My name in title from Math Reviews
My name in title from other sources
Vaserstein without Math. Reviews 3 items
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: Aug1980. URI: http://hdl.handle.
net/1813/15168. Appears in Collections: Vaserstein, Leonid N. Files in This Item: ...
张兆基  浙江大学学报: 自然科学版, 1994  cqvip.com
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 2529 2011
STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume: 123 Issue: 9 Pages: 35183541 DOI: 10.1016/j.spa.2013.04.016 Published: SEP 2013
Wasserstein 19731989 without Math. Reviews 4 items
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, 99101, 197912 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)
LpWassersteinMetriken [LpWassersteinMetriken] und Approximationen stochastischer Differentialgleichungen
Matthias Gelbrich, 1989 154 pages
Wasserstein 19901993 without Math. Reviews 6 items
M Gelbrich  Mathematische Nachrichten, 1990  Wiley Online Library
Abstract. For a separable metric space (X, d ) LP WASSERSTEIN metrics between probability
measures 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, 793797 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. ...
Zbl 0718.60057 Gelbrich, Matthias
L${}\sp p$WassersteinMetriken und Approximationen stochastischer Differentialgleichungen. $(L\sp p$ Wasserstein metrics and approximations of stochastic differential equations). (German)
Berlin: HumboldtUniversität 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 KantorovichRubinstein 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 KantorovichRubinstein and Wasserstein functionals. (English)
[J] Diss. Math. 299, 35 p. (1990). ISSN 00123862
Wasserstein 19941999 without Math. Reviews 7 items
JA CuestaAlbertos, 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 L2Wasserstein 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
张兆基  浙江大学学报: 自然科学版, 1994  cqvip.com
我们解答了一个Vasertein 的公开问题: 给定任意整数P, 及M, Z 中矩阵A, 是否存在M, Z 中矩阵X
与Y, 使得A= X+ Y, 且det (x)= p= det (y)? 我们的解答是: 若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 被A 中所有元的最大公因数整除.
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 26, 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
Independence of prime factors: total variation and Wasserstein metrics, insertions and deletions, and the PoissonDirichlet process. In preparation since March 1996, currently 70 pages.
Aplicaciones de las métricas de Wasserstein al análisis de datos
JM Rodríguez Rodríguez  1997  dialnet.unirioja.es
Resumen: SE DAN APLICACIONES DE LAS METRICAS DE WASSERSTEIN A LA
ESTADISTICA Y AL ANALISIS DE DATOS, LAS APLICACIONES SE BASAN EN LA
COMPARACION DE UNA DISTRIBUCION CON UNA FAMILIA DE DISTRIBUCIONES DE ...
Alison L Gibbs  1999  Citeseer
Abstract This paper gives precise bounds on the convergence time of the Gibbs sampler
used in the Bayesian restoration of a degraded image. Convergence to stationarity is
assessed using the Wasserstein metric, rather than the usual choice of total variation ...
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published 2004
W Gangbo, RJ McCann  1999  mis.mpg.de
Abstract: The KantorovichRubinsteinWasserstein 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 20002003 without Math. Reviews 7 items
Testing for Weibull scale families as a test case for Wasserstein correlation tests [Discussion of del Barrio, CuestaAlbertos and Matran]
S Csorgo  , Test 9 (2000), pp. 5470.
(Discussion of
MR1740113 (2001a:60024) del Barrio, Eustasio; CuestaAlbertos, Juan A.; Matrán, Carlos; RodríguezRodríguez, Jesús M. Tests of goodness of fit based on the $L_2$Wasserstein distance. Ann. Statist. 27 (1999), no. 4, 12301239. (Reviewer: Lajos Horváth) 60F05 (60F25 62E20) }
[PDF] Mixed L2Wasserstein 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] Wassersteinmetric
L. Rüschendorf, “Wasserstein metric”, in Hazewinkel Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, 2001.
Cited by 10  Related articles
Wassersteinmetric The ‘Wassersteinmetric’ has a colourful history with several quite diﬀerent ﬁelds of applications. It also has various historical sources. Bernulli 11(1) 2005, 131189
[CITATION] Asymptotics for L 2functionals of the quantile process with application to tests of fit based on weighted Wasserstein distances
Eustasio Del Barrio, Evarist Giné, and Frederic Utzet …  Preprint, 2002 published Bernoulli Volume 11, Number 1 (2005), 131189.
ABSTRACT Weighted L_{2} functionals of the empirical quantile process appear as a component of many test statistics, in particular in tests of fit to locationscale families of distributions based on weighted Wasserstein distances. An essentially complete set of distributional limit theorems for the squared empirical quantile process integrated with respect to general weights is presented. The results rely on limit theorems for quadratic forms in exponential random variables, and the proofs use only simple asymptotic theory for probability distributions in R^{n}. The limit theorems are then applied to determine the asymptotic distribution of the test statistics on which weighted Wasserstein tests are based. In particular, this paper contains an elementary derivation of the limit distribution of the ShapiroWilk test statistic under normality.
[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 pth moment that metrices weak
convergence plus convergence of pth moments. These metrics have interesting applications
in Probability and Statistics, remarkably in the problem of testing goodness of fit. Here we ...
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 goodnessoffit statistics based on theL 2Wasserstein 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 20042005 without Math. Reviews 16 items
J. Lott American Mathematical Society 2005
Meeting: 1007, Santa Barbara, California, SS 9A, Special Session on Ricci Flow/Riemannian Geometry. 100758105. John Lott* (lott@umich.edu), Department ...
Contractivity of Wassersteintype distances:
asymptotic profiles, equilibration rates and qualitative properties.
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José A. Carrillo. Instituci`o Catalana de. Recerca i ...
Paris 2004
L Petrelli  2004  math.cmu.edu
Abstract We employ the MongeKantorovich mass transfer theory to obtain an existence and
uniqueness result for FokkerPlanck 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
2005 by L Ambrosio, N Gigli, G
A fourthorder 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 fourthorder 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
U Gianazza, G Toscani, G Savaré  Preprint IMATICNR, 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 FokkerPlanck equations with point controls
[PDF] from cmu.eduL Petrelli  2004  math.cmu.edu
Abstract We employ the MongeKantorovich mass transfer theory to obtain an existence and
uniqueness result for FokkerPlanck 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
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
L AMBROSIO  Rendiconti della Accademia nazionale delle scienze …, 2005  L'Accademia
LAW Gangbo  2005  calcvar.sns.it
Abstract: In this paper we consider a Hamiltonian $ H $ on ${\ cal P} _2 (* R*^{2d}) $, the set
of probability measures with finite quadratic moments on the phase space $* R*^{2d} $,
which is a metric space when endowed with the Wasserstein distance $ W_2. $ We study ...
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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 ...
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 flowthrough 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 infinitedimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even nonconvexity) — 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 secondorder moments of the discrete
approximations to the heat equation arising from the JordanKinderlehrerOtto (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 largetime asymptotics of nonlinear diffusion equations
J.A. Carrillo, G. Toscani,
in New Trends in Mathematical Physics, (In Honour of the Salvatore Rionero 70th Birthday), 234244,
(2005, Hardcover) World Scientific Publishing Company, Incorporated ISBN10: 9812560777  ISBN13: 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 410, 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
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 MongeKantorovich metrics.
An extensive literature on this topic is already available, originating with the work of Otto ...
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,
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
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 ...
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 2Wasserstein contraction on any manifold evolving by reverse Ricci flow
RJ McCann…  Preprint, 2006
F Bolley  Lecture Notes in Math, 2006 pdf
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. 1214 september 2007. (pp. 107110). ISBN/ISSN: 9788860560209. 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, 697708,
Wasserstein Space and FokkerPlanck Equation
S Fang  2007 Wiley China 方诗赞
Weighted L2Wasserstein GoodnessofFit 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 goodnessoffit statistics for locationscale families,
based on L2functionals of the empirical quantile process. These functionals measure the ...
[PDF] from ubourgogne.frS FANG, J SHAO…  math.ubourgogne.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 FeyelUstünel. Carrying out the program of AmbrosioGigliSavaré, we present a ...
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. ...
by LUIGI AMBROSIO and FILIPPO SANTAMBROGIO, …
Rend. Lincei Mat. Appl. 18 (2007), 23–37
[PDF] from emsph.org RLM Appl  emsph.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 ...
[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 Presentations3 Image Segmentation and Visual GroupingHistogram Based Segmentation Using Wasserstein Distances
T Chan, S Esedoglu, K Ni  Lecture Notes in …, 2007  Berlin: SpringerVerlag, 1973
2008 without Math. Reviews 12 items
Title: Dynamic clustering of interval data using a Wassersteinbased distance
Author(s): Irpino, A; Verde, R
Source: PATTERN RECOGNITION LETTERS Volume: 29 Issue: 11 Pages: 16481658 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 continuoustime 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 ...
Wellposedness of a parabolic movingboundary 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 gradientflow framework based on the Wasserstein metric for a
parabolic movingboundary problem that models crystal dissolution and precipitation. In
doing so we derive a new weak formulation for this movingboundary 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  wwwroc.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: Nonmonotone Convergence in the Quadratic Wasserstein Distance
Author(s): Schachermayer, W; Schmock, U; Teichmann, J
Source: SEMINAIRE DE PROBABILITES XLII Volume: 1979 Pages: 131136 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: 97111 Published: 2009
A Wasserstein approach to the onedimensional 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 nonnegative 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 matrixvalued 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. 415434] $\ mathcal {G} _ {r, p} $
defined on Lipschitz curves $\ gamma $ valued in the $ p $Wasserstein space. The ...
Nonmonotone 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 nfold 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 69, 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 nonlinear FokkerPlanck type equations
[PDF] from kyotou.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.kyotou.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 MoreauYosida approximation to ...
Georgia Institute of Technology,
GromovWasserstein stable signatures for object matching and the role of persistence
[PDF] from stanford.eduF Mémoli  math.stanford.edu
Page 1. 1 GromovWasserstein 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
GromovWasserstein distance(s) mmspaces 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 ...
[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 ℐ={0, 1, 2,…} or
ℐ={0, 1, 2,…, m} for some finite m introduced in Brown and Xia (Ann. Probab. 29: 1373–
1403, 2001) is the equilibrium distribution of the birth–death process with birth rates {α i} ...
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, 巻, 号, ページ, 出版者, 参考文献, 出版年, 年から 年まで.
すべて CiNiiに本文あり CiNiiに本文あり、または連携サービスへのリンクあり.
Mathematical Institute, Tohoku University RIMS Kokyuroku 1671, 2036, 200912
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 69, 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 regionbased 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 GromovWasserstein 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
Edited by: Motoko Kotani (Tohoku University), Masanori Hino (Kyoto University), Takashi Kumagai (Kyoto University)
cvgmt.sns.it/media/doc/paper/511/XEDP.pdf · PDF file 2010
ideas from the theory of Gradient Flows in the space of ... we will give the stepbystep variational interpretation of gradient ...
2 Microscopic and Macroscopic ...
By Vavilov, N. A.; Sinchuk, S. S.. Zbl 1215.20049
L Granieri  REND. SEM. MAT. UNIV. PADOVA, 2010  archive.numdam.org
ABSTRACTWe 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.
In: LECHEVALLIER YVES, SAPORTA GILBERT. Proceedings of COMPSTAT'2010. (pp. 581589). ISBN: 9783790826036. 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,
Series: Studies in Classification, Data Analysis, and Knowledge Organization , Palumbo, Francesco; Lauro, Carlo Natale; Greenacre, Michael J. (Eds.), 2010, ISBN: 9783642037382, pages 4148.
This paper deals with the clustering of complex data. The input elements to be clustered are linear models estimated on samples arising from several subpopulations (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: 193211 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 regionbased 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 distancebased 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 twophase Wasserstein space produces the entropy solution of the ...
Wasserstein space over Hadamard space
J Bertrand  Workshop on Geometric Probability and …, 2010  atlasconferences.com
In the talk, I will consider the quadratic Wasserstein space over a metric space of nonpositive
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 casacart.netC Selinger  casacart.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) ...
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 LpWasserstein control and Lqgradient 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 largedeviations principle to the Wasserstein gradient flow: a new micromacro 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 largedeviations 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.archivesouvertes.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 29JUN 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: 435446 Published: 2012
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,1999:898903. ... Rousson M,Brox T,Deriche R.Active unsupervised texture ...
Chan T;Esedoglu S;Ni K Histogram based segmentation using wasserstein distances [外文会议] 2007
[PDF] from 210.29.99.10钱晓华， 郭树旭…  电子学报, 2010  210.29.99.10
Wasserstein distance based local energy model of segmentation
by Qian, Gio, and Li
2011 not in Math. Reviews 39 items
E Boissard  2011  thesesups.upstlse.fr
On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la
théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur
pour l'approximation particulaire des solutions de certaines équations aux dérivées ...
Dissertation
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 ...
J Trashorras  2011  hal.archivesouvertes.fr
Abstract: Let (E, d) be a compact metric space, X=(X1,..., Xn,...) and Y=(Y1,..., Yn,...) two
independent sequences of independent Evalued random variables and (LX n) n≥ 1 and
(LY n) n≥ 1 the associated sequences of empirical measures. We establish a Large ...
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 RenesseSturm over
Wasserstein space on the unit interval (probability measures on the unit interval equipped ...
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 wellposedness of different higher order ...
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 1Wasserstein distance
E Boissard  Electronic Journal of Probability}, 2011  emis.ams.org
Abstract We study the problem of nonasymptotic deviations between a reference measure µ
and its empirical version Ln, in the 1Wasserstein metric, under the standing assumption that
µ satisfies a transportentropy inequality. We extend some results of F. Bolley, A. Guillin ...
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
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 ...
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 socalled "exact" or nonasymptotic 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 transportentropy 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.
Veretennikov A. (With O.A.Butkovsky) International Mathematical Conference "50 years of IPPI", July 2529 2011 Moscow, Russia, Proceedings, ISBN 9785901158159
Go to publication Download (241.6 KB)
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, ...
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 tudarmstadt.deW Stannat  Seminar on Stochastic Analysis, Random Fields and …, Progress in Probability, 2011,
Volume 63, Part 1, 245260, 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 archivesouvertes.frJ Rabin…G Peyré  2011  hal.archivesouvertes.fr Proc. ICIP'11, pp. 15411544, 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 MongeKantorovich optimal mass transport
to define penalty terms depending on statistics from images. To cope with the com ...
J Rabin, J Fadili…  2011  basepub.dauphine.fr
[PDF] from archivesouvertes.frG Peyré, J Fadili, J Rabin  2011  hal.archivesouvertes.fr
In this paper, we propose a novel and rigorous framework for regionbased 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 MarkovWasserstein 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 nonasymptotic 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 socalled “exact” or nonasymptotic de viations between a
reference measure µ and its empirical version Ln, in the pWasserstein metric, 1 ≤ p ≤ 2, under
the standing assumption that µ satis fies a transportentropy 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 archivesouvertes.frC Caillerie, F Chazal, J Dedecker…  2011  hal.archivesouvertes.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 ...
KantorovichRubinsteinWasserstein Lp距离 (p> 2) 沈银芳  科技信息, 2011  cqvip.com
SHEN Yin Fong
KantorovichRubinsteinWasserstein Lpdistance (p> 2)
Zhejiang Finance and Economics College of Mathematics and Statistics , Zhejiang Hangzhou 310018,
Abstract: This article get Euclidean plane bounded region's diverse KantorovichRubinsteinWasserstein Lpdistance (abbreviated as an accurate representation of: KRWLp distance),
a given from the point of view of the theory of probability prove
Cahnhilliard and thin film equations as gradient flow in wassersteinlike metrics
[PDF] from tum.deS Lisini, D Matthes…  Preprint, 2011  wwwm8.ma.tum.de
Abstract. In this paper, we establish an approach to the existence theory of certain
degenerate fourthorder evolution equations which arise in applications in mathematical
physics; particular examples are the CahnHilliard and the (destabilized) thin film equation ...
Optimal Couplings of KantorovichRubinsteinWasserstein Lpdistance
[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 ...
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 masstransportation problems. We furthermore generalize the framework to support spheretype 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 masstransportation problem between their conformal densities. This mass ...
published 2011
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 archivesouvertes.frJ Trashorras  Arxiv preprint math.PR/0000000  hal.archivesouvertes.fr
Résumé en anglais: Let $(E, d) $ be a compact metric space, $ X=(X_1,\ dots, X_n,\ dots) $
and $ Y=(Y_1,\ dots, Y_n,\ dots) $ two independent sequences of independent $ E $valued
random variables and $(L^ X_n) _ {n\ geq 1} $ and $(L^ Y_n) _ {n\ geq 1} $ the associated ...
Distribution's template estimate with Wasserstein metrics
[PDF] from arxiv.orgE Boissard, TL Gouic…  Arxiv preprint arXiv:1111.5927, 2011  arxiv.org
Abstract: In this paper we tackle the problem of comparing distributions of random variables
and defining a mean pattern between a sample of random events. Using barycenters of
measures in the Wasserstein space, we propose an iterative version as an estimation of ...
Bernoulli 21 (2015), no. 2, 740–759.
Barycentre de Wasserstein J RABIN, G PEYRÉ…  smai.emath.fr
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 MongeKantorovich 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 archivesouvertes.frC Caillerie, F Chazal, J Dedecker… Electron. J. Statist. Volume 5 (2011), 13941423.  projecteuclid.org
Abstract Recently, Chazal, CohenSteiner 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 FokkerPlanck equations
[PDF] from arxiv.orgF Bolley, I Gentil…  Arxiv preprint arXiv:1110.3606, 2011  arxiv.org
Abstract: We describe conditions on nongradient drift diffusion FokkerPlanck 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 ...
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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 MongeKantorovich 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]
MoreauYosida 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 MoreauYosida 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 jumpdiffusions
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 timedomain 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 FokkerPlanck 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] Onedimensional numerical algorithms for gradient flows in the pWasserstein 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 LpWasserstein 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
EA Carlen…  Arxiv preprint arXiv:1205.6565, 2012  arxiv.org
Abstract: We investigate the MoreauYosida regularization and the associated proximal map
in the context of discrete gradient flow for the 2Wasserstein 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 ...
Archive for Rational Mechanics and Analysis, 2014
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 nonnegative
weak solutions for degenerate parabolic equations of fourth order, like the CahnHilliard and
certain thin film equations. The considered evolution equations are in the form of a ...
Cited by 1  Related articles  All 9 versions
A Irpino…  Arxiv preprint arXiv:1202.1436, 2012  arxiv.org
Abstract: In this paper we present a linear regression model for modal symbolic data. The
observed variables are histogram variables according to the definition given in the
framework of Symbolic Data Analysis and the parameters of the model are estimated ...
Adv. Data Anal. Classif. 9 (2015), no. 1, 81–106. 62J05
Classification of periodic activities using the Wasserstein distance
L Oudre, J Jakubowicz, P Bianchi…  … , IEEE Transactions on, 2012  ieeexplore.ieee.org
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING Volume: 59 Issue: 6 Pages: 16101619
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 ...
Volume: 59 Issue: 6 Pages: 16101619
[PDF] WEAK KAM ON THE WASSERSTEIN TORUS WITH MULTIDIMENSIONAL 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 ...
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 $ selfadjoint 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
李红…  计算机工程与应用, 2012  cqvip.com
针对目前区间数据模糊聚类研究中区间距离定义存在的局限性, 引入能够考虑区间数值分布特征
的Wasserstein 距离测度, 提出基于Wasserstein 距离测度的单指标和双指标自适应模糊聚类
算法及迭代模型. 通过仿真实验和CR 指数, 证实了该类模型的优势. 该算法在海量, 堆积如山 ...
[Li Hong , Sun Qiu Bi Data Mining the interval fuzzy clustering  based Wasserstein measure]
[School of Management Department of Statistics, Fuzhou 350108]
Abstract:
The Wasserstein distance measure introduced to be able to consider the limitations of fuzzy clustering interval data interval distance defined interval value distribution characteristics, proposed based on the Wasserstein distance measure single indicators and indicators adaptive fuzzy clustering algorithm and iterative model. confirmed the advantages of this kind of model simulation and CR Index, the algorithm has important practical significance in the massive mountains of data mining.
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 singularlimit problem arising in the modelling of chemical reactions. At
finite ε\,>\, 0, the system is described by a FokkerPlanck convectiondiffusion equation with
a doublewell convection potential. This potential is scaled by 1/ε, and in the limit ε\ to0, ...
Cone structure of L2Wasserstein 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" dsmall set imply subgeometric convergence ...
[PDF] WEAK KAM THEORY ON THE WASSERSTEIN TORUS WITH MULTIDIMENSIONAL 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 ...
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: 16101619 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 onedimensional measurevalued 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\ alphastable 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 nonbranching 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.archivesouvertes.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 ...
L Hélène, L JeanMichel  hal.archivesouvertes.fr
AN EXTENSION OF WASSERSTEIN CONTRACTION ASSOCIATED WITH THE CURVATUREDIMENSION 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 spacetime Lipschitz estimate of the ...
二元离散antorovichRubinsteinWasserstein 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 KantorovichRubinsteinWasserstein L2distance]
本文得到二元离散KantorovichRubinsteinWassersteinL2距离的一个精确表示。
SHEN Yin Fong
An accurate representation of the binary discrete antorovichRubinsteinWasserstein L2distance
Hangzhou 310018, Zhejiang Finance and Economics College of Mathematics and Statistics 2012
LP Lopes  2012  repositorio.bce.unb.br
Neste trabalho propomos testes nãoparamétricos para classes de distribuições de cauda
pesada, que incluem as _estáveis e as extremais de Fréchet. As estatísticas apresentadas,
funcionais do processo quantil empírico, permitem testar a pertinência da distribuição F ...
issertation
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: 16101619 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 ...
G Peyré, J Fadili, J Rabin  Proc. ICIP'12, 2012  hal.archivesouvertes.fr [bib] [pdf]
Abstract. In this paper, we propose a novel and rigorous framework for regionbased 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 55 items
Localisation de masse et espaces de Wasserstein
by Le Gouic, Thibaut 2013 Dissertation :
Le travail de cette thèse est basé sur deux outils : le packing d'un ensemble et les espaces de Wasserstein. Une première partie s'intéresse à...
pdf On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier Arnaud Guillin 2013
K KUWADA  RIMS Kokyuroku Bessatsu, 2013  ci.nii.ac.jp
... ISSN, 巻, 号, ページ, 出版者, 参考文献, 出版年, 年から 年まで. すべて CiNiiに本文あり
CiNiiに本文あり、または連携サービスへのリンクあり. 論文検索. 著者検索. 論文検索. Gradient estimate
for Markov kernels, Wasserstein control and HopfLax formula (Potential Theory and its Related ...
V Laschos  2013  opus.bath.ac.uk
In a seminal work, Jordan, Kinderlehrer and Otto proved that the FokkerPlanck equation
can be described as a gradient flow of the free energy functional in the Wasserstein space,
bringing this way the statistical mechanics point of view on the diffusion phenomenon to ...
University of Bath (United Kingdom),
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 ...
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
lowrank. Such an additive decomposition follows the dictum of factor analysis where ...
B Engquist, BD Froese  arXiv preprint arXiv:1311.4581, 2013  arxiv.org INRIA PARIS
Abstract: Seismic signals are typically compared using travel time difference or $ L_2 $
difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit
in seismology. It exhibits properties from both of the traditional measures mentioned ...
MR3187785 Communications in Mathematical Sciences
M Kersting  2013  lp.unigoettingen.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 ...
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 BorelBrascampLieb inequality for general Riemannian and Finsler manifolds and led ...
N Bonneel, J Rabin, G Peyré, H Pfister  2013  hal.archivesouvertes.fr
Abstract This article details two approaches to compute barycenters of measures using 1D
Wasserstein distances along radial projections of the input measures. The first method
makes use of the Radon transform of the measures, and the second is the solution of a ...
J. Math. Imaging Vision 51 (2015), no. 1, 22–45. 9
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 socalled 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 ...
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 meanfield 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 timedomain 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 MongeKantorovich 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 frequencydomain formula is given. The geometric interpretation helps us in comparing Wasserstein distance with classical frequencydomain validation metrics like nugap.
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
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 ...
M Benning, L Calatroni, B Düring, CB Schönlieb  maths.cam.ac.uk
Abstract. We consider a nonlinear fourthorder diffusion equation that arises in denoising of
image densities. We propose an implicit timestepping scheme that employs a primaldual
method for computing the subgradient of the total variation seminorm. 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
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^ pKantorovichRubinstein
Wasserstein distance. In particular, we obtain a precise estimate for the optimal W_\ infty ...
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 ...
JA Carrillo, YP Choi, M Hauray  arXiv preprint arXiv:1304.5776, 2013  arxiv.org
Abstract: These notes are devoted to a summary on the meanfield limit of large ensembles
of interacting particles with applications in swarming models. We first make a summary of the
kinetic models derived as continuum versions of second order models for swarming. We ...
Collective Dynamics from Bacteria to …, 2014  Springer
B Schmitzer, C Schnörr  graphmod.iwr.uniheidelberg.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
SM WALCZAK  faculty.ms.utokyo.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 ...
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 ...
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 normOrlicz
norm type duality holds on Polish geodesic space without any assumption on the Markov ...
RIMS Kôkyûroku Bessatsu.
R Guan, Y Lechevallier…  … TECHNOLOGIES DE L' …, 2013  hal.archivesouvertes.fr
... REVUE DES NOUVELLES TECHNOLOGIES DE L'INFORMATION RNTI E.25 (2013) 1530.
Adaptive Dynamic Clustering Algorithm for Intervalvalued Data based on SquaredWasserstein
Distance. Rong Guan 1 , Yves Lechevallier 2 , Huiwen Wang 1. (2013). ...
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.
Wasserstein barycenters (Agueh and Carlier, 2011) define a new family of barycenters between N probability measures that builds upon optimal transport theory. We argue using a simple example that Wasserstein barycenters have interesting properties that differentiate them from other barycenters proposed recently, which all build either or both on kernel smoothing and Bregman divergences. We propose two algorithms to compute Wasserstein barycenters for finitely supported measures, one of which can be shown to be a generalization of Lloyd's algorithm. A naive implementation of these algorithms is intractable, because it would involve numerous resolutions of optimal transport problems, which are notoriously expensive to compute. We propose to follow recent work by Cuturi (2013) and smooth these transportation problems to recover faster optimization procedures. We apply these algorithms to the visualization of perturbed images and resampling in particle filters.
ICML 2014 22.06.14 Kyoto University University of Oxford
Convergence to equilibrium in Wasserstein distance for FokkerPlanck 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 nongradient drift diffusion FokkerPlanck 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.
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 HodgedeRham semigroup on 1forms.


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 BakryLedoux's refined gradient estimate involving an upper ...
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 ...
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 appearancebased data term enforcing closeness of aggregated appearance ...
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 JKOdiscretization scheme is asymptotically equivalent to a rate ...
SM WALCZAK  faculty.ms.utokyo.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 ...
JA Carrillo, YP Choi, M Hauray  arXiv preprint arXiv:1304.5776, 2013  arxiv.org
Abstract: These notes are devoted to a summary on the meanfield 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
F CAVALLETTI  cvgmt.sns.it
Abstract. We will prove a decomposition for Wasserstein geodesics in the following sense:
let (X, d, m) be a nonbranching metric measure space verifying CDloc (K, N) or equivalently
CD*(K, N). Then every geodesic µt in the L2Wasserstein space, with µt≪ m, is ...
Geometric and Functional Analysis  Springer
M Benning, L Calatroni, B Düring…  arXiv preprint arXiv: …, 2013  arxiv.org
Abstract: We consider a nonlinear fourthorder diffusion equation that arises in denoising of
image densities. We propose an implicit timestepping scheme that employs a primaldual
method for computing the subgradient of the total variation seminorm. The constraint on ...
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. ...
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 metricstransport metricsthat have stronger convexity properties than the ...
.... In recent years, there has been significant interest in gradient flow on the space of probability measures endowed with the Wasserstein metric...
Rutgers The State University of New Jersey  New Brunswick Dissertation :
L Zhu, Z Cao  Eighth International Symposium on …, 2013  proceedings.spiedigitallibrary.org
abstract Many existing bottomup saliency detection methods measure the multiscale 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 ...
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 ...
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 normOrlicz
norm type duality holds on Polish geodesic space without any assumption on the Markov ...
MH Duong, V Laschos…  … : Control, Optimisation and …, 2013  Cambridge Univ Press
Abstract We study the Fokker–Planck equation as the manyparticle limit of a stochastic
particle system on one hand and as a Wasserstein gradient flow on the other. We write the
pathspace rate functional, which characterises the large deviations from the expected ...
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 meanfield limit. For identical
Kuramoto oscillators, we present an admissible class of initial data leading to time ...
J Bigot, R Gouet, A López  arXiv preprint arXiv:1307.7721, 2013  arxiv.org
Annales de l'Institut Henri …, 2015  math.ubordeaux1.fr
Abstract: We introduce the method of Geodesic Principal Component Analysis (GPCA)
analysis on the space of probability measures on the line, with finite second moments,
endowed with the Wasserstein metric. We discuss the advantages of this approach over a ...
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 ...
DRM Renger  2013  … 2013. http://alexandria. tue. nl/extra2 …
Permalink Technische Universiteit Eindhoven Dissertation :
2014 52 items
B Kloeckner, AO Lopes, M Stadlbauer  Preprint, 2014  persomath.univmlv.fr
Abstract.—We employ techniques from optimal transport in order to prove decay of transfer
operators associated to iterated functions systems and expanding maps, giving rise to a new
proof without requiring a DoeblinFortet (or LasotaYorke) inequality.
H Haario  Statistics and Computing, 2014  Springer
The Wasserstein distance between probability distributions might be intuitively described as
a minimal effort required to map one distribution onto another. The concept has a long
history with connections to optimal transport theory. However, the applications on ...
JM Fraser  arXiv preprint arXiv:1401.1443, 2014  128.84.21.199
Abstract We study aspects of the Wasserstein distance in the context of selfsimilar
measures. Computing this distance between two measures involves minimising certain
moment integrals over the space of couplings, which are measures on the product space ...
H Lescornel, JM Loubes  iip.ist.i.kyotou.ac.jp
Abstract We consider the issue of estimating a deformation acting on measures. For this we
study a parametric deformation model on an empirical sample and provide a new matching
criterion for cloud points. The deformation estimator is obtained by minimizing the ...
Covariance estimation and study of models of deformations between distributions with the Wasserstein distance
by Lescornel, Hélène 2014 Dissertation :
La première partie de cette thèse est consacrée à l'estimation de covariance de processus stochastiques non stationnaires. Le modèle étudié amène à estimer la...
D HanKwan, M Iacobelli  arXiv preprint arXiv:1412.4023, 2014  arxiv.org
Abstract: In this work, we study the quasineutral limit of the onedimensional VlasovPoisson
equation for ions with massless thermalized electrons. We prove new weakstrong stability
estimates in the Wasserstein metric that allow us to extend and improve previously known ...
M Kell  arXiv preprint arXiv:1401.0840, 2014  arxiv.org
Abstract: Based on the idea of a recent paper by AmbrosioGigliSavar\'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 ...
YH Kim, B Pass  arXiv preprint arXiv:1412.7726, 2014  arxiv.org
Abstract: We study barycenters in the space of probability measures on a Riemannian
manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we
establish absolute continuity of the barycenter of general measures $\ Omega\ in P (P (M)) ...
M Qiao, W Wang, M Ng  globalsci.com
Abstract. We present a multiphase image segmentation method based on the histogram of
the Gabor feature space, which consists of a set of Gaborfilter responses with various
orientations, scales and frequencies. Our model replaces the error function term in the ...
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
statespace Markov chains which are not phiirreducible. Our approach is based on a ...

Author(s): Savare, Giuseppe Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume: 34 Issue: 4 Special Issue: SI Pages: 16411661 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 AnalysisJanuary 2014 Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Interval DataLI 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 CURVATUREJ Bertrand, BR Kloeckner  math.univtoulouse.fr Abstract.—We continue the geometric study of the Wasserstein space# 2 (X) of simply connected, negatively curved metric spaces X, by proving that in many cases, they are isometrically rigid: any isometry of the Wasserstein space is the action on measures of an ... A geometric study of Wasserstein spaces: Isometric rigidity in negative curvature J Bertrand, B Kloeckner  arXiv preprint arXiv:1404.1734, 2014  arxiv.org Abstract: This article deals with the space of probability measures (with finite second order moments) over a CAT (0) space. The Wasserstein metric turns this space of measures into a geodesic space called Wasserstein space. We are interested in the geometric properties ... Related articles All 8 versions Cite Save Wasserstein Propagation for SemiSupervised LearningJ 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 graphbased semisupervised ... [PDF] On gradient structures for Markov chains and the passage to Wasserstein gradient flowsK Disser, M Liero  opus4.kobv.de Abstract We study the approximation of Wasserstein gradient structures by their finitedimensional analog. We show that simple finitevolume discretizations of the linear FokkerPlanck equation exhibit the recently established entropic gradientflow structure for ... qheat flow and the gradient flow of the Renyi entropy in the pWasserstein spaceM Kell  arXiv preprint arXiv:1401.0840, 2014  arxiv.org Abstract: Based on the idea of a recent paper by AmbrosioGigliSavar\'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 selfsimilar measuresJM Fraser  arXiv preprint arXiv:1401.1443, 2014  arxiv.org Abstract: We study the Wasserstein distance between selfsimilar 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 regimeswitching diffusions in Wasserstein distancesJ Shao  arXiv preprint arXiv:1403.0291, 2014  arxiv.org Abstract: Based on the theory of Mmatrix and PerronFrobenius theorem, we provide some criteria to justify the convergence of the regimeswitching diffusion processes in Wasserstein distances. The cost function we used to define the Wasserstein distance is not necessarily ... Stochastic Process. Appl. 125 (2015), no. 2, 739–758. OD matrix structural similarity: Wasserstein metricA 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 WassersteinOrlicz spacesS 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 WassersteinOrlicz distance constructed ... 
[PDF] Performance and robustness analysis of stochastic jump linear systems using wasserstein metric
K Lee, A Halder, R Bhattacharya  arXiv preprint, 2014  people.tamu.edu
Abstract This paper focuses on the performance and the robustness analysis of stochastic
jump linear systems. The realization of the state trajectory under stochastic jump processes
becomes random variables, which brings forth the probability distributions for the system ...
MR3284787 Automatica J. IFAC 51 (2015), 341–347.
[HTML] Dynamic clustering of histogram data based on adaptive squared Wasserstein distances
A Irpino, R Verde, FAT De Carvalho  Expert Systems with Applications, 2014  Elsevier
Abstract This paper presents a Dynamic Clustering Algorithm for histogram data with an
automatic weighting step of the variables by using adaptive distances. The Dynamic
Clustering Algorithm is a kmeanslike algorithm for clustering a set of objects into a ...
Cited by 1 Related articles All 9 versions Web of Science: 1 Cite Save
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 nonrigid 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: Meanfield 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 meanfield 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
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 twodimensional domain; the elastic medium is modelled as a
continuum. We formulate the energy of this system in terms of the empirical measure of the ...
Wasserstein Distance and the Rectifiability of Doubling Measures: Part I
J Azzam, G David, T Toro  arXiv preprint arXiv:1408.6645, 2014  arxiv.org Mathematische Annalen  Springer
Abstract: Let $\ mu $ be a doubling measure in $\ mathbb {R}^ n $. We investigate
quantitative relations between the rectifiability of $\ mu $ and its distance to flat measures.
More precisely, for $ x $ in the support $\ Sigma $ of $\ mu $ and $ r> 0$, we introduce a ...
Mathematische Annalen  Springer
AN Bishop NICTA, Australian Nat. Univ., Canberra, ACT, Australia (FUSION), 2014 17th International Conference on, 2014  ieeexplore.ieee.org
Abstract—In this work, a general information fusion problem is formulated as an optimisation
protocol in the space of probability measures (ie the socalled Wasserstein metric space).
The highlevel idea is to consider the data fusion result as the probability measure that is ...
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 ...
Exponential Contractivity in the $ L^ p $Wasserstein Distance for Diffusion Processes
D Luo, J Wang  arXiv preprint arXiv:1407.1986, 2014  arxiv.org
Abstract: By adopting the coupling by reflection and choosing an auxiliary function which is
convex near infinity, we establish the exponential contractivity of diffusion semigroups $(P_t)
_ {t\ ge0} $ with respect to the standard $ L^ p $Wasserstein distance for all $ p\ in [1,\ ...
[PDF] Some evolution equations as Wasserstein gradient flows
A Takatsu  kurims.kyotou.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 ...
Related articles Cite Save More
L Wang, L Xiao, H Liu, Z Wei  IET Image Processing, 2014  IET
Colour image enhancement is an important preprocessing phase of many image analysis
tasks such as image segmentation, pattern recognition and so on. This study presents a new
local brightness adaptive variational model using Wasserstein distance for colour image ...
Transport equation with source and generalized Wasserstein distance
B Piccoli  NETCO 2014New Trends in Optimal Control, 2014  hal.inria.fr
Résumé: We will start by revising some macroscopic model, based on systems of
conservation (or balance) laws, for network flows, such as road networks, supply chains, gas
pipelines etc.. Such models were successfully employed in traffic monitoring projects. ...
[PDF] Fast Computation of Wasserstein Barycenters
A Doucet  iip.ist.i.kyotou.ac.jp
Abstract We present new algorithms to compute the mean of a set of empirical probability
measures under the optimal transport metric. This mean, known as the Wasserstein
barycenter, is the measure that minimizes the sum of its Wasserstein distances to each ...
On local wellposedness of the thinfilm 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 ...
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 ...
[PDF] The Gromov–Wasserstein Distance: A Brief Overview
F Mémoli  Axioms, 2014  mdpi.com
... Article The Gromov–Wasserstein Distance: A Brief Overview Facundo Mémoli ... Published:
2 September 2014 Abstract: We recall the construction of the Gromov–Wasserstein
distance and concentrate on quantitative aspects of the definition. ...
The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds
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 ...
Related articles All 2 versions Cite Save
The Wasserstein geometry of nonlinear sigma models and the HamiltonPerelman Ricci flow
M Carfora  arXiv preprint arXiv:1405.0827, 2014  arxiv.org
Abstract: Non linear sigma models are quantum field theories describing, in the large
deviations sense, random fluctuations of harmonic maps between a Riemann surface and a
Riemannian manifold. Via their formal renormalization group analysis, they provide a ...
Related articles All 2 versions Cite Save
Weak Solutions to a Fractional FokkerPlanck Equation via Splitting and Wasserstein Gradient Flow
M Bowles  2014  dspace.library.uvic.ca
In this thesis, we study a linear fractional FokkerPlanck equation that models nonlocal
(fractional') diffusion in the presence of a potential field. The nonlocality is due to the
appearance of thefractional Laplacian'in the corresponding PDE, in place of the classical ...
[PDF] from arxiv.org Applied Mathematics Letters, 2014  Elsevier
Globally Optimal Joint Image Segmentation and Shape Matching based on Wasserstein Modes
B Schmitzer, C Schnörr  arXiv preprint arXiv:1407.3956, 2014  arxiv.org
Abstract: A functional for joint variational object segmentation and shape matching is
developed. The formulation is based on optimal transport wrt geometric distance and local
feature similarity. Geometric invariance and modelling of objecttypical statistical ...
Journal of Mathematical Imaging and Vision, 2014  Springer
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 welldefined 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 JeanMichel  hal.inria.fr
Abstract: We consider the issue of estimating a deformation operator acting on measures.
For this we consider a parametric warping model on an empirical sample and provide a new
matching criterion for cloud points based on a generalization of the registration criterion ...
Related articles All 2 versions Cite Save More
[PDF] 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.
Related articles Cite Save More
Evolution in Measure Spaces with Wasserstein Distance
E Cristiani, B Piccoli, A Tosin  Multiscale Modeling of Pedestrian Dynamics
MS&A Volume 12, 2014, pp 169194  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 ...
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 ...
Electron. J. Stat. 9 (2015), 234–265.
高津飛鳥  数理解析研究所講究録, 2014  ci.nii.ac.jp
... ISSN, 巻, 号, ページ, 出版者, 参考文献, 出版年, 年から 年まで. すべて CiNiiに本文あり
CiNiiに本文あり、または連携サービスへのリンクあり. 論文検索. 著者検索. 論文検索. Some evolution
equations as Wasserstein gradient flows (Geometry of solutions of partial differential equations). ...
[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 & JeanMichel Loubes 2 ... 1 Institut de Mathématiques de Toulouse 118
route de Narbonne 31000 Toulouse helene.lescornel@math.univtoulouse.fr 2 Institut de ...
Related articles Cite Save More
On curvature conditions using Wasserstein spaces
This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in
pWasserstein 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 qheat ...
On Curvature Conditions Using Wasserstein Spaces
Martin Kell  2014 100 pages
Numerical methods for matching for teams and Wasserstein barycenters
E Oudet, A Oberman, G Carlier  2014  basepub.dauphine.fr
Résumé en anglais: Equilibrium multipopulation matching (matching for teams) is a prob
lem from mathematical economics which is related to multimarginal optimal transport. A
special but important case is the Wasserstein barycenter problem, which has applications ...
Numerical methods for matching for teams and Wasserstein barycenters
G Carlier, A Oberman, E Oudet  2014  hal.archivesouvertes.fr
Abstract Equilibrium multipopulation matching (matching for teams) is a problem from
mathematical economics which is related to multimarginal 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
OD matrix structural similarity: Wasserstein metric
TRB 93rd Annual Meeting Compendium of Papers
Transportation Research Board 93rd Annual Meeting
Location: Washington DC Date: 2014112 to 2014116
2015 60 publications
[PDF] " A random locational Mestimation problem based on the L2Wasserstein distance
A Daouia, I Van Keilegom  2015  dial.uclouvain.be
Abstract The fair placement of a facility often depends on other existing players and on an
optimal assignment map of clients to these facilities. This problem arises in various contexts
in decision mathematics such as, for instance, location theory in operational research and ...
Scalable Bayes via Barycenter in Wasserstein Space
S Srivastava, C Li, DB Dunson  arXiv preprint arXiv:1508.05880, 2015  arxiv.org
Abstract: We propose a novel approach WASP for Bayesian inference when massive size of
the data prohibits posterior computations. WASP is estimated in three steps. First, data are
divided into smaller computationally tractable subsets. Second, posterior draws of ...
V Konarovskyi, M von Renesse  arXiv preprint arXiv:1504.00559, 2015  arxiv.org
Abstract: Extending previous work~[arXiv: 1408.0628] by the first author we present a variant
of the Arratia flow of a field of coalescing Brownian motions starting from every point of the
unit interval. The important new feature of the model is that individual particles carry mass ...
D Zaev  arXiv preprint arXiv:1505.03721, 2015  arxiv.org
Abstract: We consider $ L^ p $Wasserstein distances on a subset of probability measures. If
the subset of interest appears to be a simplex, these distances are determined by their
values on extreme points of the simplex. We show that this fact is a corollary of the ...
J Shao, B Wu  arXiv preprint arXiv:1507.07995, 2015  arxiv.org
Abstract: When the Ricci curvature of a Riemannian manifold is not lower bounded by a
constant, but lower bounded by a continuous function, we give a new characterization of this
lower bound through the convexity of relative entropy on the probability space over the ...
C Ketterer  arXiv preprint arXiv:1509.02178, 2015  arxiv.org
Abstract: In this note we continue the analysis of metric measure space with variable ricci
curvature bounds. First, we study $(\ kappa, N) $convex functions on metric spaces where
$\ kappa $ is a lower semicontinuous function, and gradient flow curves in the sense of a ...
F Santambrogio  Optimal Transport for Applied Mathematicians, 2015  Springer
Abstract In this chapter we use the minimal value of transport problems between two
probabilities in order to define a distance on the space of probabilities. We mainly consider
costs of the form c (x, y)= x− y pc (x, y)=  xy ^ p in Ω⊂ ℝ d\ varOmega ⊂ R^ d. We ...
K Craig  arXiv preprint arXiv:1512.07255, 2015  arxiv.org
Abstract: Over the past fifteen years, the theory of Wasserstein gradient flows of convex (or,
more generally, semiconvex) energies has led to advances in several areas of partial
differential equations and analysis. In this work, we extend the wellposedness theory for ...
M Hauray  arXiv preprint arXiv:1512.01986, 2015  arxiv.org
Abstract: We study here a very popular 1D jump model introduced by Kac: it consists of $ N $
velocities encountering random binary collisions at which they randomly exchange energy.
We show the uniform (in $ N $) exponential contractivity of the dynamics in a nonstandard ...
FX Vialard  MATH ON THE ROCKS  researchgate.net
Abstract This note gives a summary of the presentation that I gave at the workshop on shape
analysis1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to
measures that have different total masses. This generalization enjoys most of the ...
S Kolouri, Y Zou, GK Rohde  arXiv preprint arXiv:1511.03198, 2015  arxiv.org
Abstract: Optimal transport distances, otherwise known as Wasserstein distances, have
recently drawn ample attention in computer vision and machine learning as a powerful
discrepancy measure for probability distributions. The recent developments on alternative ...
JD Benamou, G Carlier, M Laborde  2015  hal.archivesouvertes.fr
Taking advantage of the BenamouBrenier dynamic formulation of optimal transport, we
propose a convex formulation for each step of the JKO scheme for Wasserstein gradient
flows which can be attacked by an augmented Lagrangian method which we call the ...
J Ye  personal.psu.edu
ABSTRACT Learning from probability measures is an emerging problem that has potential
benefiting multiple domains. Different from previous computational learning concentrated on
neural representations and parametric statistical models, my research focuses on ...
T Le Gouic, JM Loubes  Geometric Science of Information, 2015  Springer
Abstract We study barycenters in the Wasserstein space P_p(E) of a locally compact
geodesic space (E, d). In this framework, we define the barycenter of a measure ℙ on P_p(E)
as its Fréchet mean. The paper establishes its existence and states consistency with ...
FAT de Carvalho, A Irpino…  Fuzzy Systems (FUZZIEEE …, 2015  ieeexplore.ieee.org
Abstract—In this paper, a fuzzy cmeans algorithm based on an adaptive L2Wasserstein
distance for histogramvalued data is proposed. The adaptive distance induces a set of
weights associated with the components of histogramvalued data and thus of the ...
F Bolley, I Gentil, A Guillin, K Kuwada  arXiv preprint arXiv:1510.07793, 2015  arxiv.org
Abstract: The curvaturedimension condition is a generalization of the Bochner inequality to
weighted Riemannian manifolds and general metric measure spaces. It is now known to be
equivalent to evolution variational inequalities for the heat semigroup, and quadratic ...
J Ye, P Wu, JZ Wang, J Li  arXiv preprint arXiv:1510.00012, 2015  arxiv.org
Abstract: In a variety of research areas, the bag of weighted vectors and the histogram are
widely used descriptors for complex objects. Both can be expressed as discrete
distributions. D2clustering pursues the minimum total withincluster variation for a set of ...
J Bigot, T Klein  arXiv preprint arXiv:1212.2562, 2015  halpjse.archivesouvertes.fr
Abstract This paper is concerned by the study of barycenters for random probability
measures in the Wasserstein space. Using a duality argument, we give a precise
characterization of the population barycenter for various parametric classes of random ...
H Lescornel, E del Barrio, JM Loubes  papersjds15.sfds.asso.fr
1 INRIA Saclay, 1 rue Honoré d'Estienne d'Orves, 91 120 Palaiseau.
helene.lescornel@inria.fr 2 Universitad de Valladolid, Facultad de Sciencas, C/ Prado de la Magdalena
s/n, 47005 Valladolid, ESPAGNE. tasio@eio.uva.es 3 Institut de Mathématiques de ...
基于 Wasserstein 距离和改进 Kmedoids 聚类的风电/光伏经典场景集生成算法
王群， 董文略， 杨莉  中国电机工程学报, 2015
M Laborde  arXiv preprint arXiv:1506.00126, 2015  arxiv.org
Abstract: This paper presents existence and uniqueness results for a class of parabolic
systems with non linear diffusion and nonlocal interaction. These systems can be viewed as
regular perturbations of Wasserstein gradient flows. Here we extend results known in the ...
S Imani, SA Ghorashi, T Bouchoucha, MFA Ahmed…  ieeexplore.ieee.org
LETTERS On Wasserstein Barycenters and MMOSPA Estimation ...................... M. Baum, PK
Willett, and UD Hanebeck ... Objective Consumer Device Photo Quality Evaluation .................
........... MA Saad, P. Corriveau, and R. Jaladi ... Transmit Signal and Receive Filter ...
S Srivastava, C Li, DB Dunson  arXiv preprint arXiv:1508.05880, 2015  arxiv.org
Abstract: We propose a novel approach WASP for Bayesian inference when massive size of
the data prohibits posterior computations. WASP is estimated in three steps. First, data are
divided into smaller computationally tractable subsets. Second, posterior draws of ...
D HanKwan, M Iacobelli  arXiv preprint arXiv:1503.06097, 2015  arxiv.org
Abstract: This work is concerned with the quasineutral limit of the VlasovPoisson system in
two and three dimensions. We justify the formal limit for very small but rough perturbations of
analytic initial data, generalizing the results of\ cite {HI} to higher dimension.
C Jin  Nonlinear Analysis: Theory, Methods & Applications, 2015  Elsevier
Abstract We prove the well posedness of nonhomogeneous pressureless Euler system in 2
Wasserstein space with the initial mass and energy being finite. Our method is based on a
main observation pioneered by Brenier and Grenier that we can recover the solution of the ...
C Frogner, C Zhang, H Mobahi, M ArayaPolo…  arXiv preprint arXiv: …, 2015  arxiv.org Advances in Neural …, 2015 
Abstract: Learning to predict multilabel outputs is challenging, but in many problems there is
a natural metric on the outputs that can be used to improve predictions. In this paper we
develop a loss function for multilabel learning, based on the Wasserstein distance. The ...
C Ketterer  arXiv preprint arXiv:1509.02178, 2015  arxiv.org
Abstract: In this note we continue the analysis of metric measure space with variable ricci
curvature bounds. First, we study $(\ kappa, N) $convex functions on metric spaces where
$\ kappa $ is a lower semicontinuous function, and gradient flow curves in the sense of a ...
J Bigot, R Gouet, T Klein, A López  2015  math.ubordeaux1.fr
Abstract We introduce the method of Geodesic Principal Component Analysis (GPCA) on the
space of probability measures on the line, with finite second moment, endowed with the
Wasserstein metric. We discuss the advantages of this approach, over a standard ...
YH Kim, B Pass  arXiv preprint arXiv:1503.06460, 2015  arxiv.org
Abstract: This paper connects nonpositive sectional curvature of a Riemannian manifold with
the displacement convexity of the variance functional on the space $ P (M) $ of probability
measures over $ M $. We show that $ M $ has nonpositive sectional curvature and has ...
E Del Barrio, L Hélène, L JeanMichel  arXiv preprint arXiv:1508.06465, 2015  arxiv.org
Abstract: We propose a study of a distribution registration model for general deformation
functions. In this framework, we provide estimators of the deformations as well as a
goodness of fit test of the model. For this, we consider a criterion which studies the Fr {\'e} ...
T Rippl, A Munk, A Sturm  arXiv preprint arXiv:1507.04090, 2015  arxiv.org
Abstract: We derive central limit theorems for the Wasserstein distance between the
empirical distributions of Gaussian samples. The cases are distinguished whether the
underlying laws are the same or different. Results are based on the (quadratic) Fr\'echet ...
E Anderes, S Borgwardt, J Miller  arXiv preprint arXiv:1507.07218, 2015  arxiv.org
Abstract: Wasserstein barycenters correspond to optimal solutions of transport problems for
several marginals, and as such are at the core of applications ranging from economics to
statistics and computer science. The corresponding theory for data in the form of ...
D Loibl, D Matthes, J Zinsl  arXiv preprint arXiv:1507.05507, 2015  arxiv.org
Abstract: We prove the globalintime existence of nonnegative weak solutions to a class of
fourth order partial differential equations on a convex bounded domain in arbitrary spatial
dimensions. Our proof relies on the formal gradient flow structure of the equation with ...
V Seguy, M Cuturi  arXiv preprint arXiv:1506.07944, 2015  arxiv.org
Abstract: We consider in this work the space of probability measures P (X) on a Hilbert space
X endowed with the 2Wasserstein metric. Given a family of probability measures in P (X),
we propose an algorithm to compute curves that summarize efficiently that family in the 2 ...
C Döbler  arXiv preprint arXiv:1504.05938, 2015  arxiv.org
Abstract: We prove abstract bounds on the Wasserstein and Kolmogorov distances between
nonrandomly centered random sums of real iid random variables with a finite third moment
and the standard normal distribution. Except for the case of mean zero summands, these ...
D Zaev  arXiv preprint arXiv:1505.06061, 2015  arxiv.org
Abstract: We construct an analogue of the classical $ L^ p $Wasserstein distance for the
state space of a $ C^* $algebra. Given an abstract Lipschitz gauge on a $ C^* $algebra $\
mathcal {A} $ in the sense of Rieffel, one can define the classical $ L^ p $Wasserstein ...
M Oskarsson  maths.lth.se
Abstract. In this paper we direct our attention to the problem of discretization effects in
intensity transformations of images. We propose to use the Wasserstein metric (also known
as the Earth mover distance) to bootstrap the transformation process. The Wasserstein ...
M Erbar, J Maas, M Renger  arXiv preprint arXiv:1505.05712, 2015  arxiv.org
Abstract: We study the large deviation rate functional for the empirical distribution of
independent Brownian particles with drift. In one dimension, it has been shown by Adams,
Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\ ...
Z Su, W Zeng, Y Wang, ZL Lu, X Gu  Information Processing in Medical …, 2015  Springer
Abstract Brain morphometry study plays a fundamental role in medical imaging analysis and
diagnosis. This work proposes a novel framework for brain cortical surface classification
using Wasserstein distance, based on uniformization theory and Riemannian optimal ...
G Basso  2015  n.ethz.ch
The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions
we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric
space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a ...
A Ramdas, N Garcia, M Cuturi  arXiv preprint arXiv:1509.02237, 2015  arxiv.org
Abstract: Nonparametric two sample or homogeneity testing is a decision theoretic problem
that involves identifying differences between two random variables without making
parametric assumptions about their underlying distributions. The literature is old and rich, ...
G Montavon, KR Müller, M Cuturi  arXiv preprint arXiv:1507.01972, 2015  arxiv.org
Abstract: The Boltzmann machine provides a useful framework to learn highly complex,
multimodal and multiscale data distributions that occur in the real world. The default method
to learn its parameters consists of minimizing the KullbackLeibler (KL) divergence from ...
X Li, Y Lin  arXiv preprint arXiv:1505.04954, 2015  arxiv.org
Abstract: In this paper, we define the generalized Wasserstein distance for sets of Borel
probability measures and demonstrate that the weak convergence of sublinear expectations
can be characterized by means of this distance.
PM Esfahani, D Kuhn  arXiv preprint arXiv:1505.05116, 2015  arxiv.org
Abstract: We consider stochastic programs where the distribution of the uncertain
parameters is only observable through a finite training dataset. Using the Wasserstein
metric, we construct a ball in the space of (multivariate and nondiscrete) probability ...
Y Polyanskiy, Y Wu  arXiv preprint arXiv:1504.04419, 2015  arxiv.org
Abstract: It is shown that under suitable regularity conditions, differential entropy is a
Lipschitz functional on the space of distributions on $ n $dimensional Euclidean space with
respect to the quadratic Wasserstein distance. Under similar conditions,(discrete) ...
J Solomon, F de Goes, PA Studios…  … on Graphics (Proc. …, 2015  iip.ist.i.kyotou.ac.jp
Abstract This paper introduces a new class of algorithms for optimization problems involving
optimal transportation over geometric domains. Our main contribution is to show that optimal
transportation can be made tractable over large domains used in graphics, such as ...
TL Gouic, JM Loubes  arXiv preprint arXiv:1506.04153, 2015  arxiv.org
Abstract: In this paper, based on the Fr\'echet mean, we define a notion of barycenter
corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein
barycenters of random distributions defined on a geodesic space (E, d). We also prove the ...
Rudolf, Daniel; Schweizer, Nikolaus
Perturbation theory for Markov chains via Wasserstein distance
Abstract: Perturbation theory for Markov chains addresses the question how small
differences in the transitions of Markov chains are reflected in differences between their
distributions. We prove powerful and flexible bounds on the distance of the $ n $ th step ...
Cuturi, Marco; Peyré, Gabriel; Rolet, Antoine
A Smoothed Dual Approach for Variational Wasserstein Problems
Abstract: Variational problems that involve Wasserstein distances have been recently
proposed as a mean to summarize and learn from probability measures. Despite being
conceptually simple, such problems are computationally challenging because they ...
Dedecker, Jérôme; Merlevède, Florence
Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $alpha$dependent sequences
Abstract: We study the Wasserstein distance of order 1 between the empirical distribution
and the marginal distribution of stationary $\ alpha $dependent sequences. We prove some
moments inequalities of order p for any p $\ ge $1, and we give some conditions under ...
Peyré, Gabriel
Entropic Wasserstein Gradient Flows
Abstract: This article details a novel numerical scheme to approximate gradient flows for
optimal transport (ie Wasserstein) metrics. These flows have proved useful to tackle
theoretically and numerically nonlinear diffusion equations that model for instance porous ...
Bhattacharya, Anirban; Pati, Debdeep
Bernstein von Mises Theorems in Wasserstein distance
Abstract: We study the Bernstein vonMises (BvM) phenomenon in Gaussian process
regression models by retaining the leading terms of the induced KarhunenLoeve
expansion. A recent related result by Bontemps, 2011 in a sieve prior context necessitates ...
Berman, Robert J.; Onnheim, Magnus
Propagation of chaos, Wasserstein gradient flows and toric KahlerEinstein metrics
Abstract: Motivated by a probabilistic approach to KahlerEinstein metrics we consider a
general nonequlibrium statistical mechanics model in Euclidean space consisting of the
stochastic gradient flow of a given quasiconvex N particle interaction energy. We show ...
Kinderlehrer, David; Monsaingeon, Léonard; Xu, Xiang
A Wasserstein gradient flow approach to PoissonNernstPlanck equations
Abstract: The PoissonNernstPlanck system of equations used to model ionic transport is
interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of
probability measures with finite second moment. A variational scheme is then set up and ...
Jourdain, Benjamin; Reygner, Julien
A multitype sticky particle construction of Wasserstein stable semigroups solving onedimensional diagonal hyperbolic systems with large monotonic data
Abstract: This article is dedicated to the study of diagonal hyperbolic systems in one space
dimension, with cumulative distribution functions, or more generally nonconstant monotonic
bounded functions, as initial data. Under a uniform strict hyperbolicity assumption on the ...
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K Lee, A Halder, R Bhattacharya  Automatica, 2015  Elsevier
Abstract This paper focuses on the performance and robustness analysis of stochastic jump
linear systems. In the presence of stochastic jumps, state variables evolve as random
process, with associated time varying probability density functions. Consequently, system ...
M Bowles, M Agueh  Applied Mathematics Letters, 2015  Elsevier
Abstract We study a linear fractional Fokker–Planck equation that models nonlocal diffusion
in the presence of a potential field. The nonlocality is due to the appearance of the
'fractional Laplacian'in the corresponding PDE, in place of the classical Laplacian which ...
Related articles All 6 versions Cite Save
M Baum, P Willett, U Hanebeck  2015  ieeexplore.ieee.org
Abstract—The two title concepts have been evolving rather rapidly, but independent of each
other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image
processing as it can describe a measure of similarity between images. Its minimization ...
Cite Save [PDF] from arxiv.org Signal Processing Letters, …, 2015
GramSchmidtVaserstein generators for odd sized elementary groups
by Chattopadhyay, Pratyusha; Rao, Ravi A
(Submitted on 27 Nov 2015)
SciRate Published 30 Nov 2015 arXiv preprint arXiv:1511.08688, 2015
Solomon, Justin, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas. "Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains." SIGGRAPH 2015, Los Angeles. (supplemental document; code; slides)
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SS5: Averaging Measures: Wasserstein Barycenters, MMOSPA, and more
Description: Summarizing the information encoded in (one or more) probability measures is a fundamental problem in many areas such as signal processing, machine learning, computer vision, and data fusion. In this context, the concept of an “average” measure has recently gained significant interest: Wasserstein Barycenters are used, for example, for texture mixing and fusing (empirical) probability densities. In multitarget tracking with missing target identities, the mean square error (MSE) cannot be used to calculate expected target states. Hence, instead of the MSE the Mean Optimum Subpattern Assignment (MOSPA) distance is employed, which is closely related to the Wasserstein distance. This leads to Minimum MOPSPA estimates instead of MMSE estimates. This Special Session addresses all recent research results that involve the calculation of an “average” of (one or more) probability measures in all its variants. This includes both new theoretical results and applications.
Organizers: Marcus Baum, Karlsruhe Institute of Technology; Peter Willett; and Uwe Hanebeck, Karlsruhe Institute of Technology.
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2016 not in Math Reviews 52 items
J Fasel  arXiv preprint arXiv:1606.01266, 2016  arxiv.org
Abstract: We give a necessary and sufficient topological condition for the Vaserstein symbol
to be injective on smooth affine real threefolds. More precisely, we show that the Vaserstein
symbol is a bijection for such a threefold X if and only if the set of compact connected ...
N Bonneel, G Peyré, M Cuturi, F Mazenc…  ACM Transactions on …, 2016  team.inria.fr
article IEEE Transactions on Industrial Electronics, Institute of Electrical and Electronics
Engineers, 2015, IEEE Transactions on Industrial Electronics, pp. 2.< http://ieeexplore. ieee.
org/xpl/articleDetails. jsp? arnumber= 7115092&searchWithin% 5B% 5D=% 22Authors% ...
王瑜， 闫沫  西安航空学院学报, 2016  cqvip.com
摘要: 提出一种结合Wasserstein 距离和SBGFRLS 方法的非参数化活动轮廓图像分割算法.
该算法采用二值函数作为水平集函数并利用高斯核函数对其正则化, 有效避免水平集演化中的
重新初始化过程, 提高分割速度. 算法本身具有选择局部和全局分割的属性. 利用Wasserstein ...
P Gordaliza Pastor  2016  uvadoc.uva.es
En el análisis de la homogeneidad de una colección de distribuciones y de relaciones
estructurales entre las observaciones, son muy útiles los baricentros y la variación en
distancia de Wasserstein. Estudiamos la estimación de los cuantiles del proceso empírico ...
E Cazelles, J Bigot, N Papadakis  papersjds16.sfds.asso.fr
Abstract. The concept of barycenter in the Wasserstein space allows the defintion of a notion
of Fréchet mean of a set of probability measures. However, depending on the considered
data, such barycenters may be irregular. In this paper, we thus introduce a convex ...
G Flint  arXiv preprint arXiv:1605.08996, 2016  arxiv.org
Abstract: We construct a coupling between the random walk composed of L\'evy area
increments from a $ d $dimensional Brownian motion and a random walk composed of
quadratic polynomials of Gaussian random variables. This coupling construction is used ...
Related articles All 2 versions Cite Save
J Zinsl  arXiv preprint arXiv:1603.01375, 2016  arxiv.org
Abstract: This article is concerned with the existence of nonnegative weak solutions to a
particular fourthorder partial differential equation: it is a formal gradient flow with respect to
a generalized Wasserstein transportation distance with nonlinear mobility. The ...
E Bandini, A Cosso, M Fuhrman, H Pham  arXiv preprint arXiv: …, 2016  arxiv.org
Abstract: We study a stochastic optimal control problem for a partially observed diffusion. By
using the control randomization method in [4], we prove a corresponding randomized
dynamic programming principle (DPP) for the value function, which is obtained from a flow ...
GA Hanasusanto, D Kuhn  arXiv preprint arXiv:1609.07505, 2016  arxiv.org
Abstract: Adaptive robust optimization problems are usually solved approximately by
restricting the adaptive decisions to simple parametric decision rules. However, the
corresponding approximation error can be substantial. In this paper we show that two ...
A Farchi, M Bocquet, Y Roustan, A Mathieu, A Quérel  Tellus B, 2016  tellusb.net
ABSTRACT The verification of simulations against data and the comparison of model
simulation of pollutant fields rely on the critical choice of statistical indicators. Most of the
scores are based on pointwise, that is, local, value comparison. Such indicators are ...
J Zinsl, D Matthes  arXiv preprint arXiv:1609.06907, 2016  arxiv.org
Abstract: We propose a fully discrete variational scheme for nonlinear evolution equations
with gradient flow structure on the space of finite Radon measures on an interval with
respect to a generalized version of the Wasserstein distance with nonlinear mobility. Our ...
E del Barrio, JA CuestaAlbertos, C Matrán…  arXiv preprint arXiv: …, 2016  arxiv.org
Abstract: A robust clustering method for probabilities in Wasserstein space is introduced.
This newtrimmed $ k $barycenters' approach relies on recent results on barycenters in
Wasserstein space that allow intensive computation, as required by clustering algorithms. ...
G Tartavel, G Peyré, Y Gousseau  2016  hal.archivesouvertes.fr
This paper presents a novel variational approach to impose statistical constraints to the
output of both image generation (to perform typically texture synthesis) and image
restoration (for instance to achieve denoising and superresolution) methods. The ...
J Bigot, R Gouet, T Klein, A López  arXiv preprint arXiv:1606.03933, 2016  arxiv.org
Abstract: This paper is focused on the statistical analysis of probability densities functions $
f_ {1},\ ldots, f_ {n} $ on $\ R $ that can be viewed as independent realizations of an
underlying stochastic process. We consider the situation of practical importance where the ...
J Agredo  International Journal of Pure and Applied Mathematics, 2016  ijpam.eu
Abstract. We investigate about exponential convergence for generic quantum Markov
semigroups using an generalization of the Lipschitz seminorm and a noncommutative
analogue of Wasserstein distance. We show turns out to be closely related with classical ...
M Briani, E Cristiani, E Iacomini  arXiv preprint arXiv:1608.00126, 2016  arxiv.org
Abstract: In this paper we investigate the sensitivity of the LWR model on network to its
parameters and to the network itself. The quantification of sensitivity is obtained by
measuring the Wasserstein distance between two LWR solutions corresponding to ...
D Luo, J Wang  Mathematische Nachrichten, 2016  Wiley Online Library
In this paper we consider the following Itô stochastic differential equation dXt= σ dBt+ b (Xt)
dt,(1.1) where (Bt) t≥ 0 is a standard ddimensional Brownian motion, σ∈ Rd× d is a non
degenerate constant matrix, and b: Rd→ Rd is a Borel measurable vector field. Recently ...
J Bigot, E Cazelles, N Papadakis  arXiv preprint arXiv:1606.01025, 2016  arxiv.org
Abstract: The concept of barycenter in the Wasserstein space allows to define a notion of
Fr\'echet mean of a set of probability measures. However, depending on the data at hand,
such barycenters may be irregular. In this paper, we thus introduce a convex ...
J Blanchet, Y Kang  arXiv preprint arXiv:1605.01340, 2016  arxiv.org
Abstract: We present a novel inference approach which we call Sample OutofSample (or
SOS) inference. Our motivation is to propose a method which is well suited for datadriven
stress testing, in which emphasis is placed on measuring the impact of (plausible) outof ...
J Bertrand, BR Kloeckner  … Mathematics Research Notices, 2016  imrn.oxfordjournals.org
Abstract Given a metric space $ X $, one defines its Wasserstein space ${\ mathscr {W}
_2}(X) $ as a set of sufficiently decaying probability measures on $ X $ endowed with a
metric defined from optimal transportation. In this article, we continue the geometric study ...
J Ye, JZ Wang, J Li  arXiv preprint arXiv:1608.03859, 2016  arxiv.org
Abstract: Learning under a Wasserstein loss is an emerging research topic. We call
collectively the problems formulated under this framework Wasserstein Loss Minimization
(WLM). One important appeal of WLM is the innate capability to account for the prior ...
DM Mason  High Dimensional Probability VII, 2016  Springer
Abstract We shall demonstrate that weighted approximation technology provides an effective
set of tools to study the rate of convergence of the Wasserstein distance between the
cumulative distribution function [cdf] and the empirical cdf
A Halder, EDB Wendel  American Control Conference (ACC), …, 2016  ieeexplore.ieee.org
Abstract: We formulate and solve an optimal control problem in which a finite dimensional
linear time invariant (LTI) control system steers a given Gaussian probability density function
(PDF) close to another in fixed time, while minimizing the trajectorywise expected ...
R Kiesel, R Rühlicke, G Stahl, J Zheng  Risks, 2016  mdpi.com
In the aftermath of the financial crisis, it was realized that the mathematical models used for
the valuation of financial instruments and the quantification of risk inherent in portfolios
consisting of these financial instruments exhibit a substantial model risk. Consequently, ...
PC AlvarezEsteban, E del Barrio…  Journal of Mathematical …, 2016  Elsevier
Abstract Let P 2, ac P 2, ac be the set of Borel probabilities on R d R d with finite second
moment and absolutely continuous with respect to Lebesgue measure. We consider the
problem of finding the barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k ...
R Flamary, M Cuturi, N Courty…  arXiv preprint arXiv: …, 2016  arxiv.org
Abstract: Wasserstein Discriminant Analysis (WDA) is a new supervised method that can
improve classification of highdimensional data by computing a suitable linear map onto a
lower dimensional subspace. Following the blueprint of classical Linear Discriminant ...
F Santambrogio  arXiv preprint arXiv:1609.03890, 2016  arxiv.org
Abstract: This is an expository paper on the theory of gradient flows, and in particular of
those PDEs which can be interpreted as gradient flows for the Wasserstein metric on the
space of probability measures (a distance induced by optimal transport). The starting point ...
S Li, XD Li  arXiv preprint arXiv:1604.02596, 2016  arxiv.org
Abstract: We introduce Perelman's $ W $entropy and prove the $ W $entropy formula along
geodesic flow on the Wasserstein space $ P^\ infty_2 (M,\ mu) $ over compact Riemannian
manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we ...
A Alfonsi, J Corbetta, B Jourdain  arXiv preprint arXiv:1606.02994, 2016  arxiv.org
Abstract: In this paper, we are interested in the time derivative of the Wasserstein distance
between the marginals of two Markov processes. As recalled in the introduction, the
Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the ...
JG Liu, RL Pego, D Slepčev  arXiv preprint arXiv:1604.03387, 2016  arxiv.org
Abstract: We study a distance between shapes defined by minimizing the integral of kinetic
energy along transport paths constrained to measures with characteristicfunction densities.
The formal geodesic equations for this shape distance are Euler equations for ...
Y Shen  arXiv preprint arXiv:1603.02882, 2016  arxiv.org
Abstract: We prove a duality theorem of the FenchelMoreau type for convex and lower
semicontinuous functions of probability measures on Polish spaces equipped with the
Wasserstein metric of order 1. The derived dual representation is in form of its conjugate ...
Y Chen, J Ye, J Li  European Conference on Computer Vision, 2016  Springer
Abstract We propose a framework, named Aggregated Wasserstein, for computing a
dissimilarity measure or distance between two Hidden Markov Models with state conditional
distributions being Gaussian. For such HMMs, the marginal distribution at any time spot ...
A Irpino, F De Carvalho, R Verde  arXiv preprint arXiv:1605.00513, 2016  arxiv.org
Abstract: Distributional (or distributionvalued) data are a new type of data arising from
several sources and are considered as realizations of distributional variables. A new set of
fuzzy cmeans algorithms for data described by distributional variables is proposed.
FY Wang  arXiv preprint arXiv:1603.05749, 2016  arxiv.org
Abstract: Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted
Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a
convex boundary. It is well known that the BakryEmery curvature is bounded below by a ...
R Gao, AJ Kleywegt  arXiv preprint arXiv:1604.02199, 2016  arxiv.org
Abstract: Stochastic programming is a powerful approach for decisionmaking under
uncertainty. Unfortunately, the solution may be misleading if the underlying distribution of the
involved random parameters is not known exactly. In this paper, we study distributionally ...
JC VALENCIAGUEVARA, LCF FERREIRA  Livro de Resumos do IX ENAMA  enama.org
Abstract We develop a gradientflow theory for timedependent functionals in abstract metric
spaces. Results about global wellposedness and asymptotic behavior of solutions are
obtained. Conditions on functionals and metric spaces allow to consider the Wasserstein ...
D Luo, J Wang  arXiv preprint arXiv:1604.07206, 2016  adsabs.harvard.edu
Abstract We establish the exponential convergence with respect to the $ L^ 1$Wasserstein
distance and the total variation for the semigroup corresponding to the stochastic differential
equation (SDE) $ $ d X_t= d Z_t+ b (X_t)\, dt, $ $ where $(Z_t) _ {t\ ge0} $ is a pure jump L\' ...
G Peyré  crm.umontreal.ca
Optimal transport is the defacto standard to compare and average probability distributions
defined on the same metric space. In order to compare distributions on different metric
spaces, the GromovWasserstein (GW) distance introduced by Mémoli [1](see also [2]) ...
A Baíllo, J Cárcamo, KV Getman  arXiv preprint arXiv:1603.06806, 2016  arxiv.org
Abstract: Given a positive random variable X, we are interested in measuring how well the
exponential distribution with the same mean approximates the probability distribution of X,
based on the information provided by a sample from X. Specifically, we consider the ...
G Legendre, G Turinici  2016  hal.archivesouvertes.fr
The time discretization of gradient flows in metric spaces uses variants of the celebrated
implicit Eulertype scheme of Jordan, Kinderlehrer and Otto. We propose in this Note a
different approach which allows to construct two second order in time numerical schemes. ...
XS Shen  arXiv preprint arXiv:1604.03504, 2016  arxiv.org
Abstract: In this short note, we would like to give a construction of parallel transport for
tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete
proof for the linear part of the tangent space, and show that a construction for the full ...
Related articles All 2 versions Cite Save
A Rolet, M Cuturi, G Peyré  … of the 19th International Conference on …, 2016  jmlr.org
Abstract We consider in this paper the dictionary learning problem when the observations
are normalized histograms of features. This problem can be tackled using nonnegative
matrix factorization approaches, using typically Euclidean or KullbackLeibler fitting errors. ...
J Wang  Bernoulli, 2016  projecteuclid.org
Abstract Coupling by reflection mixed with synchronous coupling is constructed for a class of
stochastic differential equations (SDEs) driven by Lévy noises. As an application, we
establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ ge0} $ ...
M Hauray  Journal of Statistical Physics, 2016  Springer
Abstract We study here a very popular 1D jump model introduced by Kac: it consists of N
velocities encountering random binary collisions at which they randomly exchange energy.
We show the uniform (in N) exponential contractivity of the dynamics in a nonstandard ...
F Al Reda, B Maury  2016  hal.archivesouvertes.fr
This paper establishes a link between some space discretization strategies of the Finite
Volume type for the FokkerPlanck equation in general meshes (Voronoï tesselations) and
gradient flows on the underlying networks of cells, in the framework of discrete ...
J Shi, W Zhang, Y Wang  Proceedings of the IEEE Conference on …, 2016  cvfoundation.org
Abstract Shape space is an active research field in computer vision study. The shape
distance defined in a shape space may provide a simple and refined index to represent a
unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein ...
A Zhai  arXiv preprint arXiv:1602.05565, 2016  arxiv.org
Abstract: Let $ X_1,\ ldots, X_n $ be iid random vectors in $\ mathbb {R}^ d $ with $\ X_1\\
le\ beta $. Then, we show that $\ frac {1}{\ sqrt {n}}(X_1+\ ldots+ X_n) $ converges to a
Gaussian in Wasserstein2 distance at a rate of $ O\ left (\ frac {\ sqrt {d}\ beta\ log n}{\ sqrt { ...
F Baudoin  arXiv preprint arXiv:1602.04177, 2016  arxiv.org
Abstract: Gradient bounds had proved to be a very efficient tool for the control of the rate of
convergence to equilibrium for parabolic evolution equations. Among the gradient bounds
methods, the celebrated Bakry\'Emery criterion is a powerful way prove to convergence to ...
T Bonis  arXiv preprint arXiv:1602.02616, 2016  arxiv.org
Abstract: We study the problem of sampling from a distribution $\ target $ using the Langevin
Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of
Wasserstein distance of order $2 $. Our result holds as long as the continuous diffusion ...
R Hendrikson  2016  dspace.ut.ee
In many fields such as social sciences or biology, relations between data or variables are
presented as networks. To compare these networks, a meaningful notion of distance
between networks is highly desired. The aim of this Master thesis is to study, implement, ...
Y Chen, T Georgiou, M Pavon  arXiv preprint arXiv:1601.04891, 2016  arxiv.org
Abstract: Since the early nineties, it has been observed that the Schroedinger bridge
problem can be formulated as a stochastic control problem with atypical boundary
constraints. This in turn has a fluid dynamic counterpart where the flow of probability ...
B Arras, E Azmoodeh, G Poly, Y Swan  arXiv preprint arXiv:1601.03301, 2016  arxiv.org
Abstract: In the first part of the paper we use a new Fourier technique to obtain a Stein
characterizations for random variables in the second Wiener chaos. We provide the
connection between this result and similar conclusions that can be derived using Malliavin ...
G Peyré, M Cuturi, J Solomon  ICML 2016, 2016  hal.archivesouvertes.fr
This paper presents a new technique for computing the barycenter of a set of distance or
kernel matrices. These matrices, which define the interrelationships between points sampled
from individual domains, are not required to have the same size or to be in rowbyrow ...

117 items + 39 (2011) + 41 (2012) + 55 (2013) + 52 (2014) + 60 (2015) + 52 (2016) = 437 items

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