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Vaserstein   without Math. Reviews  1980-2017   8   items

Leonid Vaserstein Interview

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: ... 


关于一个 Vaserstein 问题  [About a Vaserstein question]

张兆基 - 浙江大学学报: 自然科学版, 1994 - cqvip.com


Dennis–Vaserstein type decompositions

Journal of Mathematical Sciences (2010) 171: 331-337 , November 17, 2010

By  Vavilov, N. A.; Sinchuk, S. S.. Zbl 1215.20049



On asymptotics of Vaserstein's coupling for a Markov chain 

File Format: PDF/Adobe Acrobat  

by OA Butkovsky - 

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

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
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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

[pdf] On asymptotics for Vaserstein coupling of a Markov chain


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 ...


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


Транспортная задача Монжа-Канторовича, пространство Васерштейна и его геометрия

[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.


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)






Wasserstein  1973-1989  without Math. Reviews   43items




代数的 K 群に関する Wasserstein の仕事 (Analytic Varieties 及び ...

(Problems on Stratified Spaces and Analytic Varieties) Wasserstein work on algebraic group RIMS Kokyuroku 0372, 99-101, 1979-12 Kyoto University

AOMOTO KAZUHIKO  Nagoya University of Liberal Arts


Addendum: Calculation of the Wasserstein Distance between Probability Distributions on the Line  

S.S. Vallander

Theory Probab. Appl. 26 435 (1982)  


Lp-Wasserstein-Metriken [Lp-Wasserstein-Metriken] und  Approximationen stochastischer Differentialgleichungen

Matthias Gelbrich,  1989 154 pages



Wasserstein  1990-1993  without Math. Reviews  6 items


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 ...


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,


Skorhod representation theorem and Wasserstein metrics

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


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


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 ...

Cited by 1 - Related articles - Cached - All 2 versions


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





Wasserstein  1994-1999  without Math. Reviews  6 items


[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


 

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 small prime factors of a uniformly distributed integer: total variation and Wasserstein metrics

R Arratia - 1996 - Manuscrit 

Cited by 2 - Related articles

Independence of prime factors: total variation and Wasserstein metrics, insertions and deletions, and the Poisson-Dirichlet process. In preparation since March 1996, currently 70 pages.


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


[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 ...

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published 2004


Shape recognition via Wasserstein distance

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. ...





Wasserstein  2000-2003  without Math. Reviews   7 items


Testing for Weibull scale families as a test case for Wasserstein correlation tests [Discussion of del Barrio, Cuesta-Albertos and Matran]

S Csorgo - , Test 9 (2000), pp. 54-70.

Cited by 2 - Related articles

(Discussion of 

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) }


[PDF] Mixed L2-Wasserstein Optimal Mapping Between Prescribed Densities Functions

[PDF] from psu.eduJDBY Brenier - 2000 - Citeseer

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 ...

Related articles - View as HTML - All 3 versions


[CITATION] Wasserstein-metric

 L. Rüschendorf, “Wasserstein metric”, in Hazewinkel Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, 2001.

Cited by 10 - Related articles

Wasserstein-metric - Abteilung für Mathematische …

Wasserstein-metric The ‘Wasserstein-metric’ has a colourful history with several quite dierent fields of appli-cations. It also has various historical sources. Bernulli 11(1) 2005, 131-189



[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

Del Barrio , Giné , Utzet : Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances.


[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 –


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 ... 


Goodnes-of-fit tests for location and scale families based on a weighted L 2-Wasserstein distance measure

T De Wet - Test, 2002 - Springer

Abstract 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 theL 2-Wasserstein distance. They derive 

the limiting distribution of these statistics and show that the normal distribution is the only ...

Cited by 20 Related articles All 7 versions Cite





Wasserstein  2004-2005 without Math. Reviews  16 items 


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 ...


Contractivity of Wasserstein-type distances: 

 asymptotic profiles, equilibration rates and qualitative properties.

File Format: PDF/Adobe Acrobat

José A. Carrillo. Instituci`o Catalana de. Recerca i ...

Paris 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 ...


[pdf]  Gradient Flows: In Metric Spaces and in the Space of Probability ...

[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures

LANGG Savare - 2004 - Birkhäuser

2005 by L Ambrosio, N Gigli, G

DF]Review on the book Gradient flows in metric spaces and in the space ...

by W Gangbo - ‎2006 - ‎Related articles

The first part is about nonsmooth analysis and ordinary differential equations on metric spaces. The tools developed in this first part apply mainly to gradient flow differential equations. ... The second part focuses on some particular metric spaces, the set of probability measures, endowed with a Wasserstein distance.


A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces

[PDF] from cnr.itU Gianazza, G Savaré… - Preprint, Universita di Pavia, Italy, 2004 - imati.cnr.it

Page 1. A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein

spaces Giuseppe Savar ´e ... Page 2. Plan 1. The fourth order equation and its structure 2. Gradient

flows and Wasserstein distance 3. Main results and ideas involved in the proof ... 

Cited by 11 - Related articles - View as HTML - All 3 versions


[CITATION] A fourth order parabolic equation and the Wasserstein distance

U Gianazza, G Toscani, G Savaré - Preprint IMATI-CNR, Pavia, 2004

 U. Gianazza, G. Toscani, and G. Savaré, A fourth order parabolic

equation and the Wasserstein distance, tech. rep., IMATI-CNR, Pavia, 2004.

to appear.



Wasserstein metrics and empirical distributions in stability of stochastic programs

[PDF] from jcu.czM Houda - … of the International Conference Quantitative Methods …, 2004 - ef.jcu.cz

Abstract Practical economic problems often ask for optimization procedures, not 

unfrequently with random inputs leading thus to stochastic programming models. The 

randomness is modelled through the underlying probability distribution, which is assumed ...

Cited by 2 - Related articles - View as HTML


Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

[PDF] from cmu.eduL 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 ...

Cited by 1 - Related articles - View as HTML - All 5 versions


基于 Wasserstein 距离的目标识别中的研究

[Research for image recognition based on Wasserstein distance]

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

[摘要]: 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 ...

Wasserstein distance of target recognition research based




[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



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 ...

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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) 

Cited by 270 Related articles All 18 versions MR2209130 (2006j:76121) C


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 ...

Cited by 2 - Related articles - All 7 versions


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 ...

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 [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








2006 without Math. Reviews   15  items 


Path functionals over Wasserstein spaces

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 …

Cited by 56 Related articles All 7 versions

[PDF] semanticscholar.org     MR2250166 (2007j:49051)


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 …

Cited by 22 Related articles All 13 versions   MR2274850 (2008f:62025) 

[PDF] psu.edu


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 …

Cited by 18 Related articles All 12 versions    MR2287892 (2007k:35315) 


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  


A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data

[PDF] from turingbirds.comA Irpino… - Data Science and Classification, 2006 - Springer

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 variables. In the ...

Cited by 69 Related articles All 14 versions


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 ...

Cited by 46 Related articles All 6 versions


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 ...

Cited by 14 Related articles All 15 versions


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 ...

Related articles All 3 versions


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,

Related articles All 2 versions


[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

Related articles All 8 versions


Wasserstein distance on configuration space

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)


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 ...

Cited by 126 Related articles All 22 versions

U Gianazza, G Savaré, G Toscani - Archive for rational mechanics and …, 2009 - Springer



[CITATION] Diffusion is a 2-Wasserstein contraction on any manifold evolving by reverse Ricci flow

RJ McCann… - Preprint, 2006

Cited by 2 - Related articles

RICCI FLOW, ENTROPY AND OPTIMAL TRANSPORTATION 1 ...

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 πΓ(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

F Bolley - Lecture Notes in Math, 2006   pdf 



2007 without Math. Reviews 15  items



. 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)



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)



arXiv:math/0006044 [pdf, ps, other]

Particle Approximation of the Wasserstein Diffusion

Sebastian Andres, Max-K. von Renesse

(Submitted on 14 Dec 2007)



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    


Wasserstein Space and Fokker-Planck Equation

S Fang - 2007 Wiley China  诗赞

Fang Shi-Chan -Wasserstein Space and Fokker-Planck Equation



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 ...


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. ...


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 ...


 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,+∞).( ...


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



2008 without Math. Reviews  19 items 




 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)


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)


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)


arXiv:0801.2250 [pdf, ps, other]

On Wasserstein geometry of the space of Gaussian measures

Asuka Takatsu

Comments: 15pages, 1figures

Subjects: Differential Geometry (math.DG); Probability (math.PR)




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


On Wasserstein geometry of the space of Gaussian measures

[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 ...


Eulerian calculus for the displacement convexity in the Wasserstein distance

[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 ...


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 ...


[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 ...


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 ...





2009 without Math. Reviews  17 items


Title: Non-monotone Convergence in the Quadratic Wasserstein Distance 

Author(s): Schachermayer, W; Schmock, U; Teichmann, J

Source: SEMINAIRE DE PROBABILITES XLII   Volume: 1979   Pages: 131-136   Published: 2009 


Title: Local Histogram Based Segmentation Using the Wasserstein Distance

Author(s): Ni, K; Bresson, X; Chan, T, et al.

Source: INTERNATIONAL JOURNAL OF COMPUTER VISION   Volume: 84   Issue: 1   Pages: 97-111   Published: 2009 

 Cited by 181 Related articles All 24 versions



A Wasserstein approach to the one-dimensional sticky particle system

[PDF] from arxiv.orgL Natile… - Arxiv preprint arxiv:0902.4373, 2009 - arxiv.org

Abstract. We present a simple approach to study the one–dimensional pressureless Euler system 

via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic 

moments. Starting from a discrete system of a finite number of “sticky” particles, we obtain ...


[PDF] Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

[PDF] from sns.itS Lisini - ESAIM Control Optim. Calc. Var, 2009 - cvgmt.sns.it

Abstract 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 ...

Cited by 26 Related articles All 16 versions


Estimates on path functionals over Wasserstein spaces

[PDF] from sissa.itS Bianchini… - 2009 - digitallibrary.sissa.it

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] $\ mathcal {G} _ {r, p} $ 

defined on Lipschitz curves $\ gamma $ valued in the $ p $-Wasserstein space. The ...


Non-monotone convergence in the quadratic Wasserstein distance

[PDF] from arxiv.orgW Schachermayer, U Schmock… - Séminaire de Probabilités …, 2009 - Springer

Summary. We give an easy counterexample to Problem 7.20 from C. Villani's book on mass 

transport: in general, the quadratic Wasserstein distance between n-fold normalized 

convolutions of two given measures fails to decrease monotonically.


Wasserstein distance for the fusion of multisensor multitarget particle filter clouds

[PDF] from isif.orgD Danu, T Kirubarajan… - Information Fusion, 2009. …, 2009 - ieeexplore.ieee.org

12th International Conference on Information Fusion Seattle, WA, USA, July 6-9, 2009

Abstract 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 ...


Wasserstein geometry of non-linear Fokker-Planck type equations

[PDF] from kyoto-u.ac.jp東北大学大学院理学研究科高津飛鳥 - 数理解析研究所講究録, 2009 - kurims.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 ...

Cited by 1 - Related articles - View as HTML - All 3 versions


Hamiltonian systems and the calculus of differential forms on the Wasserstein space

[PDF] from gatech.eduHK 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 ...

Georgia Institute of Technology,


Gromov-Wasserstein stable signatures for object matching and the role of persistence

[PDF] from stanford.eduF Mémoli - math.stanford.edu

Page 1. 1 Gromov-Wasserstein stable signatures for object matching and the role of persistence

Facundo Mémoli memoli@math.stanford.edu Page 2. 2 ... tiants. Page 28. 19 Construction of the

Gromov-Wasserstein distance(s) mm-spaces and their invariants Page 29. 3/4 1/4 1 1/2 ...


Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations cieulike

M Hairer… - 2009 - citeulike.org

Abstract 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 ...

aarXiv:math/0602479 [pdf, ps, other]


Numerical Algorithm for Computation of the 2-Wasserstein Distance, and Applications to the Foundations of Diffusion

[PDF] from tue.nlS Srivastava, MA Peletier - 2009 - alexandria.tue.nl


Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance

[PDF] from arxiv.orgA Xia… - Journal of Theoretical Probability, 2009 - Springer Aihua Xia, Fuxi Zhang

Abstract The polynomial birth–death distribution (abbreviated, PBD) on ={0, 1, 2,…} or 

={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} ...


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

... 論文名, 著者名, 著者所属, 刊行物名, ISSN, , , 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. 

Mathematical Institute, Tohoku University   RIMS Kokyuroku 1671, 20-36, 2009-12


Wasserstein distance for the fusion of multisensor multitarget particle filter clouds

[PDF] from isif.orgD Danu, T Kirubarajan… - Information Fusion, 2009. …, 2009 - ieeexplore.ieee.org

Abstract 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 ...

12th International Conference on Information Fusion Seattle, WA, USA, July 6-9, 2009


Local histogram based segmentation using the Wasserstein distance

[PDF] from escholarship.orgK Ni, X Bresson, T Chan… - International journal of computer …, 2009 - Springer

Abstract 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 ...


Spectral Gromov-Wasserstein distances for shape matching

[PDF] from stanford.eduF Mémoli - … Vision Workshops (ICCV Workshops), 2009 IEEE …, 2009 - ieeexplore.ieee.org

Abstract 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 ...




2010 not in Math. Reviews  26  items  


[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


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)


On Wasserstein Geometry of Gaussian Measures (A Takatsu) in

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)


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 ...


[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.


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 

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 ...


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 ...


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 ...


Wasserstein distance based local energy model of segmentation

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 ...



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 ...


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.


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 ...


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]). ...

publ. 2012


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


Wasserstein Barycenter and its Application to Texture Mixing

R Julien, G Peyré, J Delon… - 2010 - hal.archives-ouvertes.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 ...

Book Editor(s): Bruckstein, AM; Romeny, BMT; Bronstein, AM; 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

Source: SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION  Book Series: Lecture Notes in Computer Science   Volume: 6667   Pages: 435-446   Published: 2012



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] 2007



 基于 Wasserstein 距离的局部能量分割模型

[PDF] from 210.29.99.10钱晓华, 树旭… - 电子学报, 2010 - 210.29.99.10

Wasserstein distance based local energy model of segmentation 

by Qian,  Gio, and Li





2011  not in Math. Reviews  41 items  






[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

Related articles All 2 versions

 

[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

Cited by 3 Related articles

[PDF] archives-ouvertes.fr


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)


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- ...

Cited by 2 Related articles All 3 versions


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 ...


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 ...


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 ...


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 ...


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 ...


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 


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 ...

MR 2013


Functional inequalities for the Wasserstein Dirichlet Form

[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 ... 


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 ...


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


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 ...

Related articles All 8 versions


Kantorovich-Rubinstein-Wasserstein Lp-距离 (p> 2)  银芳 - 科技信息, 2011 - cqvip.com

SHEN Yin Fong

Kantorovich-Rubinstein-Wasserstein Lp-distance (p> 2)

 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


Cahn-hilliard and thin film equations as gradient flow in wasserstein-like metrics

[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 ...


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 ...


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 ...


Distribution's template estimate with Wasserstein metrics

[PDF] from arxiv.orgE Boissard, TL Gouic… - Arxiv preprint arXiv:1111.5927, 2011 - arxiv.org

Abstract: 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 ...

 Bernoulli 21 (2015), no. 2, 740–759.


Barycentre de Wasserstein  J RABIN, G PEYRÉ… - smai.emath.fr

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 ...


Wasserstein barycenter and its application to texture mixing

[PDF] from google.comJ Rabin, G Peyré, J Delon… - Proc. of SSVM, 2011 - sites.google.com

Abstract. 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 ...



Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

[PDF] from arxiv.orgF Bolley, I Gentil… - Arxiv preprint arXiv:1110.3606, 2011 - arxiv.org

Abstract: 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 ...

Related articles - All 6 versions






2012  not in Math. Reviews   39 items



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.


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 ...


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] Further Results on Probabilistic Model Validation in Wasserstein Metric

A Halder, R Bhattacharya - 51st IEEE Conference on Decision …, 2012 - people.tamu.edu

Abstract—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, ...

View as HTML  [PDF] from arxiv.org


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 ...

Related articles - All 6 versions  [PDF] from harvard.edu


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 ...

Cited by 1 - Related articles [PDF] from uvic.ca 


[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 ...

Related articles - View as HTML [PDF] from arxiv.org MR2887832

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 ...

[PDF] from arxiv.org

Archive for Rational Mechanics and Analysis, 2014


Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

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 ...

Cited by 1 - Related articles - All 9 versions


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 ...

[PDF] from arxiv.org

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]

… - 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

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. 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, 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.


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]


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 ...


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 ...


[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 ...



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] An extension of the Weak KAM theory to the Wasserstein torus

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 ...


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 ...


二元离散antorovich-Rubinstein-Wasserstein L2-距离的精确表示在线 ...

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


Testes de similaridade na distância de Mallows-Wasserstein ponderada para distribuições de cauda pesada

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


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 ...


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 ...





2013 not in Math Reviews 54 items


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)

K KUWADA - RIMS Kokyuroku Bessatsu, 2013 - ci.nii.ac.jp

... ISSN, , , 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 ...


Entropic Gradient Flows on the Wasserstein Space via Large Deviations from Thermodynamic Limits

V Laschos - 2013 - opus.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 ...

University of Bath (United Kingdom),


On the rate of convergence in Wasserstein distance of the empirical measure

N Fournier, A Guillin - arXiv preprint arXiv:1312.2128, 2013 - arxiv.org

Abstract: 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 ...


[pdf]  On the rate of convergence in Wasserstein distance of the empirical measure

Nicolas Fournier  Arnaud Guillin  2013



The Wasserstein metric in Factor Analysis

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 ...


Application of the Wasserstein metric to seismic signals

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 ...

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 ...


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


[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.


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


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


[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 ...


[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 ...

RIMS Kôkyûroku Bessatsu.


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



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 ...


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- ...


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 ...


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 ...


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 ...


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 ...


[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


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 ...


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 ...


[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 ...


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 ...


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 :




2014  53 items  


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


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 ...

Related articles All 2 versions Cite Save

[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...


The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

D Han-Kwan, M Iacobelli - arXiv preprint arXiv:1412.4023, 2014 - arxiv.org

Abstract: 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 ...


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)) ...


[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 ...


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


Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem Fabio Cavalletti Geometric and Functional Analysis

January 2014


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 ...


[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 ...

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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 ...


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 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 ...

Cited by 1 Related articles All 9 versions Web of Science: 1 Cite Save

[PDF] from 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

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 ...


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 ...

Cited by 1 Related articles All 5 versions Cite Save More

[PDF] from arxiv.org


Zbl 06804337

Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement

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 ...


[PDF] from arxiv.org

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


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 ...

[PDF] from arxiv.org


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 ...

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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 ...

[PDF] from arxiv.org


Transport equation with source and generalized Wasserstein distance

B Piccoli - NETCO 2014-New Trends in Optimal Control, 2014 - hal.inria.fr

Résumé: 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. ...

[PDF] from kyoto-u.ac.jp


[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 ...

[PDF] from arxiv.org


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. ...

[PDF] from arxiv.org


The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds arXiv

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 ...

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[PDF] from arxiv.org



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 ...

Related articles All 2 versions Cite Save More

[PDF] from uc.cl


[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.

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Evolution in Measure Spaces with Wasserstein Distance

E Cristiani, B Piccoli, A Tosin - Multiscale Modeling of Pedestrian Dynamics

MS&A Volume 12, 2014, pp 169-194  - Springer

Abstract 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 ...

Cite Save More


[PDF] from arxiv.org

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one arXiv

J Dedecker, A Fischer, B Michel - arXiv preprint arXiv:1404.0646, 2014 - arxiv.org

Abstract: 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\ geq 1$. The d

istribution of the errors is assumed to be ...

 Electron. J. Stat. 9 (2015), 234–265. 


[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, , , 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). ...

Cite Save More


[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 ...

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On curvature conditions using Wasserstein spaces

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 ...

On Curvature Conditions Using Wasserstein Spaces

Martin Kell - 2014  100 pages


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 ...

Cited by 1 Related articles All 6 versions Cite Save

[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



2015  60  publications  


[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 ...


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 ...


Decomposition of the Kantorovich problem and Wasserstein distances on simplexes arXiv

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 arXiv

J 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 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 ...


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 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 ...


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

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 ...


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 ...


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.


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 ...

MR3399536 


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


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 ...


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

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 ...


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- ...


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

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 ...


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 $\ ...


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.


Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

PM Esfahani, D Kuhn - arXiv preprint arXiv:1505.05116, 2015 - arxiv.org

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 ...


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) ...


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 ...


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 ...



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 ...


2015arXiv150302533C

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 ...


 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 ...


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 ...


2015arXiv150104437K

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 ...

Related articles All 16 versions Cite Save


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 ...


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 ...

Related articles All 6 versions Cite Save


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, …, 2015



 "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




————————————

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.

——————————————————

2016 Wasserstein  not in Math Reviews  65 items 

arXiv:1612.05075 [pdf, other]

Application of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion

Yunan Yang, Björn Engquist, Junzhe Sun, Brittany D. Froese


arXiv:1611.04323 [pdf, ps, other]

Central Limit Theorem and bootstrap procedure for Wasserstein's variations with application to structural relationships between distributions

Eustasio Del Barrio, Hélène Lescornel (IMT), Jean-Michel Loubes (IMT)


[PDF] 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.


Interpretation 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 Wasserstein


[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.


Geometric construction of Wasserstein Barycenters

N Bonneel, J Digne - 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


A dimensional Wasserstein contraction characterizing the curvature ... pdf

A dimensional Wasserstein contraction characterizing the curvature-dimension condition. Kazumasa Kuwada. (Tokyo Institute of Technology). (Joint work with F. Bolley, I. Gentil and A. Guillin). Stochastic Analysis and Applications (Tohoku University) Aug. 31–Sept. 4, 2015 ...

[CITATION] A dimensional Wasserstein contraction characterizing the curvature-dimension condition

桒田和正 - … Wasserstein contraction characterizing the curvature …, 2016 - t2r2.star.titech.ac.jp

... Home >. news ヘルプ. 論文・著書情報. タイトル, 和文: A dimensional Wasserstein contraction

characterizing the curvature-dimension condition. 英文: A dimensional Wasserstein contraction

characterizing the curvature-dimension condition. 著者, 和文: 桒田和正. 英文: Kazumasa Kuwada.


[PDF] Matricial Wasserstein and Unsupervised Tracking

L Ning, R Sandhu, TT Georgiou, A Tannenbaum - ee.umn.edu

Abstract 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


Refined basic couplings and Wasserstein-type distances for SDEs with L\'{e} vy noises

D Luo, J Wang - arXiv preprint arXiv:1604.07206, 2016 - adsabs.harvard.edu

Abstract 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 (SDE) $ $ d X_t= d Z_t+ b (X_t)\, dt, $ $ where $(Z_t) _ {t\ ge0} $ is a pure jump 

Cited by 1 Related articles All 2 versions Cite Save


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

Abstract: We consider an iterated function scheme composed of k contractions on the unit 

interval with disjoint images. We find the first Kantorovich-Wasserstein distance between the 

two stationary measures associated to the iterative function schemes when we choose two


[PDF] Learning in Wasserstein Space

J Ye - pdfs.semanticscholar.org

ABSTRACT 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,


Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry arXiv

AB Kashlak - arXiv preprint arXiv:1610.08405, 2016 - arxiv.org

Abstract: 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


[HTML] Wasserstein Barycentric Coordinates: Histogram Regression Using Optimal Transport

N Bonneel, G Peyré, M Cuturi, F Mazenc… - ACM Transactions on …, 2016 - team.inria.fr

article IEEE Transactions on Industrial Electronics, Institute of Electrical and Electronics 

Engineers, 2015, IEEE Transactions on Industrial Electronics, pp. 2.< http://ieeexplore. ieee. 

org/xpl/articleDetails. jsp? arnumber= 7115092&searchWithin% 5B% 5D=% 22Authors% ...

ACM TRANSACTIONS ON GRAPHICS   Volume: 35   Issue: 4     Published: JUL 2016


基于 Wasserstein 距离和 SBGFRLS 方法的活动轮廓模型图像分割算法

[ Image segmentation algorithm of active contour model based on Wasserstein distance and Sbgfrls method '

王瑜, 闫沫 - 西安航空学院学报, 2016 - cqvip.com

摘要: 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 ...


Baricentros en 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 ...


[PDF] Regularized Wasserstein barycenter

E Cazelles, J Bigot, N Papadakis - papersjds16.sfds.asso.fr

Abstract. 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 ...


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

Abstract: 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 ...

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The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances arXiv

J Zinsl - arXiv preprint arXiv:1603.01375, 2016 - arxiv.org

Abstract: 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 ...

arXiv:1603.01375 [math.AP]

By: Zinsl, Jonathan

Conference: PDE Workshop on Theory and Applications of Partial Differential Equations Location: Weierstrass Inst, Berlin, GERMANY Date: NOV 30-DEC 04, 2015

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S   Volume: 10   Issue: 4   Pages: 919-933   Published: AUG 2017



Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem arXiv

E Bandini, A Cosso, M Fuhrman, H Pham - arXiv preprint arXiv: …, 2016 - arxiv.org

Abstract: We study a stochastic optimal control problem for a partially observed diffusion. By 

using the control randomization method in [4], we prove a corresponding randomized 

dynamic programming principle (DPP) for the value function, which is obtained from a flow ...


Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls arXiv

GA Hanasusanto, D Kuhn - arXiv preprint arXiv:1609.07505, 2016 - arxiv.org

Abstract: 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- ...


[HTML] 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, A Mathieu, A Quérel - Tellus B, 2016 - tellusb.net

ABSTRACT 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 ...


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

Abstract: 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 ...


Robust k-barycenters in Wasserstein Space and Wide Consensus Clustering arXiv

E del Barrio, JA Cuesta-Albertos, C Matrán… - arXiv preprint arXiv: …, 2016 - arxiv.org

Abstract: A robust clustering method for probabilities in Wasserstein space is introduced. 

This newtrimmed $ k $-barycenters' approach relies on recent results on barycenters in 

Wasserstein space that allow intensive computation, as required by clustering algorithms. ...


Wasserstein Loss for Image Synthesis and Restoration

G Tartavel, G Peyré, Y Gousseau - 2016 - hal.archives-ouvertes.fr

This paper presents a novel variational approach to impose statistical constraints to the 

output of both image generation (to perform typically texture synthesis) and image 

restoration (for instance to achieve denoising and super-resolution) methods. The ...


Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line arXiv

J Bigot, R Gouet, T Klein, A López - arXiv preprint arXiv:1606.03933, 2016 - arxiv.org

Abstract: This paper is focused on the statistical analysis of probability densities functions $ 

f_ {1},\ ldots, f_ {n} $ on $\ R $ that can be viewed as independent realizations of an 

underlying stochastic process. We consider the situation of practical importance where the ...

Cite Save


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

Abstract. 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 ...


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

Abstract: 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 ...


Exponential convergence in Lp‐Wasserstein distance for diffusion processes without uniformly dissipative drift

D Luo, J Wang - Mathematische Nachrichten, 2016 - Wiley Online Library

In this paper we consider the following Itô stochastic differential equation dXt= σ dBt+ b (Xt) 

dt,(1.1) where (Bt) t≥ 0 is a standard d-dimensional Brownian motion, σ Rd× d is a non-

degenerate constant matrix, and b: Rd Rd is a Borel measurable vector field. Recently ...


Regularization of barycenters in the Wasserstein space

J Bigot, E Cazelles, N Papadakis - arXiv preprint arXiv:1606.01025, 2016 - arxiv.org

Abstract: The concept of barycenter in the Wasserstein space allows to define a notion of 

Fr\'echet mean of a set of probability measures. However, depending on the data at hand, 

such barycenters may be irregular. In this paper, we thus introduce a convex ...


Sample Out-Of-Sample Inference Based on Wasserstein Distance

J Blanchet, Y Kang - arXiv preprint arXiv:1605.01340, 2016 - arxiv.org

Abstract: 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- ...


A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

J Bertrand, BR Kloeckner - … Mathematics Research Notices, 2016 - imrn.oxfordjournals.org

Abstract Given a metric space $ X $, one defines its Wasserstein space ${\ mathscr {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 ...


A Simulated Annealing based Inexact Oracle for Wasserstein Loss Minimization arXiv

J Ye, JZ Wang, J Li - arXiv preprint arXiv:1608.03859, 2016 - arxiv.org

Abstract: Learning under a Wasserstein loss is an emerging research topic. We call 

collectively the problems formulated under this framework Wasserstein Loss Minimization 

(WLM). One important appeal of WLM is the innate capability to account for the prior ...


A Weighted Approximation Approach to the Study of the Empirical Wasserstein Distance

DM Mason - High Dimensional Probability VII, 2016 - Springer

High Dimensional Probability VII pp 137-154 |

Abstract We shall demonstrate that weighted approximation technology provides an effective 

set of tools to study the rate of convergence of the Wasserstein distance between the 

cumulative distribution function [cdf] and the empirical cdf

HIGH DIMENSIONAL PROBABILITY VII: THE CARGESE VOLUME   Book Series: Progress in Probability   Volume: 71   Pages: 137-154   Published: 2016


Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost

A Halder, EDB Wendel - American Control Conference (ACC), …, 2016 - ieeexplore.ieee.org

Abstract: 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 ...

2016 AMERICAN CONTROL CONFERENCE (ACC)   Book Series: Proceedings of the American Control Conference   Pages: 7249-7254   Published: 2016


[HTML] The Wasserstein Metric and Robustness in Risk Management

R Kiesel, R Rühlicke, G Stahl, J Zheng - Risks, 2016 - mdpi.com

Risks 2016, 4(3), 32; doi:10.3390/risks4030032

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, ...


A fixed-point approach to barycenters in Wasserstein space

PC Alvarez-Esteban, E del Barrio… - Journal of Mathematical Analysis  2016 - Elsevier

Volume 441, Issue 2, 15 September 2016

Abstract Let P 2, ac P 2, ac be the set of Borel probabilities on R d 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 ...


Wasserstein Discriminant Analysis arXiv

R Flamary, M Cuturi, N Courty… - arXiv preprint arXiv: …, 2016 - arxiv.org

Abstract: Wasserstein Discriminant Analysis (WDA) is a new supervised method that can 

improve classification of high-dimensional data by computing a suitable linear map onto a 

lower dimensional subspace. Following the blueprint of classical Linear Discriminant ...


{Euclidean, Metric, and Wasserstein} Gradient Flows: an overview arXiv

F Santambrogio - arXiv preprint arXiv:1609.03890, 2016 - arxiv.org

Abstract: 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 ...


$ W $-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds arXiv

S Li, XD Li - arXiv preprint arXiv:1604.02596, 2016 - arxiv.org

Abstract: 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 ...


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

Abstract: 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 ...


Euler sprays and Wasserstein geometry of the space of shapes

JG Liu, RL Pego, D Slepčev - arXiv preprint arXiv:1604.03387, 2016 - arxiv.org

Abstract: 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 ...


A Dual Representation of Functions on Wasserstein Spaces

Y Shen - arXiv preprint arXiv:1603.02882, 2016 - arxiv.org

Abstract: We prove a duality theorem of the Fenchel-Moreau type for convex and lower 

semicontinuous functions of probability measures on Polish spaces equipped with the 

Wasserstein metric of order 1. The derived dual representation is in form of its conjugate ...


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

Abstract 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 ...


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

Abstract: 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.


Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature

FY Wang - arXiv preprint arXiv:1603.05749, 2016 - arxiv.org

Abstract: 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 ...


Distributionally Robust Stochastic Optimization with Wasserstein Distance

R Gao, AJ Kleywegt - arXiv preprint arXiv:1604.02199, 2016 - arxiv.org

Abstract: Stochastic programming is a powerful approach for decision-making under 

uncertainty. Unfortunately, the solution may be misleading if the underlying distribution of the 

involved random parameters is not known exactly. In this paper, we study distributionally ...


[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 - enama.org

Abstract 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 ...


Refined basic couplings and Wasserstein-type distances for SDEs with L\'{e} vy noises

D Luo, J Wang - arXiv preprint arXiv:1604.07206, 2016 - adsabs.harvard.edu

Abstract 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 (SDE) $ $ d X_t= d Z_t+ b (X_t)\, dt, $ $ where $(Z_t) _ {t\ ge0} $ is a pure jump L\' ...


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]) ...


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 ...


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 ...

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] 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. ...


$ 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} $ ...


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 { ...


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 ...


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 ...


Using Gromov-Wasserstein distance to explore sets of networks

R Hendrikson - 2016 - dspace.ut.ee

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, ...

master thesis


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 ...


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.






2017  Wasserstein not in Math Reviews   155  items 


 

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]

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Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui 

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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

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[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

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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 - 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

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[HTML] Vers un théorème de la limite centrale dans l'espace de Wasserstein?

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

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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

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G CARLIER, I Journées - math.u-bordeaux.fr

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING   Volume: 112   Issue: 9   Pages: 1175-1193   Published: NOV 30 2017


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AN INTRINSIC PARALLEL TRANSPORT IN WASSERSTEIN SPACE

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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Volume: 145   Issue: 12   Pages: 5329-5340   Published: DEC 2017



Coupling and exponential ergodicity for stochastic differential equations driven by Levy processes

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS   Volume: 127   Issue: 12   Pages: 4083-4125   Published: DEC 2017



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


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 

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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


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



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


Sinkhorn-AutoDiff: Tractable Wasserstein Learning of Generative Models

… 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 …


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


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

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function 

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M Agueh, G Carlier - COMPTES …, 2017 - ELSEVIER FRANCE-EDITIONS …

Comptes Rendus Mathematique

Volume 355, Issue 7, July 2017, Pages 812-818

Vers un théorème de la limite centrale dans l'espace de Wasserstein ?



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


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. 

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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


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 

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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

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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

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arXiv:1712.07528 [pdf, ps, other]

Harmonic mappings valued in the Wasserstein space

Hugo Lavenant (LM-Orsay)

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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)

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Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

José A. Carrillo, Young-Pil Choi, Oliver Tse

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On reproduction of On the regularization of Wasserstein GANs

Junghoon Seo, Taegyun Jeon

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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.

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Wasserstein Distributional Robustness and   Regularization in Statistical Learning

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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 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


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

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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...

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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

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

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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


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 $$L^1$$


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...


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


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...


Automatic Color Correction for Multisource Remote Sensing Images with Wasserstein CNN

by Jiayi Guo; Zongxu Pan; Bin Lei; More...

Remote Sensing, 01/2017, Volume 9, Issue 5

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...

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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


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



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 Auto-Encoders

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...


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...

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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...


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...


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...


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 ...


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...


Improved Training of Wasserstein GANs    arXiv

by Gulrajani, Ishaan; Ahmed, Faruk; Arjovsky, Martin; More...

03/2017

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes...

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


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


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...


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...


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

by Whiteley, Nick

08/2017

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...


Sliced Wasserstein Kernel for Persistence Diagrams arXiv

by Carrière, Mathieu; Cuturi, Marco; Oudot, Steve

06/2017

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...


A canonical barycenter via Wasserstein regularization arXiv

by Kim, Young-Heon; Pass, Brendan

03/2017

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...


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

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


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...


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...


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...

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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...


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

Related articles All 3 versions



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.


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...

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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...


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 th


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...


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



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


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 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

We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability...


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...


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 Learning of Deep Generative Point Process Models 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


Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric arXiv

by Luo, Fengqiao; Mehrotra, Sanjay

04/2017

We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO...


Inferenc

e 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...


Fr\'echet Means and Procrustes Analysis in Wasserstein Space arXiv

by Zemel, Yoav; Panaretos, Victor M

01/2017

We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the...


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....


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 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 R....


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


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...

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Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment arXiv

by Hühnerbein, Ruben; Savarino, Fabrizio; Åström, Freddie; More...

10/2017

We introduce a novel approach to Maximum A Posteriori inference based on discrete graphical models. By utilizing local Wasserstein distances for co


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...

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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...

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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:

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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.



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: 2017,...

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, 2017 

Sponsor(s): IEEE; EMB; IEEE Signal Proc Soc

2017 IEEE 14TH INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING (ISBI 2017)   Pages: 520-524   Published: 2017




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

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Reports from University of British Columbia Highlight Recent Findings in Mathematics (Wasserstein barycenters over Riemannian manifolds)

Journal of Technology & Science, 10/2017

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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

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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

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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

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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, 04/2017

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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, 04/2017

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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, 04/2017

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Findings from M. Carfora et al Has Provided New Information about Mathematical Physics (The Wasserstein geometry of nonlinear sigma models and the Hamilton-Perelman Ricci flow)

Journal of Technology & Science, 03/2017

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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


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

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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...

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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 ...


Accelerated Discrete Distribution Clustering under Wasserstein Distance  ResearchGate

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. 



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

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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 ...


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

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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  XueqianFuaQinglaiGuoaHongbinSunaZhaoguangPanaWenXiongbLiWangb

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

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[pdf] Detecting changes in forced climate attractors with Wasserstein distance



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

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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)

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...

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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...

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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...

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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

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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...

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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...

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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...

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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...


Gromov-Hausdorff limit of Wasserstein spaces on point clouds arXiv

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...


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






2018 Wasserstein without MR  33  items




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 2018

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


Findings on Statistics Reported by A. Munk et al (Inference for empirical Wasserstein distances on finite spaces)

Journal of Technology & Science, 01/2018

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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

Cited by 2 Related articles All 3 versions

[PDF] arxiv.org


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,

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[PDF] arxiv.org


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

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[PDF] arxiv.org


Wasserstein-Riemannian Geometry of Positive-definite Matrices

L Malagò, L Montrucchio, G Pistone - arXiv preprint arXiv:1801.09269, 2018 - arxiv.org

Abstract: 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

[PDF] arxiv.org


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

All 2 versions  [PDF] arxiv.org


Characterization of probability distribution convergence in Wasserstein distance by -quantization error function

Y Liu - arXiv preprint arXiv:1801.06148, 2018 - arxiv.org

Abstract: We establish the condition for probability measure characterization by $ L^{p} $-

quantization error function in $\mathbb {R}^{d} $. There are two types of characterization: the 

static characterization for the identity of two probability measures, and the characterization

Related articles All 2 versions  [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

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

Related articles  [PDF] crest.science


[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

Related articles


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

Cited by 21 Related articles

[PDF] arxiv.org


[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

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,

All 4 versions  [PDF] arxiv.org


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


[PDF] arxiv.org

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

All 2 versions  [PDF] arxiv.org


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


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

ABSTRACT 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

Cited by 7 Related articles All 5 versions  [PDF] openreview.net


[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,


[PDF] arxiv.org

Free complete Wasserstein algebras

R Mardare, P Panangaden, GD Plotkin - arXiv preprint arXiv:1802.07366, 2018 - arxiv.org

Abstract: We present an algebraic account of the Wasserstein distances $ W_p $ on 

complete metric spaces. 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

All 2 versions  [PDF] arxiv.org


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

All 2 versions


Generalised Wasserstein Dice Score for Imbalanced Multi-class Segmentation Using Holistic Convolutional Networks

J Ekanayake, N Kitchen, S Ourselin… - … Sclerosis, Stroke and …, 2018 - books.google.com

Abstract. 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

Related articles


Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

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


[PDF] arxiv.org

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-

All 2 versions  [PDF] arxiv.org


The existence of geodesics in Wasserstein spaces over path groups and loop groups

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

All 2 versions  [PDF] arxiv.org


Minimax Distribution Estimation in Wasserstein Distance

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

All 2 versions  [PDF] semanticscholar.org


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

Related articles All 2 versions  [PDF] arxiv.org


Stochastic Wasserstein Barycenters

S Claici, E Chien, J Solomon - arXiv preprint arXiv:1802.05757, 2018 - arxiv.org

Abstract: 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

All 2 versions  [PDF] arxiv.org

 

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


Wasserstein Auto-Encoders: Latent Dimensionality and Random Encoders

PK Rubenstein, B Schoelkopf, I Tolstikhin - 2018 - openreview.net

Paul Rubenstein, Bernhard Schölkopf, Ilya Tolstikhin Empirical Inference Max Planck Institute 

for Intelligent Systems, Tübingen {paul.rubenstein,bs,ilya}@tuebingen.mpg.de … We study the 

role of latent space dimensionality in Wasserstein auto-encoders (WAEs). Through experimentation


A note on 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

Abstract: In this note 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,

All 2 versions [PDF] arxiv.org


On the Latent Space of Wasserstein Auto-Encoders

PK Rubenstein, B Schoelkopf, I Tolstikhin - arXiv preprint arXiv …, 2018 - arxiv.org

Abstract: 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

All 2 versions [PDF] arxiv.org

 

Discrete Wasserstein Generative Adversarial Networks (DWGAN)

R Fathony, N Goela - 2018 - openreview.net

Abstract: 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] arxiv.org

On Wasserstein isometries of probability measures on unit spheres

D Virosztek - arXiv preprint arXiv:1802.03305, 2018 - arxiv.org

Abstract: We consider the space of all Borel probability measures on the unit sphere of a 

Euclidean space endowed with the Wasserstein metric $ W_p $ for arbitrary $ p\geq 1. $ Our 

goal is to describe the isometry group of this metric space. We make some progress in the

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138  items   + 41  (2011) + 39  (2012)     +   54  (2013)   + 53 (2014)  + 60  (2015) + 65 (2016) 

+  155   (2017) + 33  (2018) = 651  items  

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