.02827, 2018 - arxiv.org

Particle-based variational inference offers a flexible way of approximating complex posterior

distributions with a set of particles. In this paper we introduce a new particle-based …

2018

2018 [PDF] wvu.edu

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

A Tudorascu - Calculus of Variations and Partial Differential …, 2008 - Springer

We prove the monotonicity of the second-order moments of the discrete approximations to

the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This …

2018

A Wasserstein GAN model with the total variational regularization

L Zhang, Y Zhang, Y Gao - arXiv preprint arXiv:1812.00810, 2018 - arxiv.org

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train.

The recently proposed Wasserstein GAN (WGAN) creates principled research directions …

2018 [PDF] researchgate.net

[PDF] Regularized Wasserstein Means Based on Variational Transportation

L Mi, W Zhang, Y Wang - CoRR, 2018 - researchgate.net

We raise the problem of regularizing Wasserstein means and propose several terms tailored

to tackle different problems. Our formulation is based on the variational transportation to …

2018 [PDF] core.ac.uk

[PDF] Shape Space in Terms of Wasserstein Geometry and Application to Quantum Physics

B Lessel - 2018 - core.ac.uk

The core idea of this thesis and its main motivation is a philosophical thought concerning the

description of nature. This idea, inspired by Mach's principle, says that it should be possible …

[BOOK] A Comparative Assessment of the Impact of Various Norms on Wasserstein Generative Adversarial Networks

2018 [PDF] rit.edu

C Ramesh - 2018 - search.proquest.com

Abstract Generative Adversarial Networks (GANs) provide a fascinating new paradigm in

machine learning and artificial intelligence, especially in the context of unsupervised …

-Wasserstein distances of tracial -algebras and their disintegration problem

<——2018—-— 2018———1650—

2018 [PDF] arxiv.org

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with …

2018 see 2015 [PDF] jmlr.org

[PDF] Scalable Bayes via barycenter in Wasserstein space

S Srivastava, C Li, DB Dunson - The Journal of Machine Learning …, 2018 - jmlr.org

Divide-and-conquer based methods for Bayesian inference provide a general approach for

tractable posterior inference when the sample size is large. These methods divide the data …

-Wasserstein distances of tracial -algebras and their disintegration problem

DF Hornshaw - arXiv preprint arXiv:1806.01073, 2018 - arxiv.org

We introduce $ L^{2} $-Wasserstein distances on densities of tracial $ W^{*} $-algebras

based on a Benamou-Brenier formulation, replacing multiplication by densities with …

Markov type constants, flat tori and Wasserstein spaces

V Zolotov - Geometriae Dedicata, 2018 - Springer

Abstract Let M_p (X, T) M p (X, T) denote the Markov type p constant at time T of a metric

space X, where p ≥ 1 p≥ 1. We show that M_p (Y, T) ≤ M_p (X, T) M p (Y, T)≤ M p (X, T) in …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PEC de Raynal, N Frikha - arXiv preprint arXiv:1811.06904, 2018 - arxiv.org

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under …

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

PE Chaudru de Raynal, N Frikha - arXiv e-prints, 2018 - ui.adsabs.harvard.edu

In this paper, we investigate the well-posedness of the martingale problem associated to

non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under …

The wasserstein distance as a dissimilarity measure for mass spectra with application to spectral deconvolution

2018

2018 [PDF] dagstuhl.de

S Majewski, MA Ciach, M Startek… - … on Algorithms in …, 2018 - drops.dagstuhl.de

We propose a new approach for the comparison of mass spectra using a metric known in the

computer science under the name of Earth Mover's Distance and in mathematics as the …

2018

Geodesic PCA versus log-PCA of histograms in the Wasserstein space

E Cazelles, V Seguy, J Bigot, M Cuturi… - SIAM Journal on Scientific …, 2018 - SIAM

This paper is concerned with the statistical analysis of datasets whose elements are random

histograms. For the purpose of learning principal modes of variation from such data, we …

Wasserstein distributionally robust Kalman filtering

S Shafieezadeh-Abadeh, VA Nguyen, D Kuhn… - arXiv preprint arXiv …, 2018 - arxiv.org

We study a distributionally robust mean square error estimation problem over a nonconvex

Wasserstein ambiguity set containing only normal distributions. We show that the optimal

estimator and the least favorable distribution form a Nash equilibrium. Despite the non …

Wasserstein Distributionally Robust Kalman Filtering

S Shafieezadeh Abadeh, VA Nguyen… - Advances in Neural …, 2018 - papers.nips.cc

We study a distributionally robust mean square error estimation problem over a nonconvex

Wasserstein ambiguity set containing only normal distributions. We show that the optimal

estimator and the least favorable distribution form a Nash equilibrium. Despite the non …

[HTML] Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - Mathematical Programming, 2018 - Springer

We consider stochastic programs where the distribution of the uncertain parameters is only

observable through a finite training dataset. Using the Wasserstein metric, we construct a

ball in the space of (multivariate and non-discrete) probability distributions centered at the …

Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric

C Duan, W Fang, L Jiang, L Yao… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org

Chance constrained optimal power flow (OPF) has been recognized as a promising

framework to manage the risk from variable renewable energy (VRE). In the presence of

VRE uncertainties, this paper discusses a distributionally robust chance constrained …

<——2018—-— 2018———1660—

Risk-based distributionally robust optimal gas-power flow with wasserstein distance

C Wang, R Gao, W Wei, M Shafie-khah… - … on Power Systems, 2018 - ieeexplore.ieee.org

Gas-fired units and power-to-gas facilities provide pivotal backups for power systems with

volatile renewable generations. The deepened system interdependence calls for elaborate

consideration of network models of both natural gas and power systems, as well as …

Wasserstein distance and the distributionally robust TSP

JG Carlsson, M Behroozi, K Mihic - Operations Research, 2018 - pubsonline.informs.org

Recent research on the robust and stochastic traveling salesman problem and the vehicle

routing problem has used many different approaches for describing the region of ambiguity

including taking convex combinations of observed demand vectors or imposing constraints …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so …

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu… - IET Generation …, 2018 - ieeexplore.ieee.org

In order to address the wind power uncertainty in the security constrained economic

dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve

and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

2018

Distributionally robust games: Wasserstein metric

J Gao, H Tembine - 2018 International Joint Conference on …, 2018 - ieeexplore.ieee.org

Deep generative models are powerful but difficult to train due to its instability, saturation

problem and high dimensional data distribution. This paper introduces a game theory

framework with Wasserstein metric to train generative models, in which the unknown data …

Applications of Wasserstein Distance in Distributionally Robust Optimization

Y Wang - 2018 - search.proquest.com

Recent research on formulating and solving distributionally robust optimization problems

has seen many different approaches for describing one's ambiguity set, such as moment

based approach and statistical distance based approach. In this dissertation, we use …

Measuring distributional asymmetry with Wasserstein distance and Rademacher symmetrization

AB Kashlak - Electronic Journal of Statistics, 2018 - projecteuclid.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

asymmetry of the given measure. An empirical bound on this asymmetric correction term is …

2018 [PDF] uniandes.edu.co

Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DF Fonseca Valero - 2018 - repositorio.uniandes.edu.co

En el presente trabajo estudiaremos los problemas de Optimización Robusta Distribucional

DRO, estos son problemas de optimización estocástica formulados desde una visión

robusta, esta visión consiste en asumir que la distribución verdadera de la variable aleatoria …

[CITATION] Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DFF Valero - 2018 - Uniandes

2018 [PDF] uniandes.edu.co

Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DF Fonseca Valero - 2018 - repositorio.uniandes.edu.co

En el presente trabajo estudiaremos los problemas de Optimización Robusta Distribucional

DRO, estos son problemas de optimización estocástica formulados desde una visión

robusta, esta visión consiste en asumir que la distribución verdadera de la variable aleatoria …

[CITATION] G. Poly et Y. Swan. Stein's method on the second Wiener chaos: 2-Wasserstein distance

B Arras, E Azmoodeh - arXiv preprint arXiv:1601.03301, 2016

1805.11284] Wasserstein Variational Inference - arXiv

<——2018—-— 2018———1670—

Wasserstein variational inference

by L Ambrogioni · 2018 · Cited by 30 — Abstract: This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport ...

[CITATION] Maris, and van Gerven. Ambrogioni L, Güçlü U, Güçlütürk Y, Hinne M, Maris E, van Gerven MAJ (2018) Wasserstein variational inference

G Ambrogioni - Proceedings of the 32Nd International Conference on …

2018

Operations Research Letters Data-driven risk-averse ...

Data-driven risk-averse stochastic optimization with Wasserstein metric by C Zhao · 2018 · Cited by 173 — In this paper, we study data-driven risk-averse stochastic optimization approach with Wasserstein. Metric for the general distribution case.

2018 [PDF] psu.edu

Geometry-sensitive ensemble mean based on Wasserstein barycenters: Proof-of-concept on cloud simulations

J Li, F Zhang - Journal of Computational and Graphical Statistics, 2018 - Taylor & Francis

An ensemble of forecasts generated by different model simulations provides rich information

for meteorologists about impending weather such as precipitating clouds. One major form of

forecasts presents cloud images created by multiple ensemble members. Common features …

Distributionally robust mean-variance portfolio selection with Wasserstein distances

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018 - arxiv.org

We revisit Markowitz's mean-variance portfolio selection model by considering a

distributionally robust version, where the region of distributional uncertainty is around the

empirical measure and the discrepancy between probability measures is dictated by the so …

[CITATION] Distributionally robust mean–variance portfolio selection with Wasserstein distances. arXiv

J Blanchet, L Chen, XY Zhou - arXiv preprint arXiv:1802.04885, 2018

Data-driven distributionally robust reserve and energy scheduling over Wasserstein balls

L Yao, X Wang, C Duan, J Guo, X Wu… - IET Generation …, 2018 - ieeexplore.ieee.org

In order to address the wind power uncertainty in the security constrained economic

dispatch (SCED), this study proposes a two-stage data-driven distributionally robust reserve

and energy scheduling (DDRRES) model that considers the loss of wind spillage and load …

2018

Risk-based distributionally robust energy and reserve dispatch with Wasserstein-moment metric

L Yao, X Wang, C Duan, X Wu… - 2018 IEEE power & …, 2018 - ieeexplore.ieee.org

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-

based distributionally robust approach to address the wind power uncertainty in the energy

and reserve dispatch. The proposed model minimizes the total cost including dispatch cost …

Measuring distributional asymmetry with Wasserstein distance and Rademacher symmetrization

AB Kashlak - Electronic Journal of Statistics, 2018 - projecteuclid.org

We propose of an improved version of the ubiquitous symmetrization inequality making use

of the Wasserstein distance between a measure and its reflection in order to quantify the

asymmetry of the given measure. An empirical bound on this asymmetric correction term is …

Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DF Fonseca Valero - 2018 - repositorio.uniandes.edu.co

En el presente trabajo estudiaremos los problemas de Optimización Robusta Distribucional

DRO, estos son problemas de optimización estocástica formulados desde una visión

robusta, esta visión consiste en asumir que la distribución verdadera de la variable aleatoria …

[CITATION] Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones

DFF Valero - 2018 - Uniandes

Low-Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and

Perceptual Loss

- PubMed

https://pubmed.ncbi.nlm.nih.gov › ...

by Q Yang · 2018 · Cited by 707 — This paper introduces a new CT image denoising method based on the Cited by 868 Related articles All 8 versions

2018

Numerical simulation using the minimizing movement with the ...

https://www.math.u-psud.fr › IMG › pdf › rapportpf...

https://www.math.u-psud.fr › IMG › pdf › rapportpf...PDF

by T GOLVET · 2018 — We study the numerical implementation of a minimizing movement scheme using the 1-Wasserstein distance introduced in [1]. We implement this scheme using two.

46 pages

[CITATION] Numerical simulation using the minimizing movement with the 1-Wasserstein distance

T GOLVET, JD BENAMOU, G CARLIER… - 2018

<——2018—-— 2018———1680—

Life-long disentangled representation learning with cross-domain latent homologies A Achille, T Eccles, L Matthey, CP Burgess… - arXiv preprint arXiv …, 2018 - arxiv.org … For example, knowing that strawberries and bananas are not edible when they are green could be useful when deciding whether to eat a … where D is a distance between two distributions (we use the Wasserstein distance for the encoder and KL divergence for the decoder). … Cited by 78 Related articles

Data-driven risk-averse stochastic optimization with Wasserstein metric

C Zhao, Y Guan - Operations Research Letters, 2018 - Elsevier

In this paper, we study a data-driven risk-averse stochastic optimization approach with Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we can successfully reformulate the risk-averse two-stage stochastic optimization problem with …

Stochastic wasserstein autoencoder for probabilistic sentence generation

H Bahuleyan, L Mou, H Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

The variational autoencoder (VAE) imposes a probabilistic distribution (typically Gaussian) on the latent space and penalizes the Kullback--Leibler (KL) divergence between the posterior and prior. In NLP, VAEs are extremely difficult to train due to the problem of KL …

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

G Vissio, V Lucarini - Nonlinear Processes in Geophysics, 2018 - npg.copernicus.org

[PDF] dml.cz

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

V Kaňková, V Omelčenko - Kybernetika, 2018 - dml.cz

Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall eg, problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they …

2018

Evaluating a stochastic parametrization for a fast–slow system ...

https://npg.copernicus.org › articles

by G Vissio · 2018 · Cited by 8 — Abstract. Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modeling of geophysical fluids.

[CITATION] Evaluating a Stochastic Parametrization of the Coupling in a Fast-Slow System using the Wasserstein Distance

Inference for empirical Wasserstein distances on finite spaces

2018 [PDF] arxiv.org

M Sommerfeld, A Munk - Journal of the Royal Statistical Society …, 2018 - Wiley Online Library

Wasserstein variational inference

L Ambrogioni, U Güçlü, Y Güçlütürk, M Hinne… - arXiv preprint arXiv …, 2018 - arxiv.org

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and the Wasserstein …

Learning and inference with Wasserstein metrics

CCA Frogner - 2018 - dspace.mit.edu

This thesis develops new approaches for three problems in machine learning, using tools from the study of optimal transport (or Wasserstein) distances between probability distributions. Optimal transport distances capture an intuitive notion of similarity between …

2918 see 2017

Speech enhancement based on a new architecture of wasserstein generative adversarial networks

S Ye, T Jiang, S Qin, W Zou… - 2018 11th International …, 2018 - ieeexplore.ieee.org

… Firstly, we compare our model with SEGAN and MMSE-SPZC with respect to denoising

performance according to spectrograms and waveforms. Then we further use the perceptual

<—-2018—-— 2018———1690—

Unsupervised and semi-supervised learning with categorical generative adversarial networks assisted by wasserstein distance for dermoscopy image classification

X Yi, E Walia, P Babyn - arXiv preprint arXiv:1804.03700, 2018 - arxiv.org

Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis

involves initial screening with subsequent biopsy and histopathological examination if

2018

Wasserstein and total variation distance between marginals of Lévy processes

E Mariucci, M Reiß - Electronic Journal of Statistics, 2018 - projecteuclid.org

… bounds for the Wasserstein distance of order p between the marginals of Lévy processes,

including Gaussian approximations for jumps of infinite activity. Using the convolution structure,

we further derive upper bounds for the total variation … application to statistical lower bounds. …

2018 [PDF] arxiv.org

Comparison between W2 distance and Ḣ− 1 norm, and localization of wasserstein distance

R Peyre - ESAIM: Control, Optimisation and Calculus of …, 2018 - esaim-cocv.org

It is well known that the quadratic Wasserstein distance W 2 (⋅,⋅) is formally equivalent, for

infinitesimally small perturbations, to some weighted H− 1 homogeneous Sobolev norm. In

this article I show that this equivalence can be integrated to get non-asymptotic comparison …

Dissertation or Thesis Preview Available

A Comparative Assessment of the Impact of Various Norms on Wasserstein Generative Adversarial Networks

Ramesh, Chandini.Rochester Institute of Technology. ProQuest Dissertations Publishing, 2018. 13807809.

Abstract/Details Preview - PDF (436 KB)‎

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Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

Scholarly Journal Full Text

Vissio, Gabriele; Lucarini, Valerio.Nonlinear Processes in Geophysics; Gottingen Vol. 25, Iss. 2, (2018): 413-427.

Abstract/Details Full text Full text - PDF (5 MB)‎

Cited by (‎1)References (‎50)

Single Image Super-Resolution Based on Wasserstein GANs

2018

Conference Paper Citation/Abstract

Wu, Fei; Wang, Bo; Cui, Dagang; Li, Linhao.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Distributed Computation of Wasserstein Barycenters Over Networks

Conference Paper Citation/Abstract

Uribe, Cesar A; Dvinskikh, Darina; Dvurechensky, Pavel; Gasnikov, Alexander; Nedic, Angelia.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Wasserstein Introspective Neural Networks

Conference Paper Citation/Abstract

Lee, Kwonjoon; Xu, Weijian; Fan, Fan; Tu, Zhuowen.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Generative Modeling Using the Sliced Wasserstein Distance

2018

Conference Paper Citation/Abstract

Deshpande, Ishan; Zhang, Ziyu; Schwing, Alexander.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

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Sliced Wasserstein Distance for Learning Gaussian Mixture Models

Conference Paper Citation/Abstract

Kolouri, Soheil; Rohde, Gustavo K; Hoffmann, Heiko.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

<-—2018—-— 2018———1700—

Conference Paper Citation/Abstract

Zheng, Wenbo; Jin, Xin; Mo, Shaocong; Qu, Yili; Fan, Zeyu; et al.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

HashGAN: Deep Learning to Hash with Pair Conditional Wasserstein GAN

Conference Paper Citation/Abstract

Cao, Yue; Liu, Bin; Long, Mingsheng; Wang, Jianmin.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS

Conference Paper Citation/Abstract

Degottex, Gilles; Gales, Mark.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Speech Enhancement Based on A New Architecture of Wasserstein Generative Adversarial Networks

Conference Paper Citation/Abstract

Ye, Shuaishuai; Jiang, Ting; Qin, Shan; Zou, Weixia; Deng, Chengyun.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Classification of Small UAVs Based on Auxiliary Classifier Wasserstein GANs

Conference Paper Citation/Abstract

Zhao, Caidan; Chen, Caiyun; Cai, Zhibiao; Shi, Mingxian; Du, Xiaojiang; et al.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Lifted Wasserstein Matcher for Fast and Robust Topology Tracking

2018

Conference Paper Citation/Abstract

Soler, Maxime; Plainchault, Melanie; Conche, Bruno; Tierny, Julien.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Generalization error bounds using Wasserstein distances

Conference Paper Citation/Abstract

Lopez, Adrian Tovar; Jog, Varun.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

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Cited by 26 Related articles

Conference Paper Citation/Abstract

Distributionally Robust Games: Wasserstein Metric

Gao, Jian; Tembine, Hamidou.The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings; Piscataway, (2018).

Wasserstein Stationary Subspace Analysis

Scholarly Journal Citation/Abstract

Kaltenstadler, Stephan; Nakajima, Shinichi; Klaus-Robert Muller; Samek, Wojciech.IEEE Journal of Selected Topics in Signal Processing; New York Vol. 12, Iss. 6, (2018): 1213.

Abstract/Details
Cited by (‎1)
Cited by 8 Related articles All 3 versions

Scholarly Journal Full Text

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
Bigot, Jérémie; Klein, Thierry.ESAIM. Probability and Statistics; Les Ulis Vol. 22, (2018).

Abstract/Details Get full textLink to external site, this link will open in a new window

Cited by (‎1)
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<——2018—-— 2018———1710—

Conference Paper Citation/Abstract

Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation
Wu, Hao; Ma, Peter C; Yu, Lv; Ihme, Matthias.American Institute of Aeronautics and Astronautics. AIAA Meeting Papers; Reston, (2018).

2018

A Feature Metric Algorithm Combining the Wasserstein Distance and Mutual Information

M Lu, J Yin - 2018 IEEE International Conference on Progress …, 2018 - ieeexplore.ieee.org

… , based on Wasserstein distance [13] and mutual information. Wasserstein distance is used

to measure the distance between two different probability distributions. We use it to measure

the separation ability of features. By combining mutual information with Wasserstein distance …

2018 [PDF] joig.org

[PDF] Automatic liver segmentation using U-Net with Wasserstein GANs

Y Enokiya, Y Iwamoto, YW Chen, XH Han - Journal of Image and Graphics, 2018 - joig.org

… an automatic liver segmentation using U-Net with a Wasserstein Generative Adversarial Network

(GAN). The Wasserstein GAN was used to … In the present study, we propose an automatic

liver segmentation method based on U-Net with a Wasserstein GAN (WGAN). WGAN [18], […

2018 [PDF] rit.edu

[BOOK] A Comparative Assessment of the Impact of Various Norms on Wasserstein Generative Adversarial Networks

C Ramesh - 2018 - search.proquest.com

… Recognizing the crucial and central role played by both the cost function and the order of the

Wasserstein distance used in WGAN, this thesis seeks to provide a comparative assessment

of the effect of a various common used norms on WGANs. Inspired by the impact of norms …

An Novel Face Image Super-Resolution Based on Sparse Representation and Wasserstein Distance

2018 [PDF] openreview.net

[PDF] Learning disentangled representations with wasserstein auto-encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

… We apply Wasserstein auto-encoders (WAEs) to the problem of disentangled

representation learning. We highlight the potential of WAEs with promising results on a

benchmark disentanglement task. … In this work, we apply WAEs to the problem of …

2018

W Zheng, X Jin, S Mo, Y Qu, Z Fan… - 2018 IEEE 4th …, 2018 - ieeexplore.ieee.org

… novel sparse representation and Wasserstein distance based face super-resolution approach

that seem the measure of between LR and HR as Wasserstein … To solve this problem, we

propose a novel sparse representation and Wasserstein distance based face super-resolution …

2018 [PDF] Learning disentangled representations with wasserstein auto-encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

… We apply Wasserstein auto-encoders (WAEs) to the problem of disentangled

representation learning. We highlight the potential of WAEs with promising results on a

benchmark disentanglement task. … The authors show that by tuning β, they are able to …

Bayes and maximum likelihood for L 1 -Wasserstein deconvolution of Laplace mixtures

C Scricciolo - Statistical Methods & Applications, 2018 - Springer

… Fourier transform, into any $L^p$-Wasserstein distance, $p\ge 1$, between the

corresponding mixing distributions, provided their Laplace … $L^1$-Wasserstein metric for

the Bayes’ and maximum likelihood estimators of the mixing distribution. Merging in the $L^1$-Wasserstein …

2018 [PDF] cam.ac.uk

A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS

G Degottex, M Gales - 2018 IEEE Spoken Language …, 2018 - ieeexplore.ieee.org

… In this paper, we suggest a new loss function, by mixing the LS error and the loss of a

discriminator trained with Wasserstein GAN, while weighting this mixture differently through

the frequency domain. Using listening tests, we show that, using this mixed loss, the generated …

Data-driven chance constrained programs over Wasserstein balls

Z Chen, D Kuhn, W Wiesemann - arXiv preprint arXiv:1809.00210, 2018 - arxiv.org

… -driven chance constrained programs over Wasserstein balls. For individual chance

constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation

amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-…

<——2018—-— 2018———1720—

LEARNING EMBEDDINGS INTO ENTROPIC WASSERSTEIN ...

https://openreview.net › pdf

https://openreview.net › pdfPDF

by C Frogner · 2018 · Cited by 10 — distributions in a Wasserstein space, endowed with an optimal transport metric ... metrics on symbolic data, with a finite set of symbols; we are unaware of.

2018

Batch norm #1 - cameronfabbri/Improved-Wasserstein-GAN

https://github.com › Improved-Wasserstein-GAN › issues

Feb 26, 2018 — Hi dear author! I notice that in your code, there is no update_ops for updating batch norm statistics, and update collections for batch norm ...

2018 youtube video

Darina Dvinskikh "Randomized distributed computation of Wasserstein barycenter with mini batch"335 viewsMay 15, 2018
[1810.07793] The Wasserstein transform - arXivhttps://arxiv.org › cs

https://arxiv.org › cs

by F Mémoli · 2018 · Cited by 5 — Abstract: We introduce the Wasserstein transform, a method for enhancing and denoising

datasets defined on general metric spaces.

Darina Dvinskikh "Randomized distributed computation of Wasserstein barycenter with mini batch"

May 15, 2018

2018

or 2- Wasserstein distance between collections of point masses

https://math.stackexchange.com › questions › computin...

Aug 9, 2018 — Is either W1 or W2 (the Wasserstein distances) available in closed form when comparing two collections of point masses?

2018

Stochastic Wasserstein Barycenters - Proceedings of Machine ...

http://proceedings.mlr.press › ...

http://proceedings.mlr.press › ...PDF

by S Claici · 2018 · Cited by 60 — We present a stochastic algorithm to compute the barycenter of a set of probability distributions un- der the Wasserstein metric from optimal transport.

tochastic Wasserstein Barycenters

2018

Wasserstein Auto-Encoders | OpenReviewhttps://openreview.net › forum
https://openreview.net › forum
by I Tolstikhin · 2018 · Cited by 735 — Abstract: We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution.

2018 [PDF] openreview.net

Generative model based on minimizing exact empirical wasserstein distance

A Iohara, T Ogawa, T Tanaka - 2018 - openreview.net

… the Wasserstein distance in the dual domain, which requires some approximation, so that

it may fail to optimize the true Wasserstein … Experiments on the MNIST dataset show that

our method is significantly stable to converge, and achieves the lowest Wasserstein distance …

On the minimizing movement with the 1-Wasserstein distance

2018 [PDF] psl.eu

M Agueh, G Carlier, N Igbida - ESAIM: Control, Optimisation and …, 2018 - esaim-cocv.org

We consider a class of doubly nonlinear constrained evolution equations which may be viewed

as a nonlinear extension of the growing sandpile model of [L. Prigozhin, Eur. J. Appl. Math.

7 (1996) 225–235.]. We prove existence of weak solutions for quite irregular sources by a …

2016 [PDF] arxiv.org

Discrete approximation of the minimizing movement scheme for evolution equations of Wasserstein gradient flow type with nonlinear mobility

J Zinsl, D Matthes - arXiv preprint arXiv:1609.06907, 2016 - arxiv.org

… Wasserstein distance with nonlinear mobility. Our scheme relies on a spatially discrete

approximation of the semi-discrete (in time) minimizing … problem converge to solutions of

the spatially continuous original minimizing movement scheme using the theory of Γ-convergence, …

Wasserstein convolutional neural network (WCNN) - Allie (アリー ...

<——2018—-— 2018———1730—

Wasserstein Variational Inference - NASA/ADShttps://ui.adsabs.harvard.edu › abs › abstract
https://ui.adsabs.harvard.edu › abs › abstract
by L Ambrogioni · 2018 · Cited by 32 — This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory.
Wasserstein variational inference

2018

http://allie.dbcls.jp › pubmed › WCNN

http://allie.dbcls.jp › pubmed › WCNN · Translate this page

Compare KS test and Wasserstein distance or Earth mover's ...

Sep 18, 2018

Equivalent Forms of Wasserstein Metric - Cross Validated

https://stats.stackexchange.com › questions › equivalent...

Jun 16, 2018 — In a paper I read, the authors mention that the infimum is attained by the inverse c.d.f. transformation of a random variable U uniformly ...

8 Research article
Inequalities for the Wasserstein mean of positive definite matrices
Linear Algebra and its Applications13 March 2018...

Rajendra BhatiaTanvi JainYongdo Lim

2018

018 Research article
Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions
Journal of Multivariate Analysis19 October 2018...

Eustasio del BarrioPaula GordalizaJean-Michel Loubes

2018 Research article
The existence of geodesics in Wasserstein spaces over path groups and loop groups
Stochastic Processes and their Applications4 March 2018...

Jinghai Shao

2018 esearch article
The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation
Journal of Computational and Applied Mathematics31 December 2018...

Luca DieciJ. D. Walsh III

2018 Research article
A bound on the Wasserstein-2 distance between linear combinations of independent random variables
Stochastic Processes and their Applications18 July 2018...

Benjamin ArrasEhsan AzmoodehYvik Swan

2018 Research article
Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises
Stochastic Processes and their Applications11 September 2018...

Dejun LuoJian Wang

<-—2018—-— 2018———1740—

2018 see 2017 Research article
Auto-painter: Cartoon image generation from sketch by using conditional Wasserstein generative adversarial networks
Neurocomputing22 May 2018...

Yifan LiuZengchang QinZhenbo Luo

ow that …

2018 Research article
On differentiability in the Wasserstein space and well-posedness for Hamilton–Jacobi equations
Journal de Mathématiques Pures et Appliquées12 September 2018...

Wilfrid GangboAdrian Tudorascu

2019 Research article
Typical wind power scenario generation for multiple wind farms using conditional improved Wasserstein generative adversarial network
International Journal of Electrical Power & Energy Systems2 July 2019...

Yufan ZhangQian AiTianguang Lu

2018 Research articleOpen access
Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape
Comptes Rendus Mathematique30 April 2018...

Julian Tugaut

2018 [PDF] arxiv.org

On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function

A Liu, JG Liu, Y Lu - arXiv preprint arXiv:1807.08365, 2018 - arxiv.org

… The purpose of this paper is to prove the rate of convergence of νn to ν wrt ∞Wasserstein

distance W∞ when the density function ρ of ν is unbounded. For simplicity, we will focus on

the one dimensional case, but the arguments of the proof are expected to be generalized to …

2018

2018 Research article
Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem
Stochastic Processes and their Applications4 April 2018...

Elena BandiniAndrea CossoHuyên Pham

2018

Gabriel Peyré on Twitter: "Sheep Wasserstein gradient flows ...

https://twitter.com › gabrielpeyre › status

Jan 23, 2018 — Sheep Wasserstein gradient flows: the perfect illustration of the crowd motion with congestion model of Maury/Roudneff-Chupin/Santambrogio: ..

Stochastic Wasserstein autoencoder for probabilistic sentence generation

H Bahuleyan, L Mou, H Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

… In this paper, we address the difficulty of training VAE by using a Wasserstein autoencoder

(WAE) for probabilistic sentence generation. WAE implementation can be carried out with

either a deterministic encoder or a stochastic one. The deterministic version achieves high …

Stochastic Wasserstein Autoencoder for Probabilistic Sentence Generation

[PDF] rit.edu

[BOOK] A Comparative Assessment of the Impact of Various Norms on Wasserstein Generative Adversarial Networks

C Ramesh - 2018 - search.proquest.com

… Recognizing the crucial and central role played by both the cost function and the order of the

Wasserstein distance used in WGAN, this thesis seeks to provide a comparative assessment

of the effect of a various common used norms on WGANs. Inspired by the impact of norms …

AE/WGAN-based image representation learning for pose-preserving seamless identity replacement in facial images

2018

H Kawai, J Chen, P Ishwar… - 2019 IEEE 29th …, 2019 - ieeexplore.ieee.org

We present a novel variational generative adversarial network (VGAN) based on Wasserstein

loss to learn a latent representation from a face image that is invariant to identity but …

<——2018—-— 2018———1750—

2018 [PDF] neurips.cc

Generalizing point embeddings using the wasserstein space of elliptical distributions

B Muzellec, M Cuturi - Advances in Neural Information …, 2018 - proceedings.neurips.cc

… 2-Wasserstein metric, with two important benefits: (i) For such measures, the squared 2-Wasserstein

metric … Euclidean distance between means and the squared Bures metric between …

2018 [PDF] neurips.cc

Robust hypothesis testing using Wasserstein uncertainty sets

R Gao, L Xie, Y Xie, H Xu - Advances in Neural Information …, 2018 - proceedings.neurips.cc

… Wasserstein metric … Wasserstein metric for hypothesis testing and drew connections between

different test statistics. Our focus is different from theirs as we consider Wasserstein metric …

PDF] arxiv.org

Multilevel optimal transport: a fast approximation of Wasserstein-1 distances

J Liu, W Yin, W Li, YT Chow - arXiv preprint arXiv:1810.00118, 2018 - arxiv.org

… We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a

particular type of optimal transport distance with homogeneous of degree one transport cost. …

2018 [PDF] github.io

[PDF] Natural gradient in Wasserstein statistical manifold

Y Chen, W Li - arXiv preprint arXiv:1805.08380, 2018 - yifanc96.github.io

… Ground cost related distance Optimal transport provides the Wasserstein distance among

histograms, relying on the structure of sample … ► Wasserstein metric as geodesic distance …

[PDF] washington.edu

[PDF] Using Wasserstein GAN to Generate Adversarial Examples

Z Xiong, P Moulin - homes.cs.washington.edu

… examples using a GAN, specifically a Wasserstein GAN [12]. We … Our Wasserstein GANbased

method will be introduced in … Specifically, we will use the Wasserstein GAN because it is …

2018

Wasserstein Riemannian geometry of Gaussian densities

L Malago, L Montrucchio, G Pistone - Information Geometry, 2018 - Springer

… 3 we discuss known results about the metric geometry induced by the Wasserstein distance. These results are re-stated in Prop. 3 and, for sake of completeness, we provide a further …

Cited by 47 Related articles

Banach wasserstein gan

J Adler, S Lunz - Advances in Neural Information …, 2018 - proceedings.neurips.cc

… all separable Banach spaces are Polish spaces and we can hence define Wasserstein metrics … Banach spaces, allowing us to effectively train a Wasserstein GAN using arbitrary norms. …

2018 see 2015

Snowflake universality of Wasserstein spaces

A Andoni, A Naor, O Neiman - Annales Scientifiques de l'Ecole …, 2018 - cris.bgu.ac.il

… probability measures on ℝ 3 , equipped with the Wasserstein p metric W p . We prove that for … , coarse, or quasisymmetric embedding into any Banach space of nontrivial type. Links to …

A new approach for the construction of a Wasserstein diffusion

V Marx - Electronic Journal of Probability, 2018 - projecteuclid.org

… motion taking values on the Wasserstein space P2(R), defined … a strong Markov process called Wasserstein diffusion on P2(M), … First, the energy of the martingale part of the Wasserstein …

Wasserstein riemannian geometry of positive definite matrices

L Malago, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

… (1), the W distance is more precisely called L2-Wasserstein distance. Other exponents or … [4], who derived the notion of both Fisher metric and natural gradient, from the second order …

<——2018—–— 2018———1760—

Extremal flows in Wasserstein space

G Conforti, M Pavon - Journal of mathematical physics, 2018 - aip.scitation.org

… a suitable Newton-like law in the Wasserstein space. In … IV, we introduce the basic geometric tools in the Wasserstein … V, we show that the entropic interpolation satisfies a Newton-type …

Convergence in the Wasserstein Distance

R Douc, E Moulines, P Priouret, P Soulier - Markov Chains, 2018 - Springer

… 12, we will consider Markov kernels on metric spaces, and we will investigate the … in the Wasserstein distances. We will begin this chapter with a minimal introduction to the Wasserstein …

[PDF] siam.org

Image labeling based on graphical models using Wasserstein messages and geometric assignment

R Hühnerbein, F Savarino, F Åström… - SIAM Journal on Imaging …, 2018 - SIAM

… this paper, in connection with the local Wasserstein distances of (1.4), … Smoothing of the Wasserstein distance and Sinkhorn’s … Fisher–Rao metric. At a point p ∈ S, this metric is given by …

Measuring distributional asymmetry with Wasserstein distance and Rademacher symmetrization

AB Kashlak - Electronic Journal of Statistics, 2018 - projecteuclid.org

… We first require the standard notions of Wasserstein distance and Wasserstein space as … original bound for a type p Banach space is O(n1−p ) while the Wasserstein correction term is O(…

Topological data assimilation using Wasserstein distance

L Li, A Vidard, FX Le Dimet, J Ma - Inverse Problems, 2018 - iopscience.iop.org

… the optimal transport and Fisher–Rao was proposed and … Motivated by the advantages of the Wasserstein metric in the … At present, a learning-type Wasserstein metric [40] has been …

2018

Equivalence between wasserstein and value-aware loss for model-based reinforcement learning

K Asadi, E Cater, D Misra, ML Littman - arXiv preprint arXiv:1806.01265, 2018 - arxiv.org

… We consider the Markov decision process (MDP) setting in which the RL problem is formulated by the tuple 〈S, A,R,T,γ〉. Here, S denotes a state space and A denotes an action set. …

[PDF] Multi-Level Metric Learning via Smoothed Wasserstein Distance.

J Xu, L Luo, C Deng, H Huang - IJCAI, 2018 - ijcai.org

… -level metric learning method using smoothed Wasserstein distance as a measure of errors … Wasserstein distance through a shared distance matrix and local smoothed Wasserstein di

Sliced Wasserstein auto-encoders

S Kolouri, PE Pope, CE Martin… - … Conference on Learning …, 2018 - openreview.net

… characteristics of the Wasserstein distance, we use the sliced-Wasserstein distance to measure … Penalized fisher discriminant analysis and its application to image-based morphometry. …

Cited by 87 Related articles

2018 see 2017 [PDF] arxiv.org

Wasserstein cnn: Learning invariant features for nir-vis face recognition

R He, X Wu, Z Sun, T Tan - IEEE transactions on pattern …, 2018 - ieeexplore.ieee.org

… a face photo from a pseudo-sketch by using multi-scale Markov random fields. Then, a hidden Markov model was further used to learn the nonlinear relationship between face photos …

The quadratic Wasserstein metric for earthquake location

J Chen, Y Chen, H Wu, D Yang - Journal of Computational Physics, 2018 - Elsevier

… In this study, we prefer to use the 1D quadratic Wasserstein metric. This is based on the perspective that the signal at individual receivers can be treated as one-dimensional time series …

<——2018—–— 2018———1770—

[PDF] uci.edu

Wasserstein geometry of quantum states and optimal transport of matrix-valued measures

Y Chen, TT Georgiou, A Tannenbaum - Emerging Applications of Control …, 2018 - Springer

… We overview recent results on generalizations of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices and of matrix…

A two-step computation of the exact gan wasserstein distance

H Liu, GU Xianfeng, D Samaras - … Conference on Machine …, 2018 - proceedings.mlr.press

… - We propose a new formulation to compute the Wasserstein … an exact computation of the Wasserstein distance and 2) adopt a … the exact Wasserstein distance. We name our method TS. …

Bayesian learning with Wasserstein barycenters

J Backhoff-Veraguas, J Fontbona, G Rios… - arXiv preprint arXiv …, 2018 - arxiv.org

… Namely, we propose to use the Wasserstein barycenter of the posterior law on … the Wasserstein space, and is of independent interest and applicability for the computation of Wasserstein …

Visual feature attribution using wasserstein gans

CF Baumgartner, LM Koch… - Proceedings of the …, 2018 - openaccess.thecvf.com

… To address this problem we develop a novel feature attribution technique based on Wasserstein Generative Adversarial Networks (WGAN), which does not suffer from this limitation. We …

Stochastic Wasserstein autoencoder for probabilistic sentence generation

H Bahuleyan, L Mou, H Zhou… - arXiv preprint arXiv …, 2018 - arxiv.org

… In this paper, we propose to use the Wasserstein autoencoder (WAE) for probabilistic sentence generation, where the encoder could be either stochastic or deterministic. We show …

2018

Gaussian mixture models with Wasserstein distance

B Gaujac, I Feige, D Barber - arXiv preprint arXiv:1806.04465, 2018 - arxiv.org

… In this paper, we show that such models are more amenable to training when using the Optimal Transport framework of Wasserstein Autoencoders. We find our discrete latent variable …

Decentralize and randomize: Faster algorithm for Wasserstein barycenters

P Dvurechenskii, D Dvinskikh… - Advances in …, 2018 - proceedings.neurips.cc

… of the Wasserstein barycenter problem for … entropy regularization of the Wasserstein

distance and propose a decentralized algorithm to calculate an approximation to the Wasserstein …

S Cited by 85 Related articles All 13 versions

Decentralize and randomize: Faster algorithm for wasserstein barycenters

Cross-lingual document retrieval using regularized Wassersteindistance

G Balikas, C Laclau, I Redko, MR Amini - European Conference on …, 2018 - Springer

… From the application’s perspective, we evaluate the use of Wasserstein distances in the task

… entropic regularized version that will be later used to calculate the regularized Wasserstein …

Wasserstein measure coresets

S Claici, A Genevay, J Solomon - arXiv preprint arXiv:1805.07412, 2018 - arxiv.org

… entropy-regularized Wasserstein distance is a popular approximation of the Wasserstein …

Here, we detail how this goal is achieved by leveraging the dual of the Wasserstein problem. In …

Save Cite Cited by 8 Related articles All 3 versions

2018

Research articleCentral limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions
Journal of Multivariate Analysis19 October 2018...

Eustasio del BarrioPaula GordalizaJean-Michel Loubes

<——2018—–— 2018———1780—

Wasserstein Generative Adversarial Networks (WGANs) Part 1

http://www.columbia.edu › 2018/01/18 › GANS1

Jan 18, 2018 — Wasserstein Generative Adversarial Networks (WGANs) Part 1: An Introduction ; The concept of algorithm itself is actually quite simple. GANs ...

<——2018—–— 2018———1790—

2018 patent

It is a kind of based on WGAN-GP model to the uneven classification method of …

CN CN109711452A 赵艺四川新网银行股份有限公司

Priority 2018-12-20 • Filed 2018-12-20 • Published 2019-05-03

3. a kind of method for constructing WGAN-GP model according to claim 1 or 2, which is characterized in that the step S2 packet Include following steps: The dimensional characteristics of the few class data of S2.1, basis, construct WGAN-GP structure and hyper parameter simultaneously are arranged；

2018 patent

A kind of fuzzy detection seed set generation method and generator based on WGAN …

CN CN108549597A 纪守领浙江大学

Priority 2018-03-05 • Filed 2018-03-05 • Published 2018-09-18

1. a kind of fuzzy detection seed set generator based on WGAN models, which is characterized in that including： Training set acquisition module, has the fuzzy detection tool based on mutation algorithm, the fuzzy detection tool is to common Input carries out random modification and obtains …

2018 patent

It is predicted based on difference WGAN network safety situation

CN CN109120652A 王永重庆邮电大学

Priority 2018-11-09 • Filed 2018-11-09 • Published 2019-01-01

The invention proposes a kind of network security situation prediction methods based on difference WGAN.The invention simulates the development process of situation using confrontation network (Generative adversarial network, GAN) is generated, and realizes Tendency Prediction from time dimension.

2018 patent

Hyperspectral image classification method based on semi-supervised WGAN-GP

CN CN109389080A 白静西安电子科技大学

Priority 2018-09-30 • Filed 2018-09-30 • Published 2019-02-26

Selected is had supervision batch and the semi-supervised WGAN-GP of noise inputs by (4d), marks training data to optimize the net using having Supervision loss function in network optimizes arbiter network weight； (4e) optimizes the net by selected unsupervised batch and the semi-supervised WGAN- …

2018 patent

A kind of image channel fusion method based on WGAN models

CN CN108399422A 周智恒华南理工大学

Priority 2018-02-01 • Filed 2018-02-01 • Published 2018-08-14

1. a kind of image channel fusion method based on WGAN models, which is characterized in that the image channel fusion method packet Include following steps： S1, construction are originally generated confrontation network model, generate image by generator and are input to arbiter progress network …

2018

2018 patent

A kind of feature recalibration convolution method based on WGAN model

CN CN109359667A 周智恒华南理工大学

Priority 2018-09-07 • Filed 2018-09-07 • Published 2019-02-19

5. a kind of feature recalibration convolution method based on WGAN model according to claim 1, which is characterized in that described Loss function expression formula are as follows: Wherein, D (x) indicates differentiation of the arbiter to image, and pr indicates the distribution of data …

2018 patent

Object Shape Regression Using Wasserstein Distance

EP US JP JP2020098587A ジン・サンパロアルトリサーチセンターインコーポレイテッド

Priority 2018-12-17 • Filed 2019-11-25 • Published 2020-06-25

Optimizing the parameters of the shape regression model based on the Wasserstein distances calculated by the classifier module. The method of claim 2, wherein optimizing the shape regression model comprises updating parameters of the shape regression model such that the calculated Wasserstein …

2018 patent

… plane signal identification detection algorithm based on improvement AC-WGANs

CN CN108197581A 赵彩丹厦门大学

Priority 2018-01-10 • Filed 2018-01-10 • Published 2018-06-22

4. as described in claim 1 a kind of based on the unmanned plane signal identification detection algorithm for improving AC-WGANs, feature exists In：In step S4, it is described improve AC-WGANs algorithms the specific steps are： S41, according to the characteristics of the loss function of AC-WGANs …

2018 patent

Image retrieval method fusing fast-RCNN and Wasserstein self-encoder

CN CN109086437B 冯永重庆大学

Priority 2018-08-15 • Filed 2018-08-15 • Granted 2021-06-01 • Published 2021-06-01

2. The image retrieval method fusing the fast-RCNN and Wasserstein self-encoder according to claim 1, wherein in S1, a Caffe deep learning framework is constructed. 3. The image retrieval method fusing the fast-RCNN and the Wasserstein self-encoder according to claim 1, wherein in the S1, a VGG …

2018 patent

A kind of diagnosing failure of photovoltaic array method based on Wasserstein …

CN CN109660206A 林培杰福州大学

Priority 2018-12-20 • Filed 2018-12-20 • Published 2019-04-19

Step S2: the electric current of the step S1 photovoltaic power generation array obtained is plotted on same picture and is saved with voltage data For sample； Step S3: a discriminator network D and a generator network G are designed by Wasserstein GAN； Step S4: being divided into training set for …

<——2018—–— 2018———1800——

2018 patent

System and method for unsupervised domain adaptation via sliced-wasserstein …

US US20200125982A1 Alexander J. Gabourie Hrl Laboratories, Llc

Priority 2018-02-06 • Filed 2019-12-18 • Published 2020-04-23

The computer program product as set forth in claim 11 , wherein the one or more processors further perform an operation of using sliced-Wasserstein (SW) distance as a dissimilarity measure for determining dissimilarity between the first input data distribution and the second input data distribution.

A Canonical Barycenter via Wasserstein Regularization

Young-Heon Kim and Brendan Pass

SIAM Journal on Mathematical Analysis Vol. 50, No. 2, pp. 1817–1828 2018

2018 see 2017

Wasserstein Distance Guided Representation Learning for ...

https://ojs.aaai.org › index.php › AAAI › article › view

by J Shen · 2018 · Cited by 530 — Inspired by Wasserstein GAN, in this paper we propose a novel approach to learn domain invariant feature representations, namely Wasserstein Distance Guided ...

2018 Cited by 581
ttps://dl.acm.org › doi › abs

Wasserstein distance guided representation learning for ...

by J Shen · 2018 · Cited by 581 — Wasserstein distance guided representation learning for domain adaptation · Jian Shen · Yanru Qu · Weinan Zhang · Yong Yu.

Video: John Gunnar Carlsson, "Wasserstein Distance and the .

Wasserstein Distance and the Distributionally Robust TSP

John Gunnar Carlsson speaking at BIRS workshop, Distributionally Robust

March 6, 2018

Wasserstein distance and the distributionally robust TSP

Wasserstein Generative Adversarial Networks on Intel DevCloud

595 views

Mar 9, 2018

Wasserstein Generative Adversarial Networks on Intel ...

This video is sort of a LIVE coding session. This video is affiliated with Intel. I hope this will get you started with ...

Mar 9, 2018 · Uploaded by AI Journal

2018

Conditional WGAN-GP on MNIST

441 views

•Apr 6, 2018

Conditional WGAN-GP on MNIST

YouTube · 506 views · 4/6/2018 · by Benjamin Striner
Apr 6, 2018

Video: Elsa Cazelles, "Regularization of Barycenters in the Wasserstein space

Sep 3, 2021Tuesday,

April 10, 2018 10:32 - 11:18 see May 1, 2017

Video: Gaël Raoul, "Wasserstein estimates and macroscopic ...

. and their Applications, on Monday, April 9, 2018 on the topic: Wasserstein estimates and macroscopic limits in a model from ecology.

Banff International Research Station · Banff International Research Station ·

Apr 9, 2018

Video: Wilfrid Gangbo,

"A partial Laplacian as an infinitesimal generator on the Wasserstein space"

.www.birs.ca › videos › watch › 201804101032-Gangbo

Video for "wasserstein space"46:00

A partial Laplacian as an infinitesimal generator on the Wasserstein space. Wilfrid Gangbo at 18w5069 ...

Apr 10, 2018 - Up

2018 see 2017

Wasserstein Generative adversarial Networks (WGANs) in Tensorflow ...

- Uploaded by AI Journal

Wasserstein Generative adversarial Networks (WGANs) in Tensorflow8:59. AI Journal 728 views ... wasserstein ...

Apr 10, 2018

<——2018—–— 2018———1810—

Chang Xu | Papers With Code

paperswithcode.com › search

Detecting tiny objects in aerial images: A normalized Wasserstein distance and ... scheme is essential for the success of Neural Architecture Search (NAS).

Papers With Code · Two Minute Papers ·

Apr 12, 2018

Joint Wasserstein GAN contribution - CERN Document Server

This is a merger of three individual contributions: - https://indico.cern.ch/event/668017/contributions/2947026/ ...
Apr 12, 2018

GAN Lecture 6 (2018): WGAN, EBGAN

15,391 views •

May 18, 2018

【MT】Wasserstein Generative adversarial Networks (WGANs) in ...

【MT】Wasserstein Generative adversarial Networks (WGANs) in ... 介绍WGAN和 ...

May 25, 2018

Dirac-GAN (Wasserstein-GAN, n_d=5) - YouTube

- Uploaded by Lars Mescheder

Dirac-GAN (Wasserstein-GAN, n_d=5). Lars Mescheder. Loading... Unsubscribe from Lars Mescheder ...

Jul 4, 2018

018

Nuts and Bolts of WGANs, Kantorovich-Rubistein Duality ...

- Uploaded by Crazymuse

If you have seen the last video on GANs, it may have created an illusion that training GANs is super easy. But ...

Jul 24, 2018

Video: Jonathan Scott, "Wasserstein distance for generalized ...

· Uploaded by Banff International Research Station

Homology, on Tuesday, August 7, 2018 on the topic: Wasserstein distance for generalized persistence ...

Aug 7, 2018

Approximate Bayesian computation with the Wasserstein distance

Approximate Bayesian computation with the Wasserstein ...

IDEA Talk WEDS: Andrew Yale on "Wasserstein GANs and ...

Approximate Bayesian computation with the Wasserstein distance. 1.1K views 4 years ago. Institute for Mathematical Sciences.

YouTube · Institute for Mathematical

Sciences ·

Sep 12, 2018

- Uploaded by The Rensselaer IDEA

More specifically we will be talking about the privacy of medical data and how we can use Wasserstein GANs ...
Sep 19, 2018

A short introduction to approximate Bayesian computation (ABC)

1,207 views •

Oct 3, 2018

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Faster Algorithm for Wasserstein Barycenters - YouTube

Short video describing our paper on the distributed computation of Wasserstein barycenters.

YouTube · César A. Uribe ·

Nov 22, 2018

Faster Algorithm for Wasserstein Barycenters - YouTube

Nov 23, 2018

Uncoupled Isotonic Regression and Wasserstein Deconvolution

Speaker: Jonathan Weed -- Graduate Student, MIT Abstract: Isotonic regression is a standard problem in shape-constrained estimation where ...

YouTube · Stanford Research Talks ·

Oct 26, 2018

Video: Carola-Bibiane Schönlieb, "Wasserstein for learning ...

Carola-Bibiane Schönlieb speaking at BIRS workshop, Shape Analysis, Stochastic Geometric Mechanics and ...

Dec 11, 2018 · Uploaded by Banff International Research Station

Wasserstein for learning image regularisers

Carola-Bibiane Schönlieb, University of Cambridge

Tuesday, December 11, 2018 09:42 - 10:22

Dec 11, 2018

Learning Joint Wasserstein Auto-Encoders for Joint Distribution Matching

J Cao, Y Guo, L Mo, P Zhao, J Huang, M Tan - 2018 - openreview.net

… have proposed a novel joint Wasserstein Auto-Encoders method for the joint distribution

matching problem. Instead of directly optimizing the primal problem of Wasserstein distance, we …

2018

LDAV 2018: Lifted Wasserstein Matcher for Fast and ... - Vimeo

vimeo.com › VGTCommunity › Videos

Dec 6, 2018

2018

WGANs-Part-2 Problems with distribution estimators - EdYoda

www.edyoda.com › watch

WGANs-Part-2 Problems with distribution estimators. GO TO COURSE GO TO COURSE. Like Video ... 2022 zekeLabs Technologies Private Limited ...

EdYoda ·

Oct 18, 2018

WGANs - EdYoda

www.edyoda.com › watch

WGANs-Part-2 Problems with distribution estimators. 0 likes. |. 179 views. Video Thumbnail ... 2022 zekeLabs Technologies Private Limited ...

EdYoda ·

Oct 18, 2018

2018 Peer-reviewed
Lp-WGAN: Using Lp-norm normalization to stabilize Wasserstein generative adversarial networksAuthors:Changsheng Zhou, Jiangshe Zhang, Junmin Liu
Summary:Wasserstein generative adversarial networks (Wasserstein GANs, WGAN) improve the performance of GANs significantly by imposing the Lipschitz constraints on the critic, which is implemented by weight clipping. In this work, we argue that weight clipping could result in a side effect called area collapse by modifying orientations of weights heavily. To fix this issue, a novel method called Lp-WGAN is presented, where lp -norm normalization is employed to impose the constraints. This method restricts the searching space of weights within a low-dimensional manifold and focuses on searching orientations of weights. Experiments on toy datasets show that Lp-WGAN could spread probability mass and find the underlying distribution earlier than WGAN with weight clipping. Results on the LSUN bedroom dataset and CIFAR-10 dataset show that the proposed method could stabilize training better, generate competitive images earlier and get higher evaluation scoresShow more
Article, 2018
Publication:Knowledge-Based Systems, 161, 20181201, 415
Publisher:2018

2018
WGAN domain adaptation for EEG-based emotion recognitionAuthors:Luo Y., Zhang S.-Y., Zheng W.-L., Lu B.-L., 25th International Conference on Neural Information Processing, ICONIP 2018
Article, 2018
Publication:Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 11305 LNCS, 2018, 275
Publisher:2018

3018 thesis
Image and video compression using deep networkAuthors:Nayan Singhal (Author), Philipp Krähenbühl (Degree supervisor)
Abstract:A large fraction of internet traffic revolves around the image and video transfers. All the moments, memories, and experiences that we share online are heavily dependent on strong image and video compression. Strong compression techniques significantly reduce the cost of transmission and storage. Traditional image and video compression techniques are laboriously hand-designed and hand-optimized, and thus become less efficient for current needs. In this work, we explore a series of image and video compression architectures to improve the performance of compression. On the image compression side, we explore the model that integrates auto-encoder and GANs. The results show that WGAN performs better among all the models we tried and is worth exploring in the deep video codec. On the video compression side, our model is based on Wu et al. [43] and [19]. We formulate the video compression problem as a joint rate-distortion optimization problem. This helps us to efficiently throw out a lot of information from the bottleneck layer and achieve good performance with lower bit-rates. Our deep video codec outperforms todays prevailing distance models by Wu et al. on Kinetics dataset in terms of PSNR. From the results we have on PSNR metrics, we believe that we can achieve a significantly better performance in video compressionShow more
Thesis, Dissertation, 2018
English
Publisher:[University of Texas], [Austin, Tex.], 2018

<——2018—–— 2018———1830—

2018
Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual EffectAuthors:Wei, Xiang (Creator), Gong, Boqing (Creator), Liu, Zixia (Creator), Lu, Wei (Creator), Wang, Liqiang (Creator)
Summary:Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by \cite{arjovsky2017towards}, who also propose an alternative direction to avoid the caveats in the minmax two-player training of GANs. The corresponding algorithm, called Wasserstein GAN (WGAN), hinges on the 1-Lipschitz continuity of the discriminator. In this paper, we propose a novel approach to enforcing the Lipschitz continuity in the training procedure of WGANs. Our approach seamlessly connects WGAN with one of the recent semi-supervised learning methods. As a result, it gives rise to not only better photo-realistic samples than the previous methods but also state-of-the-art semi-supervised learning results. In particular, our approach gives rise to the inception score of more than 5.0 with only 1,000 CIFAR-10 images and is the first that exceeds the accuracy of 90% on the CIFAR-10 dataset using only 4,000 labeled images, to the best of our knowledgeShow more
Downloadable Archival Material, 2018-03-05
Undefined
Publisher:2018-03-05

2018
Local Stability and Performance of Simple Gradient Penalty mu-Wasserstein GANAuthors:Kim, Cheolhyeong (Creator), Park, Seungtae (Creator), Hwang, Hyung Ju (Creator)
Summary:Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradient penalty $\mu$-WGAN(SGP $\mu$-WGAN) under suitable assumptions regarding the equilibrium and penalty measure $\mu$. The measure valued differentiation concept is employed to deal with the derivative of the penalty terms, which is helpful for handling abstract singular measures with lower dimensional support. Based on this analysis, we claim that penalizing the data manifold or sample manifold is the key to regularizing the original WGAN with a gradient penalty. Experimental results obtained with unintuitive penalty measures that satisfy our assumptions are also provided to support our theoretical resultsShow more
Downloadable Archival Material, 2018-10-05
Undefined
Publisher:2018-10-05

2018
Denoising of 3-D Magnetic Resonance Images Using a Residual Encoder-Decoder Wasserstein Generative Adversarial NetworkAuthors:Ran, Maosong (Creator), Hu, Jinrong (Creator), Chen, Yang (Creator), Chen, Hu (Creator), Sun, Huaiqiang (Creator), Zhou, Jiliu (Creator), Zhang, Yi (Creator)
Summary:Structure-preserved denoising of 3D magnetic resonance imaging (MRI) images is a critical step in medical image analysis. Over the past few years, many algorithms with impressive performances have been proposed. In this paper, inspired by the idea of deep learning, we introduce an MRI denoising method based on the residual encoder-decoder Wasserstein generative adversarial network (RED-WGAN). Specifically, to explore the structure similarity between neighboring slices, a 3D configuration is utilized as the basic processing unit. Residual autoencoders combined with deconvolution operations are introduced into the generator network. Furthermore, to alleviate the oversmoothing shortcoming of the traditional mean squared error (MSE) loss function, the perceptual similarity, which is implemented by calculating the distances in the feature space extracted by a pretrained VGG-19 network, is incorporated with the MSE and adversarial losses to form the new loss function. Extensive experiments are implemented to assess the performance of the proposed method. The experimental results show that the proposed RED-WGAN achieves performance superior to several state-of-the-art methods in both simulated and real clinical data. In particular, our method demonstrates powerful abilities in both noise suppression and structure preservationShow more
Downloadable Archival Material, 2018-08-12
Undefined
Publisher:2018-08-12

Regularized Wasserstein Means for Aligning Distributional Data

Authors:Mi, Liang (Creator), Zhang, Wen (Creator), Wang, Yalin (Creator)
Summary:We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the variational transportation to distribute a sparse discrete measure into the target domain. The resulting sparse representation well captures the desired property of the domain while reducing the mapping cost. We demonstrate the scalability and robustness of our method with examples in domain adaptation, point set registration, and skeleton layoutShow more
Downloadable Archival Material, 2018-12-02
Undefined
Publisher:2018-12-02

2018

On the latent space of wasserstein auto-encoders

PK Rubenstein, B Schoelkopf, I Tolstikhin - arXiv preprint arXiv …, 2018 - arxiv.org

… We study the role of latent space dimensionality in Wasserstein auto-encoders (WAEs).

Through experimentation on synthetic and real datasets, we argue that random encoders should …

2018

Search fo r GANs | Papers With Code

[PDF] Learning disentangled representations with wasserstein auto-encoders

PK Rubenstein, B Schölkopf, I Tolstikhin - 2018 - openreview.net

… We apply Wasserstein auto-encoders (WAEs) to the problem of disentangled

representation learning. We highlight the potential of WAEs with promising results on a …

paperswithcode.com › search

Improved Training of Wasserstein GANs ... Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum ...

Papers With Code · Tero Karras FI ·

Feb 23, 2018

Ilya Tolstikhin @ QUVA - YouTube

Wasserstein Autoencoders: From Optimal Transport to Generative Modeling (and Beyond) by Ilya Tolstikhin (Max Planck Institute)This talk is ...

YouTube · Qualcomm-UvA Deep Learning Seminars ·

Sep 4, 2018

On isometric embeddings of Wasserstein spaces - The discrete case
Authors:Geher G.P., Titkos T., Virosztek D.
Article, 2018
Publication:arXiv, 2018 09 04
Publisher:2018

<——2018—–— 2018———1840—

WASSERSTEIN DISTANCE, FOURIER SERIES AND APPLICATIONS
Author:Steinerberger S.
Article, 2018
Publication:arXiv, 2018 03 21
Publisher:2018

On the rate of convergence of empirical measure in ∞∑wasserstein distance for unbounded density function
Authors:Liu A., Liu J.-G., Lu Y.
Article, 2018
Publication:arXiv, 2018 07 22
Publisher:2018

eer-reviewed
Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape
Author:Julian Tugaut
Article, 2018
Publication:Comptes rendus.Mathématique, 356, 2018, 657
Publisher:2018

An inexact PAM method for computing Wasserstein barycenter with unknown supports
Authors:Qian Y., Pan S.
Article, 2018
Publication:arXiv, 2018 09 16
Publisher:2018

Local stability and performance of simple gradient penalty μ -Wasserstein GAN
Authors:Kim C., Park S., Hwang H.J.
Article, 2018
Publication:arXiv, 2018 10 05
Publisher:2018

2018

Cross-Lingual Document Retrieval Using Regularized Wasserstein Distance
Authors:Georgios Balikas, Charlotte Laclau, Ievgen Redko, Massih-Reza Amini
Summary:Many information retrieval algorithms rely on the notion of a good distance that allows to efficiently compare objects of different nature. Recently, a new promising metric called Word Mover’s Distance was proposed to measure the divergence between text passages. In this paper, we demonstrate that this metric can be extended to incorporate term-weighting schemes and provide more accurate and computationally efficient matching between documents using entropic regularization. We evaluate the benefits of both extensions in the task of cross-lingual document retrieval (CLDR). Our experimental results on eight CLDR problems suggest that the proposed methods achieve remarkable improvements in terms of Mean Reciprocal Rank compared to several baselinesShow mor
Chapter, 2018
Publication:Advances in Information Retrieval : 40th European Conference on IR Research, ECIR 2018, Grenoble, France, March 26-29, 2018, Proceedings, 10772, 2018, 398
Publisher:2018

Denoising of 3D magnetic resonance images using a residual encoder-decoder wasserstein generative adversarial network
Authors:Ran M., Chen H., Zhou J., Zhang Y., Hu J., Chen Y., Sun H.
Article, 2018
Publication:arXiv, 2018 08 12
Publisher:2018

Data-driven chance constrained programs over wasserstein bas
Authors:Chen Z., Kuhn D., Wiesemann W.
Article, 2018
Publication:arXiv, 2018 09 01
Publisher:2018

THE WASSERSTEIN-FISHER-RAO METRIC FOR WAVEFORM BASED EARTHQUAKE LOCATION∗
Authors:Zhou D., Chen J., Hao W.U., Yang D., Qiu L.
Article, 2018
Publication:arXiv, 2018 12 01
Publisher:2018

Behavior of the empirical Wasserstein distance in Rd under moment conditions
Authors:Dedecker J., Merlevede F.
Article, 2018
Publication:arXiv, 2018 07 24
Publisher:2018

<——2018—–— 2018———1850-

Gradient flows for frame potentials in the wasserstein space
Authors:Wickman C., Okoudjou K.
Article, 2018
Publication:arXiv, 2018 08 28
Publisher:2018

A Rademacher-type theorem ON L2-Wasserstein spaces over closed Riemannian manifolds∗
Author:Dello Schiavo L.
Article, 2018
Publication:arXiv, 2018 10 24
Publisher:2018

L2-Wasserstein distances of tracial W∗-algebras and their disintegration problem
Author:Hornshaw D.F.
Article, 2018
Publication:arXiv, 2018 06 04
Publisher:2018

Second order models for optimal transport and cubic splines on the Wasserstein space
Authors:Benamou J.-D., Gallouet T.O., Vialard F.-X.
Article, 2018
Publication:arXiv, 2018 01 12
Publisher:2018

On Distributionally Robust Chance Constrained Programs With Wasserstein Distance
Author:Weijun X.
Article, 2018
Publication:arXiv, 2018 06 19
Publisher:2018

2018

Minimax rates of distribution estimation in wasserstein distance
Authors:Singh S., Poczos B.
Article, 2018
Publication:arXiv, 2018 02 24
Publisher:2018

Multi-level metric learning via smoothed wasserstein distance
Authors:Xu J., Deng C., Huang H., Luo L., 27th International Joint Conference on Artificial Intelligence, IJCAI 2018
Article, 2018
Publication:IJCAI International Joint Conference on Artificial Intelligence, 2018-July, 2018, 2919
Publisher:2018

Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space
Authors:De Raynal P.-E.C., Frikha N.
Article, 2018
Publication:arXiv, 2018 11 16
Publisher:2018

Generalization error bounds using Wasserstein distances
Authors:Adrian Tovar Lopez, Varun Jog, 2018 IEEE Information Theory Workshop (ITW)
Summary:Generalization error of a learning algorithm characterizes the gap between an algorithm’s performance on test data versus performance on training data. In recent work, Xu & Raginsky [1] showed that generalization error may be upper- bounded using the mutual information $I(S;W)$ between the input $S$ and the output $W$ of an algorithm. In this paper, we derive upper bounds on the generalization error in terms of a certain Wasserstein distance involving the distributions of $S$ and $W$ under the assumption of a Lipschitz continuous loss function. Unlike mutual information-based bounds, these new bounds are useful even for deterministic learning algorithms, or for algorithms such as stochastic gradient descent. Moreover, we show that in some natural cases these bounds are tighter than mutual information-based boundsShow more
Chapter, 2018
Publication:2018 IEEE Information Theory Workshop (ITW), 201811, 1
Publisher:2018

Motion-Blind Blur Removal for CT Images with Wasserstein Generative Adversarial Networks
Authors:Yilin Lyu, Wei Jiang, Yaniun Lin, Laszlo Voros, Miao Zhang, Boris Mueller, Borys Mychalczak, Yulin Song, 2018 11th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI)Show more
Summary:Advanced deblurring techniques for computed tomography (CT) images are necessary and crucial to the improvement of accuracy of patient diagnosis in radiology and patient setup and treatment response assessment in radiation oncology. Currently, medical image deblurring is a challenging technical problem due to the unpredictability of patient motion. This paper introduces a new method of computed tomography image deblurring based on Conditional Generative Adversarial Networks (CGAN) that have been broadly implemented in computer vision research. A Wasserstein Generative Adversarial Network (WGAN) with adversarial loss and l1 perceptual loss was proposed and trained by a blur-sharp image pair dataset created in-house and evaluated by Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index (SSIM). These experiments showed the effectiveness of the approach, which outperforms other competing deblurring techniques both quantitatively and qualitativelyShow more
Chapter, 2018
Publication:2018 11th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), 201810, 1
Publisher:2018

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A Spectrally Weighted Mixture of Least Square Error and Wasserstein Discriminator Loss for Generative SPSS
Authors:Gilles Degottex, Mark Gales, 2018 IEEE Spoken Language Technology Workshop (SLT)
Summary:Generative networks can create an artificial spectrum based on its conditional distribution estimate instead of predicting only the mean value, as the Least Square (LS) solution does. This is promising since the LS predictor is known to oversmooth features leading to muffling effects. However, modeling a whole distribution instead of a single mean value requires more data and thus also more computational resources. With only one hour of recording, as often used with LS approaches, the resulting spectrum is noisy and sounds full of artifacts. In this paper, we suggest a new loss function, by mixing the LS error and the loss of a discriminator trained with Wasserstein GAN, while weighting this mixture differently through the frequency domain. Using listening tests, we show that, using this mixed loss, the generated spectrum is smooth enough to obtain a decent perceived quality. While making our source code available online, we also hope to make generative networks more accessible with lower the necessary resourcesShow more
Chapter, 2018
Publication:2018 IEEE Spoken Language Technology Workshop (SLT), 201812, 603
Publisher:2018

The Wasserstein Distance as a Dissimilarity Measure for Mass Spectra with Application to Spectral Deconvolution
Authors:Szymon Majewski, Michal Aleksander Ciach, Michal Startek, Wanda Niemyska, Blazej Miasojedow, Anna Gambin
Summary:We propose a new approach for the comparison of mass spectra using a metric known in the computer science under the name of Earth Mover's Distance and in mathematics as the Wasserstein distance. We argue that this approach allows for natural and robust solutions to various problems in the analysis of mass spectra. In particular, we show an application to the problem of deconvolution, in which we infer proportions of several overlapping isotopic envelopes of similar compounds. Combined with the previously proposed generator of isotopic envelopes, IsoSpec, our approach works for a wide range of masses and charges in the presence of several types of measurement inaccuracies. To reduce the computational complexity of the solution, we derive an effective implementation of the Interior Point Method as the optimization procedure. The software for mass spectral comparison and deconvolution based on Wasserstein distance is available at https://github.com/mciach/wassersteinmsShow more
Downloadable Article, 2018
Publication:Leibniz International Proceedings in Informatics, 113, 20180726, 25:1
Publisher:2018

Deep variational network embedding in wasserstein space
Authors:Zhu D., Wang D., Cui P., Zhu W., 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2018
Article, 2018
Publication:Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2018 07 19, 2827
Publisher:2018

Image inpainting using Wasserstein Generative Adversarial Network
Authors:Hua P., Liu X., Liu M., Dong L., Hui M., Zhao Y., Optics and Photonics for Information Processing XII 2018
Article, 2018
Publication:Proceedings of SPIE - The International Society for Optical Engineering, 10751, 2018
Publisher:2018

2018 see 2017 Peer-reviewed
The Pontryagin Maximum Principle in the Wasserstein Space
Authors:Benoît Bonnet, Francesco Rossi, SpringerLink (Online service)
Downloadable Article, 2018
English
Publication:Calculus of variations and partial differential equations
Publisher:2018

2018

Evaluating a stochastic parametrization for a fast-slow system using the Wasserstein distance
Authors:Gabriele Vissio, Valerio Lucarini
Downloadable Article, 2018
English
Publication:Nonlinear processes in geophysics
Publisher:2018

2018 thesis
Problemas de clasificación : una perspectiva robusta con la métrica de Wasserstein
Authors:Jorge Andrés Acosta Melo, Mauricio José Junca Peláez
Summary:El objetivo central de este trabajo es dar un contexto a los problemas de clasificación para los casos de máquinas de soporte vectorial y regresión logística. La idea central es abordar estos problemas con un enfoque robusto con ayuda de la métrica de Wasserstein que se define en el espacio de medidas de probabilidad de un espacio muestral dado. Luego, se proporciona un planteamiento equivalente y su justificación para hacer el problema robusto distribucionalmente, un problema con implementación computacional al obtener una expresión del problema inicial en el ámbito de problemas de optimización convexa con finitas restricciones. Para cumplir con este ambicioso objetivo hay que hacer un estudio relativamente minucioso en propiedades de funciones convexas, la métrica de Wasserstein, problemas cónicos lineales y el teorema de dualidad y sus distintas versiones en distintos contextosShow more
Thesis, Dissertation, 2018
Spanish
Publisher:Uniandes, Bogotá, 2018

2018 thesis
基於最佳化傳輸之對抗式領域調適 = Wasserstein Adversarial Domain Adaptation / Ji yu zui jia hua chuan shu zhi dui kang shi ling yu diao shi = Wasserstein Adversarial Domain AdaptationShow more
Authors:呂昱穎著 ; 簡仁宗指導, 呂昱穎, 著, Yu-Ying Lyu, Jen-Tzung Chien, 簡仁宗 / lu yu ying zhu ; jian ren zong zhi dao, Luyuying, Jianrenzong
Thesis, Dissertation, 2018[min 107]
English, Chu ban
Publisher:國立交通大學, Xin zhu shi, 2018[min 107]

2018 thesis
Optimización robusta distribucional con métrica de Wasserstein y algunas aplicaciones
Authors:Diego Fernando Fonseca Valero, Mauricio José Junca Peláez
Summary:En el presente trabajo estudiaremos los problemas de Optimización Robusta Distribucional DRO, estos son problemas de optimización estocástica formulados desde una visión robusta, esta visión consiste en asumir que la distribución verdadera de la variable aleatoria involucrada en el problema pertenece a un conjunto de distribuciones llamado conjunto de ambigüedad, para este caso tal conjunto se define usando la métrica de Wasserstein. Asumiendo ciertas condiciones en la función objetivo, menos restrictivas que las impuestas hasta ahora en la literatura, demostraremos que un DRO de este tipo se puede reformular como un problema de optimización semi-infinita y que dependiendo de la función objetivo dicho problema se puede formular como un problema de optimización convexa finito. Por último presentaremos una serie de aplicaciones en campos como la estadística y la economía, estas aplicaciones son todas contribuciones propias de este trabajoShow more
Thesis, Dissertation, 2018
Spanish
Publisher:Uniandes, Bogotá, 2018

Unsupervised Feature Learning for Outlier Detection with Stacked Convolutional Autoencoders, Siamese Networks and Wasserstein Autoencoders: Application to Epilepsy DetectionShow more
Authors:Zara Alaverdyan, Jiazheng Chai, Carole Lartizien
Summary:In this study we tackle the problem of detecting subtle epilepsy lesions in multiparametric (T1w, FLAIR) MR images considered as normal during a visual examination by a neurologist (MRI negative). We cast this problem as an outlier detection problem and adapt the framework proposed in [1]. It consists in learning a oc-SVM model for each voxel in the brain volume. We generalize this approach by proposing unsupervised deep architectures as feature extracting mechanisms in order to learn representations characterizing healthy subjects. We hypothesize that such architectures may capture features that allow to distinguish pathological voxels from the normal cases used in the training. As such, we exploit and compare three architectures, a novel configuration of siamese networks, stacked convolutional autoencoders and Wasserstein autoencoders. The models are trained on 75 healthy subjects and validated on 21 patients (with 18 MRI negatives) with confirmed epilepsy lesions achieving the best sensitivity of 62%Show more
Chapter, 2018
Publication:Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support : 4th International Workshop, DLMIA 2018, and 8th International Workshop, ML-CDS 2018, Held in Conjunction with MICCAI 2018, Granada, Spain, September 20, 2018, Proceedings, 11045, 2018, 210
Publisher:2018

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Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation Using Holistic Convolutional Networks
Authors:Lucas Fidon, Wenqi Li, Luis C. Garcia-Peraza-Herrera, Jinendra Ekanayake, Neil Kitchen, Sébastien Ourselin, Tom Vercauteren
Summary:The Dice score is widely used for binary segmentation due to its robustness to class imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for training convolutional neural networks (CNN). Although CNNs trained using mean-class Dice score achieve state-of-the-art results on multi-class segmentation, this loss function does neither take advantage of inter-class relationships nor multi-scale information. We argue that an improved loss function should balance misclassifications to favour predictions that are semantically meaningful. This paper investigates these issues in the context of multi-class brain tumour segmentation. Our contribution is threefold. (1) We propose a semantically-informed generalisation of the Dice score for multi-class segmentation based on the Wasserstein distance on the probabilistic label space. (2) We propose a holistic CNN that embeds spatial information at multiple scales with deep supervision. (3) We show that the joint use of holistic CNNs and generalised Wasserstein Dice score achieves segmentations that are more semantically meaningful for brain tumour segmentationShow more
Chapter, 2018
Publication:Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries : Third International Workshop, BrainLes 2017, Held in Conjunction with MICCAI 2017, Quebec City, QC, Canada, September 14, 2017, Revised Selected Papers, 10670, 2018, 64
Publisher:2018

A Variational Model for Image Artifact Correction Based on Wasserstein Distance
Authors:Isabel Narra Figueiredo, Luís Pinto, Gil Gonçalves, Björn Engquist
Summary:Uneven illumination is a recurrent problem in image processing. This is essentially due to image acquisition sensors’ malfunction or external interference. In this paper we propose a variational model for nonuniform illumination correction, that incorporates a penalty term that performs the intensity distribution transfer between two pre-defined sub-regions of the input scalar image, one uniformly illuminated and the other nonuniformly illuminated. This term representing the illumination correction is a Wasserstein distance. It corresponds to the optimal permutation minimizing the cost of rearranging the intensity distribution of the nonuniformly illuminated sub-region into the other, the uniformly illuminated. Simultaneously, this variational model also carries out a regularization of the image by means of a total variation penalty term, to reduce noise. The effectiveness of the model is illustrated for some imagesShow more
Chapter, 2018
Publication:VipIMAGE 2017 : Proceedings of the VI ECCOMAS Thematic Conference on Computational Vision and Medical Image Processing Porto, Portugal, October 18-20, 2017, 27, 2018, 43
Publisher:2018

2018 see 2017
Visual Feature Attribution Using Wasserstein GANs
Authors:Christian F. Baumgartner, Lisa M. Koch, Kerem Can Tezcan, Jia Xi Ang, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
Summary:Attributing the pixels of an input image to a certain category is an important and well-studied problem in computer vision, with applications ranging from weakly supervised localisation to understanding hidden effects in the data. In recent years, approaches based on interpreting a previously trained neural network classifier have become the de facto state-of-the-art and are commonly used on medical as well as natural image datasets. In this paper, we discuss a limitation of these approaches which may lead to only a subset of the category specific features being detected. To address this problem we develop a novel feature attribution technique based on Wasserstein Generative Adversarial Networks (WGAN), which does not suffer from this limitation. We show that our proposed method performs substantially better than the state-of-the-art for visual attribution on a synthetic dataset and on real 3D neuroimaging data from patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD). For AD patients the method produces compellingly realistic disease effect maps which are very close to the observed effectsShow mor
Chapter, 2018
Publication:2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 201806, 8309
Publisher:2018

Peer-reviewed
Comparison between W2 distance and Ḣ−1 norm, and Localization of Wasserstein distance★
Author:Rémi Peyre
Summary:It is well known that the quadratic Wasserstein distance W2(⋅, ⋅) is formally equivalent, for infinitesimally small perturbations, to some weighted H−1 homogeneous Sobolev norm. In this article I show that this equivalence can be integrated to get non-asymptotic comparison results between these distances. Then I give an application of these results to prove that the W2 distance exhibits some localization phenomenon: if μ and ν are measures on ℝn and ϕ: ℝn → ℝ+ is some bump function with compact support, then under mild hypotheses, you can bound above the Wasserstein distance between ϕ ⋅ μ and ϕ ⋅ ν by an explicit multiple of W2(μ, ν)Show more
Article, 2018
Publication:ESAIM: Control, Optimisation and Calculus of Variations, 24, 201810, 1489
Publisher:2018

Wasserstein Center 손실을 이용한 스케치 기반 3차원 물체 검색
Authors:지명근, 전준철, 김남기, Myunggeun Ji, Junchul Chun, Namgi Kim
Summary:스케치 기반 3차원 물체 검색은 다양한 3차원 물체를 사람이 손으로 그린 스케치를 질의(query)로 사용하여 물체를 편리하게 검색하는 방법이다. 본 논문에서는 스케치 기반 3차원 물체 검색을 위해 스케치 CNN(Convolutional Neural Network)과 Wasserstein CNN 모델에 Wasserstein Center 손실을 적용하여 물체의 검색 성공률을 향상시키는 새로운 방법을 제안한다. 제안된 Wasserstein Center 손실이란 각 물체의 클래스(category)의 중심을 학습하고, 동일한 클래스의 특징과 중심 간의 Wasserstein 거리가 작아지도록 만드는 방법이다. 이를 위하여 제안된 3차원 물체 검색은 다음의 단계로 수행된다. 첫 번째로, 3차원 물체의 특징은 3차원 물체를 여러 방향에서 촬영된 2차원 영상의 특징을 CNN을 이용하여 추출하고, 각 영상 특징의 Wasserstein 중심을 계산한다. 두 번째로, 스케치의 특징은 별도의 스케치 CNN을 이용하여 추출하였다. 마지막으로, 추출한 3차원 물체의 특징과 스케치의 특징을 본 논문에서 제안한 Wasserstein Center 손실을 이용하여 학습하고 스케치 기반의 3차원 물체 검색에 적용하였다. 본 논문에서 제안한 방법의 우수성을 입증하기 위하여 SHREC 13과 SHREC 14의 두 가지 벤치마크 데이터 집합을 이용하여 평가하였으며, 제안된 방법이 기존의 스케치 기반 검색방법들과 비교하여 모든 측정 기준에서 우수한 결과를 나타냄을 확인할 수 있었다.

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using human-drawn sketches as query. In this paper, we propose a new method of using Sketch CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search. Specifically, Wasserstein center loss is a method of learning the center of each object category and reducing the Wasserstein distance between center and features of the same category. To do this, the proposed 3D object retrieval is performed as follows. Firstly, Wasserstein CNN extracts 2D images taken from various directions of 3D object using CNN, and extracts features of 3D data by computing the Wasserstein barycenters of features of each image. Secondly, the features of the sketch are extracted using a separate Sketch CNN. Finally, we learn the features of the extracted 3D object and the features of the sketch using the proposed Wasserstein center loss. In order to demonstrate the superiority of the proposed method, we evaluated two sets of benchmark data sets, SHREC 13 and SHREC 14, and the proposed method shows better performance in all conventional metrics compared to the state of the art methodsShow more
Downloadable Article, 2018
Publication:Journal of Internet Computing and Services = 인터넷정보학회논문지, 19, 2018년, 91
Publisher:2018

2018

Unsupervised and semi-supervised learning with Categorical Generative Adversarial Networks assisted by Wasserstein distance for dermoscopy image Classification
Authors:Yi, Xin (Creator), Walia, Ekta (Creator), Babyn, Paul (Creator)
Summary:Melanoma is a curable aggressive skin cancer if detected early. Typically, the diagnosis involves initial screening with subsequent biopsy and histopathological examination if necessary. Computer aided diagnosis offers an objective score that is independent of clinical experience and the potential to lower the workload of a dermatologist. In the recent past, success of deep learning algorithms in the field of general computer vision has motivated successful application of supervised deep learning methods in computer aided melanoma recognition. However, large quantities of labeled images are required to make further improvements on the supervised method. A good annotation generally requires clinical and histological confirmation, which requires significant effort. In an attempt to alleviate this constraint, we propose to use categorical generative adversarial network to automatically learn the feature representation of dermoscopy images in an unsupervised and semi-supervised manner. Thorough experiments on ISIC 2016 skin lesion chal- lenge demonstrate that the proposed feature learning method has achieved an average precision score of 0.424 with only 140 labeled images. Moreover, the proposed method is also capable of generating real-world like dermoscopy imagesShow more
Downloadable Archival Material, 2018-04-10
Undefined
Publisher:2018-04-10

Generative Modeling Using the Sliced Wasserstein Distance
Authors:Deshpande I., Schwing A., Zhang Z., 31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
Article, 2018
Publication:Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2018 12 14, 3483
Publisher:2018

2018 zzz

[CITATION] Eustasio del Barrio, Juan A Cuesta-Albertos, and Carlos Matrán. Wide consensus aggregation in the Wasserstein space. application to location-scatter …

P CAlvarez-Esteban - Bernoulli, 2018