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Vaserstein   without Math. Reviews   2 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: ... 


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



Wasserstein  1973-1989  without Math. Reviews   4 items


Calculation of the Wasserstein Distance Between Probability Distributions on the Line

Submitted: 05  April  1972 Theory of Probability & Its Applications Volume 18, Issue 4 1974 , 784–786. (3 pages) S. S. Vallender


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

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

... 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  7 items


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

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

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


关于一个 Vaserstein 问题

张兆基 - 浙江大学学: 自然科学版, 1994 - cqvip.com

们解答了一个Vasertein 的公开问题: 给定任意整数P, M, Z 中矩A, 是否存在M, Z 中矩X 

Y, 使得A= X+ Y, det (x)= p= det (y)? 们的解答是: n 为偶数, 侧答案总是肯定的; 而当n 

为奇数时, 则答案是肯定的当且仅当2p A 中所有元的最大公因数整除.



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


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 ...

Related articles - View as HTML - All 5 versions

published 2004


Shape recognition via Wasserstein distance

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

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


[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  Bernoulli Volume 11, Number 1 (2005), 131-189.


[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  15 items 


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 ...


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

LANGG Savare - 2004 - Birkhäuser


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


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

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 ...

All 12 versions Cite Save More


The Wasserstein Distance and its Behaviour along Geodesics

L Ambrosio, N Gigli, G Savaré - Gradient Flows: in Metric Spaces and in …, 2005 - Springer

In this chapter we endow Pp (X), when X is a separable Hilbert space, with a kind of 

differential structure, consistent with the metric structure introduced in the previous chapter. 

Our starting point is the analysis of absolutely continuous curves µt:(a, b) Pp (X) and of ...


[PDF] Contractions in the 2-wasserstein length space and thermalization of granular media, to appear in Archive for Rational Mechanics and Analysis (2005)

by José A. Carrillo , Robert J. Mccann , Cédric Villani

Abstract An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) — if uniformly controlled — will quantify contractivity (limit expansivity) of the flow. 

Published 2006 MR2209130 (2006j:76121) 


Optimal quantizer performance and the Wasserstein distortion

S Matloub, DB O'Brien… - … , 2005. Proceedings. DCC …, 2005 - ieeexplore.ieee.org

Abstract The Wasserstein distortion has proved useful in a variety of mathematical, signal 

processing and coding problems as a measure of how different two distributions are. In this 

paper we provide an expression for the performance of the optimal entropy constrained ...

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 ...

Related articles - View as HTML - All 2 versions


 [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   11  items 



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 ...


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 13 - Related articles - View as HTML - All 3 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 9 - Related articles - BL Direct - All 12 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 ...


Asymptotic power of goodness of fit tests based on Wasserstein distance

H Boistard - personales.unican.es

We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0, 

X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein 

test is based on the statistic: n ∫ 1 ... 0 (F−1 n (t) − F−1(t)) 2 dt − an,


[PDF] Absolutely continuous curves in Wasserstein spaces with applications to continuity equation and to nonlinear diffusion equations

S Lisini - 2006 - math.sns.it

Dottorato di ricerca in Matematica e Statistica ... 1.1 Absolutely continuous curves in metric spaces 

and metric derivative . . . . . 15 ... 1.3 Metric Sobolev spaces W1,p(I; X). . . . . . . . . . . . . . . . . . . . . 

. . . . 17 ... 1.4 Borel probability measures, narrow topology and tightness . . . . . . . . . . . 19


Wasserstein distance on configuration space

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 ...


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 ...



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

RJ McCann… - Preprint, 2006

Cited by 2 - Related articles


[CITATION] Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités

F Bolley - Lecture Notes in Math, 2006








2007 without Math. Reviews 11  items


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).


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


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  12 items 


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

[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 ...


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 


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 2 - Related articles - View as HTML - All 15 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 ...


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&# 45; &# 45; Stokes equations

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 ...


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  24 items  


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 ...


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


[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 ...


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 ...


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 ...


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  39  items  


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 ...


Régularisation de Wasserstein. Application au Transfert de Couleur

G Peyré, R Julien - 2011 - basepub.dauphine.fr

Résumé en français: Ce papier introduit une nouvelle approche méthodologique pour la 

résolution de problèmes variationnels sous contraintes statistiques en grande dimension. 

Nous nous plaçons dans le cadre de la théorie du transport optimal de Monge- ...


Large Deviations for a matching problem related to the $\ infty $-Wasserstein distance

J Trashorras - 2011 - hal.archives-ouvertes.fr

Abstract: Let (E, d) be a compact metric space, X=(X1,..., Xn,...) and Y=(Y1,..., Yn,...) two 

independent sequences of independent E-valued random variables and (LX n) n≥ 1 and 

(LY n) n≥ 1 the associated sequences of empirical measures. We establish a Large ...


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.


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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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, ...


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 ...


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 ...


Barycentre de Wasserstein  J RABIN, G PEYRÉ… - 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 ...


Deconvolution for the Wasserstein metric and geometric inference

[PDF] from archives-ouvertes.frC Caillerie, F Chazal, J Dedecker… -Electron. J. Statist. Volume 5 (2011), 1394-1423. - projecteuclid.org

Abstract Recently, Chazal, Cohen-Steiner and Mérigot have defined a distance function to 

measures to answer geometric inference problems in a probabilistic setting. According to 

their result, the topological properties of a shape can be recovered by using the distance ...


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   40 items


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 ...


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 $ ...


数据挖掘中区间数据模糊聚类研究——基于 Wasserstein 测度

… - 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, ...


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 ...


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 ...


Classification of periodic activities using the Wasserstein distance

L Oudre, J Jakubowicz, P Bianchi… - … , IEEE Transactions on, 2012 - ieeexplore.ieee.org

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 ...

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING  Volume: 59   Issue: 6   Pages: 1610-1619   DOI: 10.1109/TBME.2012.2190930 Published: JUN 2012


Speed of convergence to equilibrium in Wasserstein metrics for Kac's like kinetic equations

F Bassetti, E Perversi - arXiv preprint arXiv:1205.3690, 2012 - arxiv.org

Abstract: This work deals with a class of one-dimensional measure-valued kinetic equations, 

which constitute extensions of the Kac caricature. It is known that if the initial datum belongs 

to the domain of normal attraction of an\ alpha-stable law, the solution of the equation ...


[PDF] 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 ...


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 ...


Title: Classification of Periodic Activities Using the Wasserstein Distance

Author(s): Oudre, Laurent; Jakubowicz, Jeremie; Bianchi, Pascal; et al.

Source: IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING  Volume: 59   Issue: 6   Pages: 1610-1619   DOI: 10.1109/TBME.2012.2190930   Published: JUN 2012


Consistent estimation of a population barycenter in the Wasserstein space

J Bigot, T Klein - arXiv preprint arXiv:1212.2562, 2012 - arxiv.org

Abstract: We define a notion of barycenter for random probability measures in the 

Wasserstein space. We give a characterization of the population barycenter in terms of 

existence and uniqueness for compactly supported measures. Then, the problem of ...


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


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

Nicolas Fournier  Arnaud Guillin  2013


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 ...


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 ...


The Wasserstein metric in Factor Analysis

L Ning, T Georgiou - SIAM

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

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 


[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 ...


[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

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 ...


On asymptotics for Vaserstein coupling of Markov chains

by OA Butkovsky - 2013 - Cited by 3 - Related articles

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


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 ...


[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.


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 ...


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. ...


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 ...


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 ...


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

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 …



2014  45 items  


[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 ...




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 ...


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 ...

Cited by 1 Cite Save


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 ...

Cited by 1 Cite Save More

[PDF] from arxiv.org


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



[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



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 ...

Cited by 1 Cite Save



[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

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 ...

Cited by 1 Cite Save


Information fusion via the wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown …

AN Bishop - … (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 ...

Cite Save



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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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 ...

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[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,\ ...

Cite Save

[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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[CITATION] Local brightness adaptive image colour enhancement with Wasserstein distance

L Wang, L Xiao, H Liu, Z Wei - 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 ...

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[PDF] from arxiv.org



[PDF] Bernard Wasserstein, On the Eve: The Jews of Europe before the Second World War (pp. 142

M Berkowitz, F Spier, M Linton, J Mori… - The Journal of …, 2014 - ref65.library.scu.edu.tw

JSTOR: The Journal of Modern History, Vol. 86, No. 1, March 2014 ... The Journal of Modern 

History > Vol. 86, No. 1, March 2014 ... The Journal of Modern History Publication Info ... 

Vol. 86, No. 1, March 2014 Published by: The University of Chicago Press Issue Stable ...

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[PDF] from inria.fr


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. ...

Cite Save

[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 ...

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[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 ...

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[PDF] from springer.com




On tangent cones and parallel transport in Wasserstein space

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 ...

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[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. ...

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[PDF] from arxiv.org


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

E Azmoodeh, G Peccati, G Poly - arXiv preprint arXiv:1403.7003, 2014 - arxiv.org

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


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 ...

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[PDF] from uvic.ca


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 ...

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[PDF] from arxiv.org


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 ...

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[PDF] from amstat.org



Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis Adjusted Langevin Algorithm

A Durmus, É Moulines - Statistics and Computing, 2014 - Springer

Abstract In this paper, we establish explicit convergence rates for Markov chains in 

Wasserstein distance. Compared to the more classical total variation bounds, the proposed 

rate of convergence leads to useful insights for the analysis of MCMC algorithms, and ...


[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 ...

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[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 ...

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[PDF] from arxiv.org

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

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 ...

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[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). ...

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[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 ...

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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 ...

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