My name in title from Math Reviews
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Vaserstein without Math. Reviews 19802017 8 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: ...
关于一个 Vaserstein 问题 [About a Vaserstein question]
张兆基  浙江大学学报: 自然科学版, 1994  cqvip.com
Dennis–Vaserstein type decompositions
Journal of Mathematical Sciences (2010) 171: 331337 , November 17, 2010
By Vavilov, N. A.; Sinchuk, S. S.. Zbl 1215.20049
On asymptotics of Vaserstein's coupling for a Markov chain
File Format: PDF/Adobe Acrobat
by OA Butkovsky 
On asymptotics of Vaserstein's coupling for a. Markov chain. O.A.Butkovsky. ∗. & A.Yu.Veretennikov. †. Abstract. In this paper rate of convergence to stationary ...
July 2529 2011
STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume: 123 Issue: 9 Pages: 35183541 DOI: 10.1016/j.spa.2013.04.016 Published: SEP 2013
On asymptotics for Vaserstein coupling of a Markov chain
Veretennikov A. (With O.A.Butkovsky) International Mathematical Conference "50 years of IPPI", July 2529 2011 Moscow, Russia, Proceedings, ISBN 9785901158159
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On asymptotics for Vaserstein coupling of Markov chains
by OA Butkovsky  2013  Cited by 3  Related articles
2013 Stochastic Processes and their Applications volume 123 issue 9 pp 35183541
Apr 25, 2013  We prove that strong ergodicity of a Markov process is linked with a spectral radius of a certain “associated” semigroup operator, although, not a “natura.
Stochastic Processes and their …, 2013  Elsevier
[pdf] On asymptotics for Vaserstein coupling of a Markov chain
The Vaserstein symbol on real smooth affine threefolds arXiv
J Fasel  arXiv preprint arXiv:1606.01266, 2016  arxiv.org
Abstract: We give a necessary and sufficient topological condition for the Vaserstein symbol
to be injective on smooth affine real threefolds. More precisely, we show that the Vaserstein
symbol is a bijection for such a threefold X if and only if the set of compact connected ...
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
Транспортная задача МонжаКанторовича, пространство Васерштейна и его геометрия
[Transportation prob;em of MongeKantorovich, the Vaserstein space and its geometry]
Семинар Добрушинской математической лаборатории [March 21, 2019[
17.03.2017  Ефимова Мария Александровна 21 марта 2017 г.
A Generalized Vaserstein symbol Tariq Syed Nov 23, 2017
arXiv:1711.08210 [pdf, ps, other]
A Generalized Vaserstein symbol
Comments: 36 pages
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC); KTheory and Homology (math.KT)
Wasserstein 19731989 without Math. Reviews 43items
代数的 K 群に関する Wasserstein の仕事 (Analytic Varieties 及び ...
(Problems on Stratified Spaces and Analytic Varieties) Wasserstein work on algebraic group RIMS Kokyuroku 0372, 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
On a formula for the L2 Wasserstein metric between measures on Euclidean and Hilbert spaces
M Gelbrich  Mathematische Nachrichten, 1990  Wiley Online Library Vol 147 Issue 1
Abstract. For a separable metric space (X, d ) LP WASSERSTEIN metrics between probability
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
Volume 6, Issue 1991 of Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria
... Please use this identifier to cite or link to this item: http://hdl.handle.net/10068/294976.
Authors: Cuesta Albertos, Juan
A. Matran Bea, Carlos Cantabria Univ., Santander (Spain). Dept. ...
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 6 items
[PDF] TESTS OF GOODNESS OF FIT BASED ON THE L2WASSERSTEIN DISTANCE
JA CuestaAlbertos, E Del Barrio, C Matrán  1999  Citeseer
The Annals of Statistics 1999, Vol. 27, No. 4, 1230–1239
Abstract Given P1 and P2 in the set of probabilities on the line with nite second order
moment, P2 (<); the 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
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 ...
Related articles  View as HTML  All 5 versions
published 2004
Shape recognition via Wasserstein distance
W Gangbo, RJ McCann  1999  mis.mpg.de
Quarterly of applied mathematics, 58 (2000) 4, p. 705737
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  Abteilung für Mathematische …
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.
by E Del Barrio  2005  Cited by 40  Related articles
Del Barrio , Giné , Utzet : Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances.
[CITATION] Asymptotics for empirical Wasserstein distances
Eustasio del Barrio Department of Statistics and Operations Research, University of Valladolid, Prado de la Magdalena S/N, 47005, Valladolid, Spain [tasio@eio.uva.es]
Feb 23, 2001 –
Asymptotics for Wasserstein distances pdf
E del Barrio  unavarra.es
Wp is a metric on the space of probability measures with finite 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
Wasserstein space and Ricci flow.
J. Lott American Mathematical Society 2005
Meeting: 1007, Santa Barbara, California, SS 9A, Special Session on Ricci Flow/Riemannian Geometry. 100758105. John Lott* (lott@umich.edu), Department ...
Contractivity of Wassersteintype distances:
asymptotic profiles, equilibration rates and qualitative properties.
File Format: PDF/Adobe Acrobat
José A. Carrillo. Instituci`o Catalana de. Recerca i ...
Paris 2004
[PDF] Notes on a Wasserstein metric convergence method for FokkerPlanck equations with point controls
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 ...
[pdf] Gradient Flows: In Metric Spaces and in the Space of Probability ...
[CITATION] Gradient flows in metric spaces and in the Wasserstein space of probability measures
LANGG Savare  2004  Birkhäuser
2005 by L Ambrosio, N Gigli, G
by W Gangbo  2006  Related articles
The first part is about nonsmooth analysis and ordinary differential equations on metric spaces. The tools developed in this first part apply mainly to gradient flow differential equations. ... The second part focuses on some particular metric spaces, the set of probability measures, endowed with a Wasserstein distance.
A 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
[CITATION] A fourth order parabolic equation and the Wasserstein distance
U Gianazza, G Toscani, G Savaré  Preprint IMATICNR, Pavia, 2004
U. Gianazza, G. Toscani, and G. Savaré, A fourth order parabolic
equation and the Wasserstein distance, tech. rep., IMATICNR, Pavia, 2004.
to appear.
Wasserstein metrics and empirical distributions in stability of stochastic programs
[PDF] from jcu.czM Houda  … of the International Conference Quantitative Methods …, 2004  ef.jcu.cz
Abstract Practical economic problems often ask for optimization procedures, not
unfrequently with random inputs leading thus to stochastic programming models. The
randomness is modelled through the underlying probability distribution, which is assumed ...
Cited by 2  Related articles  View as HTML
Notes on a Wasserstein metric convergence method for 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
[Research for image recognition based on Wasserstein distance]
赵春江， 施文康， 邓勇  NCIRCS2004 第一届全国信息检索与内容 …, 2004  cpfd.cnki.com.cn
[摘要]: Wasserstein 距离是定义在概率空间上的二阶矩. 首先分析了Wasserstein
距离的经典数学表达式, 和用于实际工程计算的经验公式. 然后举了一个简单的例子,
来说明Wasserstein 距离的实际作用. 通过实验和与Hausdorff 距离相比较可以看出, 完全可以 ...
Wasserstein distance of target recognition research based
[CITATION] Flussi gradiente in spazi metrici e nello spazio di Wasserstein delle misure di probability
L AMBROSIO  Rendiconti della Accademia nazionale delle scienze …, 2005  L'Accademia
Hamiltonian ODE's in the Wasserstein space of probability measures
LAW Gangbo  2005  calcvar.sns.it
Abstract: In this paper we consider a Hamiltonian $ H $ on ${\ cal P} _2 (* R*^{2d}) $, the set
of probability measures with finite quadratic moments on the phase space $* R*^{2d} $,
which is a metric space when endowed with the Wasserstein distance $ W_2. $ We study ...
All 12 versions Cite Save More
The Wasserstein Distance and its Behaviour along Geodesics
L Ambrosio, N Gigli, G Savaré  Gradient Flows: in Metric Spaces and in …, 2005  Springer
In this chapter we endow Pp (X), when X is a separable Hilbert space, with a kind of
differential structure, consistent with the metric structure introduced in the previous chapter.
Our starting point is the analysis of absolutely continuous curves µt:(a, b)→ Pp (X) and of ...
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 MR22 9130 (2006j:76121)
Cited by 270 Related articles All 18 versions MR2209130 (2006j:76121) C
Optimal quantizer performance and the Wasserstein distortion
S Matloub, DB O'Brien…  … , 2005. Proceedings. DCC …, 2005  ieeexplore.ieee.org
Abstract The Wasserstein distortion has proved useful in a variety of mathematical, signal
processing and coding problems as a measure of how different two distributions are. In this
paper we provide an expression for the performance of the optimal entropy constrained ...
Cited by 2  Related articles  All 7 versions
On constrained optimization in the Wasserstein metric
[PDF] from cmu.eduA Tudorascu  2005  math.cmu.edu
Abstract In this paper we prove the monotonicity of the 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 15 items
Path functionals over Wasserstein spaces
A Brancolini, G Buttazzo, F Santambrogio  Journal of the European …, 2006  emsph.org
Abstract. Given a metric space X we consider a general class of functionals which measure
the cost of a path in X joining two given points x0 and x1, providing abstract existence results
for optimal paths. The results are then applied to the case when X is a Wasserstein space of …
Cited by 56 Related articles All 7 versions
[PDF] semanticscholar.org MR2250166 (2007j:49051)
On Stein's factors for Poisson approximation in Wasserstein distance
AD Barbour, A Xia  Bernoulli, 2006  JSTOR
Stein's method for Poisson approximation was adapted by Chen (1975) from Stein's (1972) method
for normal approximation, and it has proved to be an extremely powerful tool for establishing
Poisson approximations to sums of dependent integervalued random variables (see Barbour …
Cited by 22 Related articles All 13 versions MR2274850 (2008f:62025)
Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws
JA Carrillo, M Di Francesco, C Lattanzio  Journal of Differential Equations, 2006  Elsevier
Abstract The aim of this paper is to analyze contractivity properties of Wassersteintype
metrics for onedimensional scalar conservation laws with nonnegative, L∞ and compactly
supported initial data and its implications on the long time asymptotics. The flux is assumed …
Cited by 18 Related articles All 12 versions MR2287892 (2007k:35315)
arXiv:math/0612562 [pdf, ps, other]
John Lott (Submitted on 19 Dec 2006 (v1), last revised 9 Apr 2007 (this version, v2))
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 ...
Cited by 69 Related articles All 14 versions
Dynamic clustering of histograms using Wasserstein metric
[PDF] from psu.eduA Irpino, R Verde…  COMPSTAT, 2006  Citeseer
In the present paper we present a new distance, based on the Wasserstein metric, in order
to cluster a set of data described by distributions with finite continue support. The proposed
distance allows to define a measure of inertia of data with respect a barycenter that ...
Cited by 46 Related articles All 6 versions
Necessary optimality conditions for geodesics in weighted Wasserstein spaces
[PDF] from arxiv.orgL Ambrosio…  Arxiv preprint math/0603435, 2006  arxiv.org
Abstract: The geodesic problem in Wasserstein spaces with a metric perturbed by a
conformal factor is considered, and necessary optimality conditions are estabilished in a
case where this conformal factor favours the spreading of the probability measure along ...
Cited by 14 Related articles All 15 versions
Remarks on the JKO variational scheme and constrained optimization in the Wasserstein metric
A Tudorascu  mathcs.emory.edu
Recent advances in evolutionary partial differential equations are based upon interpreting
the evolution as gradient flow/steepest descent with respect to MongeKantorovich metrics.
An extensive literature on this topic is already available, originating with the work of Otto ...
Related articles All 3 versions
Asymptotic power of goodness of fit tests based on Wasserstein distance
H Boistard  personales.unican.es
We present a preliminary study for the power of Wasserstein goodness of fit test. Under H0,
X1,...,Xn are iid with distribution function F, density function f and quantile function F−1. The Wasserstein
test is based on the statistic: n ∫ 1 ... 0 (F−1 n (t) − F−1(t)) 2 dt − an,
Related articles All 2 versions
S Lisini  2006  math.sns.it
Dottorato di ricerca in Matematica e Statistica ... 1.1 Absolutely continuous curves in metric spaces
and metric derivative . . . . . 15 ... 1.3 Metric Sobolev spaces W1,p(I; X). . . . . . . . . . . . . . . . . . . . .
. . . . 17 ... 1.4 Borel probability measures, narrow topology and tightness . . . . . . . . . . . 19
Related articles All 8 versions
Wasserstein distance on configuration space
L Decreusefond  arXiv preprint math/0602134, 2006  arxiv.org
Abstract: We investigate here the optimal transportation problem on configuration space for
the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is
finite, there exists one unique optimal measure and that this measure is supported by the ...
(Submitted on 7 Feb 2006)
The Wasserstein gradient flow of the Fisher information and the Quantum DriftDiffusion equation
UGGSG Toscani  2006  cvgmt.sns.it
Despite the lack of a maximum principle for fourth order equations, nonnegative solutions can
be obtained as a limit of a variational approximation scheme by exploiting the particular structure
of this equation, which is the gradient flow of the Fisher Information functional with respect ...
Cited by 126 Related articles All 22 versions
U Gianazza, G Savaré, G Toscani  Archive for rational mechanics and …, 2009  Springer
[CITATION] Diffusion is a 2Wasserstein contraction on any manifold evolving by reverse Ricci flow
RJ McCann…  Preprint, 2006
by RJ MCCANN  2008  Cited by 79  Related articles
2Wasserstein distance W2(ν, ˜ν,τ) between them evolves according to its defi nition. (3). W2. 2 (ν, ˜ν,τ) = inf π∈Γ(ν,˜ν). ∫. M×M d2(x,y,τ) dπ(x,y). Date: March 14, 2008. ∗
This paper supercedes the earlier paper Diffusion is a 2Wasserstein contraction on any manifold evolving by reverse Ricci flow (2006). c 2007, the ...
Separability and completeness for the Wasserstein distance, to appear in Séminaire de probabilités
F Bolley  Lecture Notes in Math, 2006 pdf
2007 without Math. Reviews 15 items
. arXiv:0706.1172 [pdf, ps, other]
Stein's method and Poisson process approximation for a class of Wasserstein metrics
Comments: Published in at this http URL the Bernoulli (this http URL) by the International Statistical Institute/Bernoulli Society (this http URL)
Journalref: Bernoulli 2009, Vol. 15, No. 2, 550568
Subjects: Probability (math.PR)
arXiv:0704.0876 [pdf, ps, other]
Nonmonotone convergence in the quadratic Wasserstein distance
Walter Schachermayer, Uwe Schmock, Josef Teichmann
Subjects: Probability (math.PR)
arXiv:0704.0704 [pdf, ps, other]
Entropic Measure and Wasserstein Diffusion
MaxK von Renesse, KarlTheodor Sturm
Subjects: Probability (math.PR); Analysis of PDEs (math.AP)
arXiv:math/0006044 [pdf, ps, other]
Particle Approximation of the Wasserstein Diffusion
Sebastian Andres, MaxK. von Renesse
(Submitted on 14 Dec 2007)
IRPINO A., VERDE R. (2007). Clustering linear models using Wasserstein distance. In: classification and data analysis 2007, book of short paper. cladag 2007. macerata. 1214 september 2007. (pp. 107110). ISBN/ISSN: 9788860560209. MACERATA: eum (ITALY).
by A Irpino  2010  Related articles
Nov 25, 2009  Clustering Linear Models Using Wasserstein Distance. Authors; Authors ... Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS) ... We show the properties of the proposed metric and an application to real data using a dynamic clustering algorithm.
Histogram based segmentation using Wasserstein distances
Scale Space and Variational Methods in Computer Vision
Tony Chan, Selim Esedoglu and Kangyu Ni
Lecture Notes in Computer Science, 2007, Volume 4485/2007, 697708,
Wasserstein Space and FokkerPlanck Equation
S Fang  2007 Wiley China 方诗赞
Fang ShiChan Wasserstein Space and FokkerPlanck Equation
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 19 items
arXiv:0909.2512 [pdf, ps, other]
On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals
Stefano Lisini, Antonio Marigonda
Comments: 22 pages
Subjects: Functional Analysis (math.FA); Analysis of PDEs (math.AP)
arXiv:0906.2280 [pdf, ps, other]
A new Poissontype deviation inequality for Markov jump processes with positive Wasserstein curvature
Comments: Published in at this http URL the Bernoulli (this http URL) by the International Statistical Institute/Bernoulli Society (this http URL)
Journalref: Bernoulli 2009, Vol. 15, No. 2, 532549
Subjects: Statistics Theory (math.ST)
arXiv:0812.4847 [pdf, ps, other]
Polynomial birthdeath distribution approximation in Wasserstein distance
Comments: 16 pages
Journalref: Journal of Theoretical Probability 22 (2009), 294310.
Subjects: Probability (math.PR)
arXiv:0807.1065 [pdf, ps, other]
Differential forms on Wasserstein space and infinitedimensional Hamiltonian systems
Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Comments: Version 2. Improved presentation, slight technical changes. To appear in Memoirs AMS
Subjects: Analysis of PDEs (math.AP); Symplectic Geometry (math.SG)
Eulerian calculus for the displacement convexity in the Wasserstein distance
Journalref: SIAM J. Math. Anal. 40 (2008), 11041122
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
arXiv:0801.2250 [pdf, ps, other]
On Wasserstein geometry of the space of Gaussian measures
Comments: 15pages, 1figures
Subjects: Differential Geometry (math.DG); Probability (math.PR)
Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance
by R Verde  2008  Cited by 29  Related articles
Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance. Authors ... representation of large data sets: Fisher vs piecewise linear approximations.
Title: Dynamic clustering of interval data using a 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 aeXiv
[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 ..
.arXiv:0812.1269 [pdf, ps, other]
A New Interval Data Distance Based on the Wasserstein Metric
R Verde…  Data Analysis, Machine Learning and Applications, 2008  Springer
Interval data allow statistical units to be described by means of interval values, whereas their
representation by single values appears to be too reductive or inconsistent, that is, unable to
keep the uncertainty usually inherent to the observed data. In the present paper, we ...
[PDF] A geometric study of the Wasserstein space of the line
[PDF] from inria.frB Kloeckner  Preprint, 2008  hal.inria.fr
The concept of optimal transportation raised recently a growing interest in link with the
geometry of metric spaces. In particular the L2 Wasserstein space W2 (X) have been used in
[6] and [8, 9] to define certain curvature conditions on a metric space X. Many useful ...
Kantorovich‐Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology
J Pousin  AIP Conference Proceedings, 2008  link.aip.org
Determining the influence of a biological species to the evolution of an other one strongly
depends on the choice of mathematical models in biology. In this work we consider the case
of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma, ...
Introduction to Wasserstein Spaces
[PDF] from bnu.edu.cnS Fang  2008  math.bnu.edu.cn
Page 1. Introduction to Wasserstein Spaces Shizan Fang Stochastic research Center, Beijing
Normal University Beijing, 100875, China ... The purpose of this lecture is to understand the
geometric structure of P2(Rd). 1 Wasserstein Space (P2(Rd), W2) 1.1 Wasserstein distance ...
Ordinary Least Squares for Histogram Data Based on Wasserstein Distance
R Verde…  COMPSTAT'2010 Book of Abstracts, 2008  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
Cited by 181 Related articles All 24 versions
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 26 Related articles All 16 versions
Estimates on path functionals over Wasserstein spaces
[PDF] from sissa.itS Bianchini…  2009  digitallibrary.sissa.it
In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and
Santambrogio, J. Eur. Math. Soc.(JEMS), 8 (2006), pp. 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 NavierStokes equations cieulike
M Hairer…  2009  citeulike.org
Abstract We develop a general method to prove the existence of spectral gaps for Markov
semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for
this analysis is neither a weighted supremum norm nor an $\ L^ p $type norm, but ...
aarXiv:math/0602479 [pdf, ps, other]
[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 26 items
Gradient ows in Wasserstein spaces and applications to crowd movement S eminaire XEDP, October 19th, 2010 Filippo Santambrogio November 17, 2010
Gradient flows in Wasserstein spaces and applications to crowd movement
[PDF] from sns.itF Santambrogio  2010  cvgmt.sns.it
Abstract Starting from a motivation in the modeling of crowd movement, the paper presents the
topics of gradient flows, first in Rn, then in metric spaces, and finally in the space of prob ability
measures endowed with the Wasserstein distance (induced by the quadratic trans port ...
aarXiv:1104.4223 [pdf, ps, other]
Generalized Orlicz spaces and Wasserstein distances for convexconcave scale functions
Subjects: Functional Analysis (math.FA); Probability (math.PR)
arXiv:1102.1842 [pdf, ps, other]
Central limit theorem for Markov processes with spectral gap in the Wasserstein metric
Tomasz Komorowski, Anna Walczuk
Subjects: Probability (math.PR)
On Wasserstein Geometry of Gaussian Measures (A Takatsu) in
Advanced Studies in Pure Mathematics: Volume 57
Probabilistic Approach To Geometry
Edited by: Motoko Kotani (Tohoku University), Masanori Hino (Kyoto University), Takashi Kumagai (Kyoto University)
Gradient ows in Wasserstein spaces and applications to ...
cvgmt.sns.it/media/doc/paper/511/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 ...
[PDF] Metric Currents and Geometry of Wasserstein Spaces
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 ...
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 41 items
[PDF] arxiv.org Comparison between distance and norm, and localisation of Wasserstein distance
R Peyre  arXiv preprint arXiv:1104.4631, 2011  arxiv.org
Abstract: It is well known that the quadratic Wasserstein distance $ W_2 (\mathord
{\boldsymbol {\cdot}},\mathord {\boldsymbol {\cdot}}) $ is formally equivalent, for
infinitesimally small perturbations, to some weighted $ H^{1} $ homogeneous Sobolev
Related articles All 2 versions
N Gigli  Memoirs of the American Mathematical Society, 2011  iris.sissa.it
We develop a rigorous second order analysis on the space of probability measures on a
Riemannian manifold endowed with the quadratic optimal transport distance $ W_2 $. Our
discussion comprehends: definition of covariant derivative, discussion of the problem of
arXiv:1104.4631 [pdf, ps, other]
Comparison between W_{2} distance and H˙^{ 1} 1norm, and localisation of Wasserstein distance
Comments: Added a new section about application to the localisation of Wasserstein distance
Subjects: Functional Analysis (math.FA)
arXiv:1008.3658 [pdf, ps, other]
Kramers' formula for chemical reactions in the context of Wasserstein gradient flows
Michael Herrmann, Barbara Niethammer
Comments: revised proofs, 12 pages, 1 figure
Journalref: Commun. Math. Sci., vol. 9, no. 2, pp.623635, 2011
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (mathph)
Problèmes d'interaction discretcontinu et distances de Wasserstein
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
Régularisation de Wasserstein. Application au Transfert de Couleur
G Peyré, R Julien  2011  basepub.dauphine.fr
Résumé en français: Ce papier introduit une nouvelle approche méthodologique pour la
résolution de problèmes variationnels sous contraintes statistiques en grande dimension.
Nous nous plaçons dans le cadre de la théorie du transport optimal de Monge ...
Cited by 2 Related articles All 3 versions
Large Deviations for a matching problem related to the $\ infty $Wasserstein distance
J Trashorras  2011  hal.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 ...
Wellposedness of Wasserstein Gradient Flow Solutions of Higher Order Evolution Equations
E Kamalinejad  arXiv preprint arXiv:1112.4407, 2011  arxiv.org
Abstract: A relaxed notion of displacement convexity is defined and used to establish short
time existence and uniqueness of Wasserstein gradient flows for higher order energy
functionals. As an application, local and global wellposedness of different higher order ...
Existence and uniqueness of GEXIT curves via the Wasserstein metric
S Kudekar, T Richardson… Information Theory Workshop (ITW), 2011 IEEE  ieeexplore.ieee.org
Abstract In the analysis of iterative coding systems it is often necessary to compare two
densities and to measure how close they are. Sometimes it is convenient to compare their
entropy or their Battacharyya parameter. But sometimes a more powerful measure is ...
Simple bounds for the convergence of empirical and occupation measures in 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 ...
A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces
B Kloeckner  arXiv preprint arXiv:1105.0360, 2011  arxiv.org
Abstract: A Wasserstein spaces is a metric space of sufficiently concentrated probability
measures over a general metric space. The main goal of this paper is to estimate the
largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize ...
published
Gromov–Wasserstein distances and the metric approach to object matching
F Mémoli  Foundations of Computational Mathematics, 2011  Springer
Abstract This paper discusses certain modifications of the ideas concerning the Gromov–
Hausdorff distance which have the goal of modeling and tackling the practical problems of
object matching and comparison. Objects are viewed as metric measure spaces, and ...
A spectral notion of Gromov–Wasserstein distance and related methods
F Mémoli  Applied and Computational Harmonic Analysis, 2011  Elsevier
We introduce a spectral notion of distance between objects and study its theoretical
properties. Our distance satisfies the properties of a metric on the class of isometric shapes,
which means, in particular, that two shapes are at 0 distance if and only if they are ...
Regularisation de Wasserstein et Application au Transfert de Couleur (J. Rabin, G. Peyré), Gretsi'11, 2011. [bib] [pdf]
““Exact” Deviations in Wasserstein Distance for Empirical and Occupation Measures”,
E. Boissard, and T. le Gouic,
Preprint, arXiv:1103.3188v1, 2011.
We study the problem of 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.
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 ...
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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
Conformal Wasserstein distance: II. Computational aspects and extensions
Y Lipman, J Puente, I Daubechies  arXiv preprint arXiv:1103.4681, 2011  arxiv.org
Abstract: This paper is a companion paper to [Lipman and Daubechies 2011]. We provide
numerical procedures and algorithms for computing the alignment of and distance between
two disk type surfaces. We provide a convergence analysis of the discrete approximation ...
Large Deviations for a matching problem related to the∞Wasserstein distance
[PDF] from 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
J RABIN, G PEYRÉ, J DELON  smai.emath.fr
Contexte De nombreuses applications en vision par ordinateur ou en traitement d'images
requierent une étape préliminaire d'apprentissage des statistiques “moyennes” des
caractéristiques d'une classe d'objets. Cette problématique a été principalement étudié ...
Wasserstein barycenter and its application to texture mixing
[PDF] from google.comJ Rabin, G Peyré, J Delon…  Proc. of SSVM, 2011  sites.google.com
Abstract. This paper proposes a new definition of the averaging of discrete probability
distributions as a barycenter over the MongeKantorovich optimal transport space. To
overcome the time complexity involved by the numerical solving of such problem, the ...
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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2012 not in Math. Reviews 39 items
Perelman's Wentropy and Wasserstein distance for the WittenLaplacian and the FokkerPlanck diffusions on
Riemannian manifolds
University of Kansas
Jan 22, 2012  Perelman's Wentropy and Wasserstein distance for the. WittenLaplacian and the FokkerPlanck diffusions on. Riemannian manifolds.
A GEOMETRIC STUDY OF WASSERSTEIN SPACES : EMBEDDING POWERS…  HAL
File Format: Adobe PostScript  View as HTML 2012 by. Benoˆıt Kloeckner.
Abstract. — The Wasserstein spaces #p(X) of a metric ... pdf
Optimality of the triangular lattice for a particle system with Wasserstein interaction
DP Bourne, MA Peletier, F Theil  arXiv preprint arXiv:1212.6973, 2012  arxiv.org
Abstract: We prove strong crystallization results in two dimensions for an energy that arises
in the theory of block copolymers. The energy is defined on sets of points and their weights,
or equivalently on the set of atomic measures. It consists of two terms; the first term is the ...
An extension of the Weak KAM theory to the Wasserstein torus
[PDF] from wvu.edu W Gangbo…  math.wvu.edu
Abstract The study of asymptotic behavior of minimizing trajectories on the Wasserstein
space P (Td) has so far been limited to the case d= 1 as all prior studies heavily relied on the
isometric identification of P (T) with a subset of the Hilbert space L2 (0, 1). There is no ...
Wasserstein barycenter and its application to texture mixing
J Rabin, G Peyré, J Delon…  Scale Space and Variational …, 2012  Springer
This paper proposes a new definition of the averaging of discrete probability distributions as
a barycenter over the 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 ...
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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 ...
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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 ...
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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 [Study on Fuzzy Clustering of Interval Data in Data Mining  Based on Wasserstein Measurements]
李红…  计算机工程与应用, 2012  cqvip.com
针对目前区间数据模糊聚类研究中区间距离定义存在的局限性, 引入能够考虑区间数值分布特征
的Wasserstein 距离测度, 提出基于Wasserstein 距离测度的单指标和双指标自适应模糊聚类
算法及迭代模型. 通过仿真实验和CR 指数, 证实了该类模型的优势. 该算法在海量, 堆积如山 ...
[Li Hong , Sun Qiu Bi Data Mining the interval fuzzy clustering  based Wasserstein measure]
[School of Management Department of Statistics, Fuzhou 350108]
Abstract:
The Wasserstein distance measure introduced to be able to consider the limitations of fuzzy clustering interval data interval distance defined interval value distribution characteristics, proposed based on the Wasserstein distance measure single indicators and indicators adaptive fuzzy clustering algorithm and iterative model. confirmed the advantages of this kind of model simulation and CR Index, the algorithm has important practical significance in the massive mountains of data mining.
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 ...
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 ...
[PDF] Estimation of deformations between distributions by minimal Wasserstein distance
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
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 54 items
Localisation de masse et espaces de Wasserstein
by Le Gouic, Thibaut 2013 Dissertation :
Le travail de cette thèse est basé sur deux outils : le packing d'un ensemble et les espaces de Wasserstein. Une première partie s'intéresse à...
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 ...
Entropic Gradient Flows on the Wasserstein Space via Large Deviations from Thermodynamic Limits
V Laschos  2013  opus.bath.ac.uk
In a seminal work, Jordan, Kinderlehrer and Otto proved that the 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),
On the rate of convergence in Wasserstein distance of the empirical measure
N Fournier, A Guillin  arXiv preprint arXiv:1312.2128, 2013  arxiv.org
Abstract: Let $\ mu_N $ be the empirical measure associated to a $ N $sample of a given
probability distribution $\ mu $ on $\ mathbb {R}^ d $. We are interested in the rate of
convergence of $\ mu_N $ to $\ mu $, when measured in the Wasserstein distance of ...
[pdf] On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier Arnaud Guillin 2013
The Wasserstein metric in Factor Analysis
L Ning, T Georgiou  SIAM
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 ...
Application of the Wasserstein metric to seismic signals
B Engquist, BD Froese  arXiv preprint arXiv:1311.4581, 2013  arxiv.org INRIA PARIS
Abstract: Seismic signals are typically compared using travel time difference or $ L_2 $
difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit
in seismology. It exhibits properties from both of the traditional measures mentioned ...
MR3187785 Communications in Mathematical Sciences
Volume 12 (2014) Number 5
[PDF] Wasserstein Distance on Riemannian Manifolds
M Kersting  2013  lp.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 ...
On Interpolation and Curvature via Wasserstein Geodesics
M Kell  arXiv preprint arXiv:1311.5407, 2013  arxiv.org
Abstract: In this article, a proof of the interpolation inequality along geodesics in $ p $
Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove
the BorelBrascampLieb inequality for general Riemannian and Finsler manifolds and led ...
Sliced and radon wasserstein barycenters of measures
N Bonneel, J Rabin, G Peyré, H Pfister  2013  hal.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
[PDF] On properties of the Generalized Wasserstein distance
B Piccoli, F Rossi  arXiv preprint arXiv:1304.7014, 2013  lsis.org
Abstract In this article, we continue the investigation of the generalized Wasserstein distance
Wa, bp, that we introduced in [12]. We first prove that the particular choice W1, 1 1 coincides
with the 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 ...
Contractivity of the Wasserstein metric for the kinetic Kuramoto equation
JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim  arXiv preprint arXiv: …, 2013  arxiv.org
Abstract: We present synchronization and contractivity estimates for the kinetic Kuramoto
model obtained from the Kuramoto phase model in the 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 IEEE
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.
A geometric study of Wasserstein spaces: an addendum on the boundary
J Bertrand, B Kloeckner  arXiv preprint arXiv:1302.1424, 2013  arxiv.org
Let X be a Hadamard space, by which we mean that X is a complete globally CAT(0), locally
compact metric space. The set of its Borel probability measures with finite second moment can
be endowed with a natural distance defined using optimal transportation, giving birth to ...
MR2731158 (2011h:53045) Geometric Science of Information, 2013  Springer
Minimax rates of convergences for Wasserstein deconvolution with supersmooth errors in any dimension
J Dedecker, B Michel  arXiv preprint arXiv:1302.6103, 2013  arxiv.org
Abstract: The subject of this paper is the estimation of a probability measure on ${\ mathbb
R}^ d $ from data observed with an additive noise, under the Wasserstein metric of order $ p
$(with $ p\ geq 1$). We assume that the distribution of the errors is known and belongs to ...
[PDF] A primaldual approach for a total variation Wasserstein flow
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 ...
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 ...
A geometric study of Wasserstein spaces: ultrametrics
B Kloeckner  arXiv preprint arXiv:1304.5219, 2013  arxiv.org
Abstract: We study the geometry of the space of measures of a compact ultrametric space X,
endowed with the L^ p Wassertein distance from optimal transportation. We show that the
power p of this distance makes this Wasserstein space affinely isometric to a convex ...
The derivation of Swarming models: MeanField Limit and Wasserstein distances
JA Carrillo, YP Choi, M Hauray  arXiv preprint arXiv:1304.5776, 2013  arxiv.org
Abstract: These notes are devoted to a summary on the 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
[PDF] Object Segmentation by Shape Matching with Wasserstein Modes
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
GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE
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 ...
[PDF] Gradient estimate for Markov kernels, Wasserstein control and HopfLax formula
K Kuwada  math.ocha.ac.jp
Abstract We extend the duality between gradient estimates of the Markov kernel and
Wasserstein controls of that studied by the author (2010). Especially, the gauge normOrlicz
norm type duality holds on Polish geodesic space without any assumption on the Markov ...
RIMS Kôkyûroku Bessatsu.
Adaptive Dynamic Clustering Algorithm for Intervalvalued Data based on SquaredWasserstein Distance
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). ...
Stein factors for negative binomial approximation in Wasserstein distance
A. D. Barbour, H. L. Gan, A. Xia (Submitted on 22 Oct 2013) arXiv:1310.6074 [
The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour & Xia (2006). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.
Fast Computation of Wasserstein Barycenters Marco Cuturi,
Arnaud Doucet (Submitted on 16 Oct 2013) arXiv:1310.4375
Wasserstein barycenters (Agueh and Carlier, 2011) define a new family of barycenters between N probability measures that builds upon optimal transport theory. We argue using a simple example that Wasserstein barycenters have interesting properties that differentiate them from other barycenters proposed recently, which all build either or both on kernel smoothing and Bregman divergences. We propose two algorithms to compute Wasserstein barycenters for finitely supported measures, one of which can be shown to be a generalization of Lloyd's algorithm. A naive implementation of these algorithms is intractable, because it would involve numerous resolutions of optimal transport problems, which are notoriously expensive to compute. We propose to follow recent work by Cuturi (2013) and smooth these transportation problems to recover faster optimization procedures. We apply these algorithms to the visualization of perturbed images and resampling in particle filters.
ICML 2014 22.06.14 Kyoto University University of Oxford
Convergence to equilibrium in Wasserstein distance for 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.
Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold Ivan Gentil (ICJ) (Submitted on 16 Oct 2013) arXiv:1310.4264
Abstract We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a Riemannian manifold taking account of the dimension. The result generalizesin a Riemannian context, the dimensional contraction estab
lished in [BGG13] for the Euclidean heat equation. The theorem is proved by using a dimensional c
oercive estimate for the HodgedeRham semigroup on 1forms.


Spacetime Wasserstein controls and BakryLedoux type gradient estimates
K Kuwada  arXiv preprint arXiv:1308.5471, 2013  arxiv.org
Abstract: The duality in Bakry\'Emery's gradient estimates and Wasserstein controls for heat
distributions is extended to that in refined estimates in a high generality. As a result, we find
an equivalent condition to BakryLedoux's refined gradient estimate involving an upper ...
Two Remarks on the Wasserstein Dirichlet Form
W Stannat  Seminar on Stochastic Analysis, Random Fields and …, 2013  Springer
Abstract. The Wasserstein diffusion is an Ornstein–Uhlenbeck type process on the set of all probability
measures with the Wasserstein metric as intrinsic metric. Sturm and von Renesse constructed
in [6] this process in the case of probability measures over the unit interval using Dirichlet ...
Variational Image Segmentation and Cosegmentation with the Wasserstein Distance
P Swoboda, C Schnörr  Energy Minimization Methods in Computer Vision …, 2013  Springer
Abstract. We present novel variational approaches for segmenting and cosegmenting
images. Our supervised segmentation approach extends the classical Continuous Cut approach
by a global 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 ...
GEOMETRIC APPLICATIONS OF WASSERSTEIN DISTANCE
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 ...
The derivation of Swarming models: MeanField Limit and Wasserstein distances
JA Carrillo, YP Choi, M Hauray  arXiv preprint arXiv:1304.5776, 2013  arxiv.org
Abstract: These notes are devoted to a summary on the 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 ...
Approximation in the Wasserstein distance with application to clustering
FP Carli, L Ning, TT Georgiou  arXiv preprint arXiv:1307.5459, 2013  arxiv.org
Abstract: We consider approximating distributions within the framework of optimal transport
and specialize to problems of clustering data sets. Distances between distributions are
measured in the Wasserstein metric. The main problem we consider is that of ...
Nonlinear diffusion: Geodesic Convexity is equivalent to Wasserstein Contraction
F Bolley, JA Carrillo  arXiv preprint arXiv:1309.1932, 2013  arxiv.org
Abstract: It is well known that nonlinear diffusion equations can be interpreted as a gradient
flow in the space of probability measures equipped with the Euclidean Wasserstein
distance. Under suitable convexity conditions on the nonlinearity, due to RJ McCann, the ...
Minimax rates of convergences for Wasserstein deconvolution with supersmooth errors in any dimension
J Dedecker, B Michel  arXiv preprint arXiv:1302.6103, 2013  arxiv.org
Abstract: The subject of this paper is the estimation of a probability measure on ${\ mathbb
R}^ d $ from data observed with an additive noise, under the Wasserstein metric of order $ p
$(with $ p\ geq 1$). We assume that the distribution of the errors is known and belongs to ...
A geometric study of Wasserstein spaces: ultrametrics
B Kloeckner  arXiv preprint arXiv:1304.5219, 2013  arxiv.org
Abstract: We study the geometry of the space of measures of a compact ultrametric space X,
endowed with the L^ p Wassertein distance from optimal transportation. We show that the
power p of this distance makes this Wasserstein space affinely isometric to a convex ...
Fast Computation of Wasserstein Barycenters
M Cuturi, A Doucet  arXiv preprint arXiv:1310.4375, 2013  arxiv.org
Abstract: Wasserstein barycenters (Agueh and Carlier, 2011) define a new family of
barycenters between N probability measures that builds upon optimal transport theory. We
argue using a simple example that Wasserstein barycenters have interesting properties ...
[PDF] DECOMPOSITION OF GEODESICS IN THE WASSERSTEIN SPACE AND THE GLOBALIZATION PROBLEM
F CAVALLETTI  cvgmt.sns.it
Abstract. We will prove a decomposition for Wasserstein geodesics in the following sense:
let (X, d, m) be a 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
A primaldual approach for a total variation Wasserstein flow
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 ...
Infinite horizon value functions in the Wasserstein spaces
R Hynd, HK Kim  arXiv preprint arXiv:1310.3866, 2013  arxiv.org
Abstract: We perform a systemic study of optimization problems in the Wasserstein spaces
that are analogs of infinite horizon, deterministic control problems. We derive necessary
conditions on action minimizing paths and present a sufficient condition for their existence. ...
The Exponential Formula for the Wasserstein Metric
K Craig  arXiv preprint arXiv:1310.2912, 2013  arxiv.org
Abstract: We adapt Crandall and Liggett's method from the Banach space case to give a new
proof of the exponential formula for the Wasserstein metric. In doing this, we introduce a new
class of 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 :
Salient region detection Using Wasserstein distance measure based on nonlinear scale space
L Zhu, Z Cao  Eighth International Symposium on …, 2013  proceedings.spiedigitallibrary.org
abstract Many existing 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 ...
[PDF] Gradient estimate for Markov kernels, Wasserstein control and HopfLax formula
K Kuwada  math.ocha.ac.jp
Abstract We extend the duality between gradient estimates of the Markov kernel and
Wasserstein controls of that studied by the author (2010). Especially, the gauge normOrlicz
norm type duality holds on Polish geodesic space without any assumption on the Markov ...
Wasserstein gradient flows from large deviations of manyparticle limits
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 ...
arXiv:1203.0676 [pdf, ps, other]
Contractivity of the Wasserstein metric for the kinetic Kuramoto equation
JA Carrillo, YP Choi, SY Ha, MJ Kang, Y Kim  arXiv preprint arXiv: …, 2013  arxiv.org
Abstract: We present synchronization and contractivity estimates for the kinetic Kuramoto
model obtained from the Kuramoto phase model in the meanfield limit. For identical
Kuramoto oscillators, we present an admissible class of initial data leading to time ...
Geodesic PCA in the Wasserstein space
J Bigot, R Gouet, A López  arXiv preprint arXiv:1307.7721, 2013  arxiv.org
Annales de l'Institut Henri …, 2015  math.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 ...
Value functions on a finite time horizon in the Wasserstein spaces
R Hynd, HK Kim  arXiv preprint arXiv:1307.4667, 2013  arxiv.org
Abstract: We study analogs of value functions arising in classical mechanics in the space of
probability measures endowed with the Wasserstein metric $ W_p $, for $1< p<\ infty $. Our
main result is that each of these generalized value functions is a type of viscosity solution ...
Microscopic interpretation of Wasserstein gradient flows
DRM Renger  2013  … 2013. http://alexandria. tue. nl/extra2 …
Permalink Technische Universiteit Eindhoven Dissertation :
2014 53 items
Wasserstein propagation for semisupervised learning
by J Solomon  2014  Cited by 32  Related articles
Published in: Proceeding ICML'14 Proceedings of the 31st International Conference on International Conference on Machine Learning  Volume 32 Pages I306I314
Jun 21, 2014  Probability distributions and histograms are natural representations for product ratings, traffic measurements, and other data considered in many machine learning applications. Thus, this paper introduces a technique for graphbased semisupervised learning of histograms, derived from
The Wasserstein geometry of nonlinear sigma models and the HamiltonPerelman Ricci flow
Mauro Carfora (Submitted on 5 May 2014)
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
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 ...
[PDF] First and second moments for selfsimilar couplings and Wasserstein distances
JM Fraser  arXiv preprint arXiv:1401.1443, 2014  128.84.21.199
Abstract We study aspects of the Wasserstein distance in the context of 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 ...
[PDF] Estimation of Deformations between Distributions with the Wasserstein Distance
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...
The quasineutral limit of the VlasovPoisson equation in Wasserstein metric
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 ...
qheat flow and the gradient flow of the Renyi entropy in the pWasserstein space
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 ...
Wasserstein Barycenters over Riemannian manfolds
YH Kim, B Pass  arXiv preprint arXiv:1412.7726, 2014  arxiv.org
Abstract: We study barycenters in the space of probability measures on a Riemannian
manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we
establish absolute continuity of the barycenter of general measures $\ Omega\ in P (P (M)) ...
[PDF] MultiPhase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance
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 ...
New conditions for subgeometric rates of convergence in the Wasserstein distance for Markov chains
A Durmus, E Moulines, G Fort  arXiv preprint arXiv:1402.4577, 2014  arxiv.org
Abstract: In this paper, we provide sufficient conditions for the existence of the invariant
distribution and subgeometric rates of convergence in the Wasserstein distance for general
statespace Markov chains which are not phiirreducible. Our approach is based on a ...
The Annals of Applied Probability Volume 24, Number 2 (2014), 526552.

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 Analysis January 2014 Wasserstein Metric Based Adaptive Fuzzy Clustering Methods for Symbolic Interval Data LI HONG  TELKOMNIKA Indonesian Journal of Electrical …, 2014  iaesjournal.com Abstract The aim of this paper is to present new wasserstein metric based adaptive fuzzy clustering methods for partitioning symbolic interval data. In two methods, fuzzy partitions and prototypes for clusters are determined by optimizing adequacy criteria based on ... [PDF] A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ISOMETRIC RIGIDITY IN NEGATIVE CURVATURE J Bertrand, BR Kloeckner  math.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 Learning J Solomon, R Rustamov, G Leonidas…  Proceedings of The 31st …, 2014  jmlr.org Abstract Probability distributions and histograms are natural representations for product ratings, traffic measurements, and other data considered in many machine learning applications. Thus, this paper introduces a technique for graphbased semisupervised ... [PDF] On gradient structures for Markov chains and the passage to Wasserstein gradient flows K Disser, M Liero  opus4.kobv.de Abstract We study the approximation of Wasserstein gradient structures by their finitedimensional analog. We show that simple 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 space 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 ... Wasserstein distances between selfsimilar measures JM 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 distances J 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 metric A Ruiz de Villa, J Casas, M Breen  Transportation Research Board 93rd …, 2014  trid.trb.org Abstract: In this paper the authors introduce a metric and a method, considering the spatial structure, for comparing OD matrices. It is based on mass transportation techniques, in particular the notion of Wasserstein distance. The result of the comparison is measured in ... Absolutely continuous curves in extended WassersteinOrlicz spaces S Lisini  arXiv preprint arXiv:1402.7328, 2014  arxiv.org Abstract: In this paper we extend a previous result of the author [Lis07] of characterization of absolutely continuous curves in Wasserstein spaces to a more general class of spaces: the spaces of probability measures endowed with the 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
Local brightness adaptive image colour enhancement with Wasserstein distance
L Wang, L Xiao, H Liu, Z Wei  IET Image Processing, 2014  IET
Colour image enhancement is an important preprocessing phase of many image analysis
tasks such as image segmentation, pattern recognition and so on. This study presents a new
local brightness adaptive variational model using Wasserstein distance for colour image ...
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 arXiv
J Lott  arXiv preprint arXiv:1407.7245, 2014  arxiv.org
Abstract: If M is a smooth compact Riemannian manifold, let P (M) denote the Wasserstein
space of probability measures on M. If S is an embedded submanifold of M, and mu is an
absolutely continuous measure on S, we compute the tangent cone of P (M) at mu. We ...
[PDF] The Gromov–Wasserstein Distance: A Brief Overview
F Mémoli  Axioms, 2014  mdpi.com
... Article The Gromov–Wasserstein Distance: A Brief Overview Facundo Mémoli ... Published:
2 September 2014 Abstract: We recall the construction of the Gromov–Wasserstein
distance and concentrate on quantitative aspects of the definition. ...
The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds arXiv
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
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 ...
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[PDF] Optimal Transport and the Wasserstein Metric
PN Orenstein  2014  mat.uc.cl
Abstract Orenstein, Paulo Najberg; Bochi, Jairo; Tomei, Carlos. Optimal Transport and the
Wasserstein Metric. Rio de Janeiro, 2014. 8 9p. Dissertaçao de Mestrado—Departamento
de Matemática, Pontifıcia Universidade Católica do Rio de Janeiro.
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Evolution in Measure Spaces with Wasserstein Distance
E Cristiani, B Piccoli, A Tosin  Multiscale Modeling of Pedestrian Dynamics
MS&A Volume 12, 2014, pp 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 arXiv
J Dedecker, A Fischer, B Michel  arXiv preprint arXiv:1404.0646, 2014  arxiv.org
Abstract: This paper deals with the estimation of a probability measure on the real line from
data observed with an additive noise. We are interested in rates of convergence for the
Wasserstein metric of order $ p\ geq 1$. The d
istribution of the errors is assumed to be ...
Electron. J. Stat. 9 (2015), 234–265.
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
Ruiz de Villa, Aleix Casas, Jordi Breen, Martijn
TRB 93rd Annual Meeting Compendium of Papers
Transportation Research Board 93rd Annual Meeting
Location: Washington DC Date: 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 arXiv
S Srivastava, C Li, DB Dunson  arXiv preprint arXiv:1508.05880, 2015  arxiv.org
Abstract: We propose a novel approach WASP for Bayesian inference when massive size of
the data prohibits posterior computations. WASP is estimated in three steps. First, data are
divided into smaller computationally tractable subsets. Second, posterior draws of ...
Modified Arratia flow and Wasserstein diffusion arXiv
V Konarovskyi, M von Renesse  arXiv preprint arXiv:1504.00559, 2015  arxiv.org
Abstract: Extending previous work~[arXiv: 1408.0628] by the first author we present a variant
of the Arratia flow of a field of coalescing Brownian motions starting from every point of the
unit interval. The important new feature of the model is that individual particles carry mass ...
Decomposition of the Kantorovich problem and Wasserstein distances on simplexes arXiv
D Zaev  arXiv preprint arXiv:1505.03721, 2015  arxiv.org
Abstract: We consider $ L^ p $Wasserstein distances on a subset of probability measures. If
the subset of interest appears to be a simplex, these distances are determined by their
values on extreme points of the simplex. We show that this fact is a corollary of the ...
J Shao, B Wu  arXiv preprint arXiv:1507.07995, 2015  arxiv.org
Abstract: When the Ricci curvature of a Riemannian manifold is not lower bounded by a
constant, but lower bounded by a continuous function, we give a new characterization of this
lower bound through the convexity of relative entropy on the probability space over the ...
Evolution variational inequality and Wasserstein control in variable curvature context arXiv
C Ketterer  arXiv preprint arXiv:1509.02178, 2015  arxiv.org
Abstract: In this note we continue the analysis of metric measure space with variable ricci
curvature bounds. First, we study $(\ kappa, N) $convex functions on metric spaces where
$\ kappa $ is a lower semicontinuous function, and gradient flow curves in the sense of a ...
Wasserstein distances and curves in the Wasserstein spaces
F Santambrogio  Optimal Transport for Applied Mathematicians, 2015  Springer
Abstract In this chapter we use the minimal value of transport problems between two
probabilities in order to define a distance on the space of probabilities. We mainly consider
costs of the form c (x, y)= x− y pc (x, y)=  xy ^ p in Ω⊂ ℝ d\ varOmega ⊂ R^ d. We ...
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 ...
Uniform contractivity in Wasserstein metric for the original 1D Kac's model arXiv
M Hauray  arXiv preprint arXiv:1512.01986, 2015  arxiv.org
Abstract: We study here a very popular 1D jump model introduced by Kac: it consists of $ N $
velocities encountering random binary collisions at which they randomly exchange energy.
We show the uniform (in $ N $) exponential contractivity of the dynamics in a nonstandard ...
On the WassersteinFisherRao metric
FX Vialard  MATH ON THE ROCKS  researchgate.net
Abstract This note gives a summary of the presentation that I gave at the workshop on shape
analysis1. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to
measures that have different total masses. This generalization enjoys most of the ...
Sliced Wasserstein Kernels for Probability Distributions arXiv
S Kolouri, Y Zou, GK Rohde  arXiv preprint arXiv:1511.03198, 2015  arxiv.org
Abstract: Optimal transport distances, otherwise known as Wasserstein distances, have
recently drawn ample attention in computer vision and machine learning as a powerful
discrepancy measure for probability distributions. The recent developments on alternative ...
2016 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) Book Series: IEEE Conference on Computer Vision and Pattern Recognition Pages: 52585267 Published: 2016
An augmented Lagrangian approach to Wasserstein gradient flows and applications
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 ...
ESAIM: PROCEEDINGS AND SURVEYS, June 2016, Vol. 54, p. 117
] Learning in Wasserstein Space
J Ye  personal.psu.edu
ABSTRACT Learning from probability measures is an emerging problem that has potential
benefiting multiple domains. Different from previous computational learning concentrated on
neural representations and parametric statistical models, my research focuses on ...
Barycenter in Wasserstein Spaces: Existence and Consistency
T Le Gouic, JM Loubes  Geometric Science of Information, 2015  Springer
Abstract We study barycenters in the Wasserstein space P_p(E) of a locally compact
geodesic space (E, d). In this framework, we define the barycenter of a measure ℙ on P_p(E)
as its Fréchet mean. The paper establishes its existence and states consistency with ...
Fuzzy clustering of distributionvalued data using an adaptive L 2 Wasserstein distance IEEE
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 ...
Accelerated Discrete Distribution Clustering under Wasserstein Distance
J Ye, P Wu, JZ Wang, J Li  arXiv preprint arXiv:1510.00012, 2015  arxiv.org
Abstract: In a variety of research areas, the bag of weighted vectors and the histogram are
widely used descriptors for complex objects. Both can be expressed as discrete
distributions. D2clustering pursues the minimum total withincluster variation for a set of ...
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps pdf
J Bigot, T Klein  arXiv preprint arXiv:1212.2562, 2015  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
[ Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and Revised Kmethods Clusters ]
WANG Qun, DONG Wenlue, YANG Li
王群， 董文略， 杨莉  中国电机工程学报, 2015
On some non linear evolution systems which are perturbations of Wasserstein gradient flows arXiv
M Laborde  arXiv preprint arXiv:1506.00126, 2015  arxiv.org
Abstract: This paper presents existence and uniqueness results for a class of parabolic
systems with non linear diffusion and nonlocal interaction. These systems can be viewed as
regular perturbations of Wasserstein gradient flows. Here we extend results known in the ...
by M Baum  2015 Cited by 12  Related articles
Mar 4, 2015  Abstract: The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for example, suggest the best ...
calable Bayes via Barycenter in Wasserstein Space arXiv
S Srivastava, C Li, DB Dunson  arXiv preprint arXiv:1508.05880, 2015  arxiv.org
Abstract: We propose a novel approach WASP for Bayesian inference when massive size of
the data prohibits posterior computations. WASP is estimated in three steps. First, data are
divided into smaller computationally tractable subsets. Second, posterior draws of ...
Quasineutral limit for VlasovPoisson via Wasserstein stability estimates in higher dimension arXiv
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.
Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space
C Jin  Nonlinear Analysis: Theory, Methods & Applications, 2015  Elsevier
Abstract We prove the well posedness of nonhomogeneous pressureless Euler system in 2
Wasserstein space with the initial mass and energy being finite. Our method is based on a
main observation pioneered by Brenier and Grenier that we can recover the solution of the ...
Learning with a Wasserstein Loss arXiv
C Frogner, C Zhang, H Mobahi, M 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 ...
Evolution variational inequality and Wasserstein control in variable curvature context arXiv
C Ketterer  arXiv preprint arXiv:1509.02178, 2015  arxiv.org
Abstract: In this note we continue the analysis of metric measure space with variable ricci
curvature bounds. First, we study $(\ kappa, N) $convex functions on metric spaces where
$\ kappa $ is a lower semicontinuous function, and gradient flow curves in the sense of a ...
Geodesic PCA in the Wasserstein space by Convex PCA
J Bigot, R Gouet, T Klein, A López  2015  math.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 ...
Nonpositive curvature, the variance functional, and the Wasserstein barycenter arXiv
YH Kim, B Pass  arXiv preprint arXiv:1503.06460, 2015  arxiv.org
Abstract: This paper connects nonpositive sectional curvature of a Riemannian manifold with
the displacement convexity of the variance functional on the space $ P (M) $ of probability
measures over $ M $. We show that $ M $ has nonpositive sectional curvature and has ...
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} ...
Limit laws of the empirical Wasserstein distance: Gaussian distributions arXiv
T Rippl, A Munk, A Sturm  arXiv preprint arXiv:1507.04090, 2015  arxiv.org
Abstract: We derive central limit theorems for the Wasserstein distance between the
empirical distributions of Gaussian samples. The cases are distinguished whether the
underlying laws are the same or different. Results are based on the (quadratic) Fr\'echet ...
Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data arXiv
E Anderes, S Borgwardt, J Miller  arXiv preprint arXiv:1507.07218, 2015  arxiv.org
Abstract: Wasserstein barycenters correspond to optimal solutions of transport problems for
several marginals, and as such are at the core of applications ranging from economics to
statistics and computer science. The corresponding theory for data in the form of ...
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 ...
An Algorithmic Approach to Compute Principal Geodesics in the Wasserstein Space
V Seguy, M Cuturi  arXiv preprint arXiv:1506.07944, 2015  arxiv.org
Abstract: We consider in this work the space of probability measures P (X) on a Hilbert space
X endowed with the 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 ...
$ L^ p $Wasserstein distances on state and quasistate spaces of $ C^* $algebras
D Zaev  arXiv preprint arXiv:1505.06061, 2015  arxiv.org
Abstract: We construct an analogue of the classical $ L^ p $Wasserstein distance for the
state space of a $ C^* $algebra. Given an abstract Lipschitz gauge on a $ C^* $algebra $\
mathcal {A} $ in the sense of Rieffel, one can define the classical $ L^ p $Wasserstein ...
[PDF] Regularizing Image Intensity Transformations Using the Wasserstein Metric
M Oskarsson  maths.lth.se
Abstract. In this paper we direct our attention to the problem of discretization effects in
intensity transformations of images. We propose to use the Wasserstein metric (also known
as the Earth mover distance) to bootstrap the transformation process. The Wasserstein ...
From large deviations to Wasserstein gradient flows in multiple dimensions
M Erbar, J Maas, M Renger  arXiv preprint arXiv:1505.05712, 2015  arxiv.org
Abstract: We study the large deviation rate functional for the empirical distribution of
independent Brownian particles with drift. In one dimension, it has been shown by Adams,
Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\ ...
Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis
Z Su, W Zeng, Y Wang, ZL Lu, X Gu  Information Processing in Medical …, 2015  Springer
Abstract Brain morphometry study plays a fundamental role in medical imaging analysis and
diagnosis. This work proposes a novel framework for brain cortical surface classification
using Wasserstein distance, based on uniformization theory and Riemannian optimal ...
DF] A Hitchhiker's guide to Wasserstein distances
G Basso  2015  n.ethz.ch
The main references of this section are [Edw11] and [Kel85]. For measure theoretic notions
we refer to [Bog07]. In the following we introduce some notation. Let (X, d) denote a metric
space and let B (X) denote the Borel σalgebra of (X, d). Suppose that µ: B (X)→ R is a ...
On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests
A Ramdas, N Garcia, M Cuturi  arXiv preprint arXiv:1509.02237, 2015  arxiv.org
Abstract: Nonparametric two sample or homogeneity testing is a decision theoretic problem
that involves identifying differences between two random variables without making
parametric assumptions about their underlying distributions. The literature is old and rich, ...
Wasserstein Training of Boltzmann Machines
G Montavon, KR Müller, M Cuturi  arXiv preprint arXiv:1507.01972, 2015  arxiv.org
Abstract: The Boltzmann machine provides a useful framework to learn highly complex,
multimodal and multiscale data distributions that occur in the real world. The default method
to learn its parameters consists of minimizing the KullbackLeibler (KL) divergence from ...
Generalized Wasserstein distance and weak convergence of sublinear expectations
X Li, Y Lin  arXiv preprint arXiv:1505.04954, 2015  arxiv.org
Abstract: In this paper, we define the generalized Wasserstein distance for sets of Borel
probability measures and demonstrate that the weak convergence of sublinear expectations
can be characterized by means of this distance.
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 ...
Wasserstein continuity of entropy and outer bounds for interference channels
Y Polyanskiy, Y Wu  arXiv preprint arXiv:1504.04419, 2015  arxiv.org
Abstract: It is shown that under suitable regularity conditions, differential entropy is a
Lipschitz functional on the space of distributions on $ n $dimensional Euclidean space with
respect to the quadratic Wasserstein distance. Under similar conditions,(discrete) ...
Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains pdf
J Solomon, F de Goes, PA Studios…  … on Graphics (Proc. …, 2015  iip.ist.i.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 ...
Existence and consistency of Wasserstein barycenters
TL Gouic, JM Loubes  arXiv preprint arXiv:1506.04153, 2015  arxiv.org
Abstract: In this paper, based on the Fr\'echet mean, we define a notion of barycenter
corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein
barycenters of random distributions defined on a geodesic space (E, d). We also prove the ...
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 ...
Related articles All 16 versions Cite Save
Performance and robustness analysis of stochastic jump linear systems using wasserstein metric
K Lee, A Halder, R Bhattacharya  Automatica, 2015  Elsevier
Abstract This paper focuses on the performance and robustness analysis of stochastic jump
linear systems. In the presence of stochastic jumps, state variables evolve as random
process, with associated time varying probability density functions. Consequently, system ...
Weak solutions to a fractional Fokker–Planck equation via splitting and Wasserstein gradient flow
M Bowles, M Agueh  Applied Mathematics Letters, 2015  Elsevier
Abstract We study a linear fractional Fokker–Planck equation that models 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
On Wasserstein Barycenters and MMOSPA Estimation
M Baum, P Willett, U Hanebeck  2015  ieeexplore.ieee.org
Abstract—The two title concepts have been evolving rather rapidly, but independent of each
other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image
processing as it can describe a measure of similarity between images. Its minimization ...
Cite Save [PDF] from arxiv.org Signal Processing Letters, …, 2015
"Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains." pdf
SIGGRAPH 2015, Los Angeles.
(supplemental document; code; slides)
Solomon, Justin, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas.
————————————
FUSION 2015 SPECIAL SESSIONS July 69, Washington, DC
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 Wasserstein not in Math Reviews 65 items
Application of Optimal Transport and the Quadratic Wasserstein Metric to FullWaveform Inversion
Yunan Yang, Björn Engquist, Junzhe Sun, Brittany D. Froese
arXiv:1611.04323 [pdf, ps, other]
Central Limit Theorem and bootstrap procedure for Wasserstein's variations with application to structural relationships between distributions
Eustasio Del Barrio, Hélène Lescornel (IMT), JeanMichel Loubes (IMT)
[PDF] Fast Dictionary Learning with a Smoothed Wasserstein Loss
A Rolet, M Cuturi, G Peyré  … of the 19th International Conference on …, 2016  jmlr.org
Abstract We consider in this paper the dictionary learning problem when the observations
are normalized histograms of features. This problem can be tackled using nonnegative
matrix factorization approaches, using typically Euclidean or KullbackLeibler fitting errors.
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 Wasserstein
[PDF] Cortical Surface Classification with Hyperbolic Wasserstein Distance
J Shi, Y Wang  gsl.lab.asu.edu
The Wasserstein space consists of all probability measures that are defined on a
Riemannian manifold. The Wasserstein distance defines a Riemannian metric for the
Wasserstein space and it intrinsically measures the similarities between shapes.
Geometric construction of Wasserstein Barycenters
N Bonneel, J Digne  liris.cnrs.fr
Optimal Transport theory consists in finding a map T pushing forward an input measure µ to
a target measure ν, which minimizes a “transport cost”. This cost often consists in the sum of
the squared distances travelled by all particles during their motion. Formally, the Monge
A dimensional Wasserstein contraction characterizing the curvaturedimension condition. Kazumasa Kuwada. (Tokyo Institute of Technology). (Joint work with F. Bolley, I. Gentil and A. Guillin). Stochastic Analysis and Applications (Tohoku University) Aug. 31–Sept. 4, 2015 ...
[CITATION] A dimensional Wasserstein contraction characterizing the curvaturedimension condition
桒田和正  … Wasserstein contraction characterizing the curvature …, 2016  t2r2.star.titech.ac.jp
... Home >. news ヘルプ. 論文・著書情報. タイトル, 和文: A dimensional Wasserstein contraction
characterizing the curvaturedimension condition. 英文: A dimensional Wasserstein contraction
characterizing the curvaturedimension condition. 著者, 和文: 桒田和正. 英文: Kazumasa Kuwada.
[PDF] Matricial Wasserstein and Unsupervised Tracking
L Ning, R Sandhu, TT Georgiou, A Tannenbaum  ee.umn.edu
Abstract The context of this work is spectral analysis of multivariable timesseries as this may
arise in processing signals originating in antenna and sensor arrays. The salient feature of
these time signals is that they contain information about moving scatterers/targets which may
Refined basic couplings and Wassersteintype distances for SDEs with L\'{e} vy noises
D Luo, J Wang  arXiv preprint arXiv:1604.07206, 2016  adsabs.harvard.edu
Abstract We establish the exponential convergence with respect to the $ L^ 1$Wasserstein
distance and the total variation for the semigroup corresponding to the stochastic differential
equation (SDE) $ $ d X_t= d Z_t+ b (X_t)\, dt, $ $ where $(Z_t) _ {t\ ge0} $ is a pure jump
Cited by 1 Related articles All 2 versions Cite Save
I Cipriano  arXiv preprint arXiv:1611.00092, 2016  arxiv.org
Abstract: We consider an iterated function scheme composed of k contractions on the unit
interval with disjoint images. We find the first KantorovichWasserstein distance between the
two stationary measures associated to the iterative function schemes when we choose two
[PDF] Learning in Wasserstein Space
J Ye  pdfs.semanticscholar.org
ABSTRACT Learning from empirical probability measures is an emerging problem that has
potential benefiting multiple domains. My research focuses on developing scalable and
effective learning algorithms that handle largescale data in form of measures. In particular,
Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry arXiv
AB Kashlak  arXiv preprint arXiv:1610.08405, 2016  arxiv.org
Abstract: We propose of an improved version of the ubiquitous symmetrization inequality
making use of the Wasserstein distance between a measure and its reflection in order to
quantify the symmetry of the given measure. An empirical bound on this asymmetric
[HTML] Wasserstein Barycentric Coordinates: Histogram Regression Using Optimal Transport
N Bonneel, G Peyré, M Cuturi, F Mazenc…  ACM Transactions on …, 2016  team.inria.fr
article IEEE Transactions on Industrial Electronics, Institute of Electrical and Electronics
Engineers, 2015, IEEE Transactions on Industrial Electronics, pp. 2.< http://ieeexplore. ieee.
org/xpl/articleDetails. jsp? arnumber= 7115092&searchWithin% 5B% 5D=% 22Authors% ...
ACM TRANSACTIONS ON GRAPHICS Volume: 35 Issue: 4 Published: JUL 2016
基于 Wasserstein 距离和 SBGFRLS 方法的活动轮廓模型图像分割算法
[ Image segmentation algorithm of active contour model based on Wasserstein distance and Sbgfrls method '
王瑜， 闫沫  西安航空学院学报, 2016  cqvip.com
摘要: 提出一种结合Wasserstein 距离和SBGFRLS 方法的非参数化活动轮廓图像分割算法.
该算法采用二值函数作为水平集函数并利用高斯核函数对其正则化, 有效避免水平集演化中的
重新初始化过程, 提高分割速度. 算法本身具有选择局部和全局分割的属性. 利用Wasserstein ...
Baricentros en el espacio de Wasserstein: aplicación a modelos estadísticos de deformación
P Gordaliza Pastor  2016  uvadoc.uva.es
En el análisis de la homogeneidad de una colección de distribuciones y de relaciones
estructurales entre las observaciones, son muy útiles los baricentros y la variación en
distancia de Wasserstein. Estudiamos la estimación de los cuantiles del proceso empírico ...
[PDF] Regularized Wasserstein barycenter
E Cazelles, J Bigot, N Papadakis  papersjds16.sfds.asso.fr
Abstract. The concept of barycenter in the Wasserstein space allows the defintion of a notion
of Fréchet mean of a set of probability measures. However, depending on the considered
data, such barycenters may be irregular. In this paper, we thus introduce a convex ...
G Flint  arXiv preprint arXiv:1605.08996, 2016  arxiv.org
Abstract: We construct a coupling between the random walk composed of L\'evy area
increments from a $ d $dimensional Brownian motion and a random walk composed of
quadratic polynomials of Gaussian random variables. This coupling construction is used ...
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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 ...
arXiv:1603.01375 [math.AP]
By: Zinsl, Jonathan
Conference: PDE Workshop on Theory and Applications of Partial Differential Equations Location: Weierstrass Inst, Berlin, GERMANY Date: NOV 30DEC 04, 2015
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMSSERIES S Volume: 10 Issue: 4 Pages: 919933 Published: AUG 2017
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 ...
Robust kbarycenters in Wasserstein Space and Wide Consensus Clustering arXiv
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. ...
Wasserstein Loss for Image Synthesis and Restoration
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 ...
ON EXPONENTIAL CONVERGENCE OF GENERIC QUANTUM MARKOV SEMIGROUPS IN A WASSERSTEINTYPE DISTANCE
J Agredo  International Journal of Pure and Applied Mathematics, 2016  ijpam.eu
Abstract. We investigate about exponential convergence for generic quantum Markov
semigroups using an generalization of the Lipschitz seminorm and a noncommutative
analogue of Wasserstein distance. We show turns out to be closely related with classical ...
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 ...
Regularization of barycenters in the Wasserstein space
J Bigot, E Cazelles, N Papadakis  arXiv preprint arXiv:1606.01025, 2016  arxiv.org
Abstract: The concept of barycenter in the Wasserstein space allows to define a notion of
Fr\'echet mean of a set of probability measures. However, depending on the data at hand,
such barycenters may be irregular. In this paper, we thus introduce a convex ...
Sample OutOfSample Inference Based on Wasserstein Distance
J Blanchet, Y Kang  arXiv preprint arXiv:1605.01340, 2016  arxiv.org
Abstract: We present a novel inference approach which we call Sample 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 ...
A geometric study of Wasserstein spaces: isometric rigidity in negative curvature
J Bertrand, BR Kloeckner  … Mathematics Research Notices, 2016  imrn.oxfordjournals.org
Abstract Given a metric space $ X $, one defines its Wasserstein space ${\ mathscr {W}
_2}(X) $ as a set of sufficiently decaying probability measures on $ X $ endowed with a
metric defined from optimal transportation. In this article, we continue the geometric study ...
A Simulated Annealing based Inexact Oracle for Wasserstein Loss Minimization arXiv
J Ye, JZ Wang, J Li  arXiv preprint arXiv:1608.03859, 2016  arxiv.org
Abstract: Learning under a Wasserstein loss is an emerging research topic. We call
collectively the problems formulated under this framework Wasserstein Loss Minimization
(WLM). One important appeal of WLM is the innate capability to account for the prior ...
A Weighted Approximation Approach to the Study of the Empirical Wasserstein Distance
DM Mason  High Dimensional Probability VII, 2016  Springer
High Dimensional Probability VII pp 137154 
Abstract We shall demonstrate that weighted approximation technology provides an effective
set of tools to study the rate of convergence of the Wasserstein distance between the
cumulative distribution function [cdf] and the empirical cdf
HIGH DIMENSIONAL PROBABILITY VII: THE CARGESE VOLUME Book Series: Progress in Probability Volume: 71 Pages: 137154 Published: 2016
Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost
A Halder, EDB Wendel  American Control Conference (ACC), …, 2016  ieeexplore.ieee.org
Abstract: We formulate and solve an optimal control problem in which a finite dimensional
linear time invariant (LTI) control system steers a given Gaussian probability density function
(PDF) close to another in fixed time, while minimizing the trajectorywise expected ...
2016 AMERICAN CONTROL CONFERENCE (ACC) Book Series: Proceedings of the American Control Conference Pages: 72497254 Published: 2016
[HTML] The Wasserstein Metric and Robustness in Risk Management
R Kiesel, R Rühlicke, G Stahl, J Zheng  Risks, 2016  mdpi.com
Risks 2016, 4(3), 32; doi:10.3390/risks4030032
In the aftermath of the financial crisis, it was realized that the mathematical models used for
the valuation of financial instruments and the quantification of risk inherent in portfolios
consisting of these financial instruments exhibit a substantial model risk. Consequently, ...
A fixedpoint approach to barycenters in Wasserstein space
PC AlvarezEsteban, E del Barrio…  Journal of Mathematical Analysis 2016  Elsevier
Volume 441, Issue 2, 15 September 2016
Abstract Let P 2, ac P 2, ac be the set of Borel probabilities on R d R d with finite second
moment and absolutely continuous with respect to Lebesgue measure. We consider the
problem of finding the barycenter (or Fréchet mean) of a finite set of probabilities ν 1,…, ν k ...
Wasserstein Discriminant Analysis arXiv
R Flamary, M Cuturi, N Courty…  arXiv preprint arXiv: …, 2016  arxiv.org
Abstract: Wasserstein Discriminant Analysis (WDA) is a new supervised method that can
improve classification of highdimensional data by computing a suitable linear map onto a
lower dimensional subspace. Following the blueprint of classical Linear Discriminant ...
{Euclidean, Metric, and Wasserstein} Gradient Flows: an overview arXiv
F Santambrogio  arXiv preprint arXiv:1609.03890, 2016  arxiv.org
Abstract: This is an expository paper on the theory of gradient flows, and in particular of
those PDEs which can be interpreted as gradient flows for the Wasserstein metric on the
space of probability measures (a distance induced by optimal transport). The starting point ...
S Li, XD Li  arXiv preprint arXiv:1604.02596, 2016  arxiv.org
Abstract: We introduce Perelman's $ W $entropy and prove the $ W $entropy formula along
geodesic flow on the Wasserstein space $ P^\ infty_2 (M,\ mu) $ over compact Riemannian
manifolds equipped with Otto's infinite dimensional Riemannian metric. As a corollary, we ...
Evolution of the Wasserstein distance between the marginals of two Markov processes
A Alfonsi, J Corbetta, B Jourdain  arXiv preprint arXiv:1606.02994, 2016  arxiv.org
Abstract: In this paper, we are interested in the time derivative of the Wasserstein distance
between the marginals of two Markov processes. As recalled in the introduction, the
Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the ...
Euler sprays and Wasserstein geometry of the space of shapes
JG Liu, RL Pego, D Slepčev  arXiv preprint arXiv:1604.03387, 2016  arxiv.org
Abstract: We study a distance between shapes defined by minimizing the integral of kinetic
energy along transport paths constrained to measures with characteristicfunction densities.
The formal geodesic equations for this shape distance are Euler equations for ...
A Dual Representation of Functions on Wasserstein Spaces
Y Shen  arXiv preprint arXiv:1603.02882, 2016  arxiv.org
Abstract: We prove a duality theorem of the 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 ...
A Distance for HMMs Based on Aggregated Wasserstein Metric and State Registration
Y Chen, J Ye, J Li  European Conference on Computer Vision, 2016  Springer
Abstract We propose a framework, named Aggregated Wasserstein, for computing a
dissimilarity measure or distance between two Hidden Markov Models with state conditional
distributions being Gaussian. For such HMMs, the marginal distribution at any time spot ...
Fuzzy clustering of distributionvalued data using adaptive L2 Wasserstein distances
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.
Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature
FY Wang  arXiv preprint arXiv:1603.05749, 2016  arxiv.org
Abstract: Let $ P_t $ be the (Neumann) diffusion semigroup $ P_t $ generated by a weighted
Laplacian on a complete connected Riemannian manifold $ M $ without boundary or with a
convex boundary. It is well known that the BakryEmery curvature is bounded below by a ...
Distributionally Robust Stochastic Optimization with Wasserstein Distance
R Gao, AJ Kleywegt  arXiv preprint arXiv:1604.02199, 2016  arxiv.org
Abstract: Stochastic programming is a powerful approach for 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 ...
Refined basic couplings and Wassersteintype distances for SDEs with L\'{e} vy noises
D Luo, J Wang  arXiv preprint arXiv:1604.07206, 2016  adsabs.harvard.edu
Abstract We establish the exponential convergence with respect to the $ L^ 1$Wasserstein
distance and the total variation for the semigroup corresponding to the stochastic differential
equation (SDE) $ $ d X_t= d Z_t+ b (X_t)\, dt, $ $ where $(Z_t) _ {t\ ge0} $ is a pure jump L\' ...
From Monge to GromovWasserstein: Optimal transport and barycenters between several metric spaces
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]) ...
The estimation of Wasserstein and Zolotarev distances to the class of exponential variables
A Baíllo, J Cárcamo, KV Getman  arXiv preprint arXiv:1603.06806, 2016  arxiv.org
Abstract: Given a positive random variable X, we are interested in measuring how well the
exponential distribution with the same mean approximates the probability distribution of X,
based on the information provided by a sample from X. Specifically, we consider the ...
Second order in time schemes for gradient flows in Wasserstein and geodesic metric spaces
G Legendre, G Turinici  2016  hal.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. ...
On Parallel Transport in Wasserstein Space arXiv
XS Shen  arXiv preprint arXiv:1604.03504, 2016  arxiv.org
Abstract: In this short note, we would like to give a construction of parallel transport for
tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete
proof for the linear part of the tangent space, and show that a construction for the full ...
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] Fast Dictionary Learning with a Smoothed Wasserstein Loss
A Rolet, M Cuturi, G Peyré  … of the 19th International Conference on …, 2016  jmlr.org
Abstract We consider in this paper the dictionary learning problem when the observations
are normalized histograms of features. This problem can be tackled using nonnegative
matrix factorization approaches, using typically Euclidean or KullbackLeibler fitting errors. ...
$ L^{p} $Wasserstein distance for stochastic differential equations driven by Lévy processes
J Wang  Bernoulli, 2016  projecteuclid.org
Abstract Coupling by reflection mixed with synchronous coupling is constructed for a class of
stochastic differential equations (SDEs) driven by Lévy noises. As an application, we
establish the exponential contractivity of the associated semigroups $(P_ {t}) _ {t\ ge0} $ ...
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 ...
Shape analysis with hyperbolic wasserstein distance
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 ...
2016 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) Book Series: IEEE Conference on Computer Vision and Pattern Recognition Pages: 50515061 Published: 2016
A multivariate CLT in Wasserstein distance with near optimal convergence rate arXiv
A Zhai  arXiv preprint arXiv:1602.05565, 2016  arxiv.org
Abstract: Let $ X_1,\ ldots, X_n $ be iid random vectors in $\ mathbb {R}^ d $ with $\ X_1\\
le\ beta $. Then, we show that $\ frac {1}{\ sqrt {n}}(X_1+\ ldots+ X_n) $ converges to a
Gaussian in Wasserstein2 distance at a rate of $ O\ left (\ frac {\ sqrt {d}\ beta\ log n}{\ sqrt { ...
Wasserstein contraction properties for hypoelliptic diffusions arXiv
F Baudoin  arXiv preprint arXiv:1602.04177, 2016  arxiv.org
Abstract: Gradient bounds had proved to be a very efficient tool for the control of the rate of
convergence to equilibrium for parabolic evolution equations. Among the gradient bounds
methods, the celebrated Bakry\'Emery criterion is a powerful way prove to convergence to ...
Guarantees in Wasserstein Distance for the Langevin Monte Carlo Algorithm arXiv
T Bonis  arXiv preprint arXiv:1602.02616, 2016  arxiv.org
Abstract: We study the problem of sampling from a distribution $\ target $ using the Langevin
Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of
Wasserstein distance of order $2 $. Our result holds as long as the continuous diffusion ...
Using GromovWasserstein distance to explore sets of networks
R Hendrikson  2016  dspace.ut.ee
In many fields such as social sciences or biology, relations between data or variables are
presented as networks. To compare these networks, a meaningful notion of distance
between networks is highly desired. The aim of this Master thesis is to study, implement, ...
Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces arXiv
Y Chen, T Georgiou, M Pavon  arXiv preprint arXiv:1601.04891, 2016  arxiv.org
Abstract: Since the early nineties, it has been observed that the Schroedinger bridge
problem can be formulated as a stochastic control problem with atypical boundary
constraints. This in turn has a fluid dynamic counterpart where the flow of probability ...
Stein's method on the second Wiener chaos: 2Wasserstein distance arXiv
B Arras, E Azmoodeh, G Poly, Y Swan  arXiv preprint arXiv:1601.03301, 2016  arxiv.org
Abstract: In the first part of the paper we use a new Fourier technique to obtain a Stein
characterizations for random variables in the second Wiener chaos. We provide the
connection between this result and similar conclusions that can be derived using Malliavin ...
GromovWasserstein Averaging of Kernel and Distance Matrices HAL
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 ...
Wasserstein training of restricted Boltzmann machines arXiv
G Montavon, KR Müller, M Cuturi  Advances in Neural Information …, 2016  papers.nips.cc
Abstract Boltzmann machines are able to learn highly complex, multimodal, structured and
multiscale realworld data distributions. Parameters of the model are usually learned by
minimizing the KullbackLeibler (KL) divergence from training samples to the learned model.
2017 Wasserstein not in Math Reviews 155 items
A Le Rhun, F Bonnans, P Martinon, T Leroy  smai.emath.fr
We present a stochastic gradient approach to compute barycenters of probability
distributions, in the sense of Wassertein. The objective is to devise a fast method which can
be used for instance to perform clustering for machine learning. The optimal transport [1]
J Tierny  annonces.assoafig.fr
Fig. 1. Le sujet en une image–L'homologie persistante est un outil théorique puissant, qui
permet en pratique d'introduire une mesure de bruit sur les structures topologiques, comme
les singularités (sphères de couleur) dans cet exemple de carte d'élévation. Cette mesure
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王瑜， 闫沫  电子设计工程, 2017  cqvip.com
针对基于CV 模型的活动轮廓分割算法无法应用于灰度非均匀图像分割的问题.
采用Wasserstein 距离作为区域直方图相似性测度, 提出基于该测度的非参数活动轮廓分割模型.
在模型求解时引入全局凸分割和分裂Bregman 方法, 减少了计算量. 大量实验结果表明该模型不
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曹小鹿， 辛云宏  计算机应用, 2017  joca.cn
摘要: 降维是大数据分析和可视化领域中的核心问题, 其中基于概率分布模型的的降维算法通过
最优化高维数据模型和低维数据模型之间的代价函数来实现降维. 这种策略的核心在于构建最能
体现数据特征的概率分布模型. 基于此, 本文将Wasserstein 距离引入降维, 提出一个基于
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郑昌金， 章登义， 苏科华， 武小平， 洪程  计算机与数字工程, 2017  cqvip.com
针对K 最近邻分类中相似度量的量化问题, 结合最优传输理论中Wasserstein 距离数学特性,
提出一种基于LBP 特征和熵正则化Wasserstein 距离的K 近邻分类方法. 首先对人脸表情图像
进行预处理, 然后使用LBP 算子对图像进行特征提取获得LBP 特征直方图, 最后使用熵正则化的
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M Agueh, G Carlier  Comptes Rendus Mathematique, 2017  Elsevier
Résumé Les barycentres dans l'espace de Wasserstein constituent une manière naturelle
d'interpoler entre plusieurs mesures de probabillité, utile dans différents domaines
appliqués comme le traitement d'images ou l'apprentissage statistique. Nous conjecturons
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J BionNadal, D Talay  2017  hal.inria.fr
In this paper we introduce a Wassersteintype distance on the set of the probability
distributions of strong solutions to stochastic differential equations. This new distance is
defined by restricting the set of possible coupling measures. We prove that it may also be
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G CARLIER, I Journées  math.ubordeaux.fr
Page 1. 1 Barycentres dans l'espace de Wasserstein Guillaume CARLIER a Journées IOPS 
Image, Optimisation, Probabilités et Statistique Réserve ornithologique du Teich, 58 Juillet 2017.
aCEREMADE, Université Paris Dauphine et MOKAPLAN, InriaParis /1 Page 2. Plan 2 Plan ➀
By: Lawson, Jimmie D.; Lim, Yongdo
JOURNAL OF OPERATOR THEORY Volume: 77 Issue: 1 Pages: 87107 Published: WIN 2017
By: Fedeli, L.; Pandolfi, A.; Ortiz, M.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Volume: 112 Issue: 9 Pages: 11751193 Published: NOV 30 2017
Framework Planning of Active Distribution Network Considering Active Management
By: Gao, Peng; Chen, Hongkun; Zheng, Xu; et al.
JOURNAL OF ENGINEERINGJOE Published: NOV 16 2017
From optimal transportation to optimal teleportation
By: Wolansky, G.
ANNALES DE L INSTITUT HENRI POINCAREANALYSE NON LINEAIRE Volume: 34 Issue: 7 Pages: 16691685 Published: DEC 2017
Convergence order of upwind type schemes for transport equations with discontinuous coefficients
By: Delarue, Francois; Lagoutiere, Frederic; Vauchelet, Nicolas
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES Volume: 108 Issue: 6 Pages: 918951 Published: DEC 2017
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By: Lott, John
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume: 145 Issue: 12 Pages: 53295340 Published: DEC 2017
Coupling and exponential ergodicity for stochastic differential equations driven by Levy processes
By: Majka, Mateusz B.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume: 127 Issue: 12 Pages: 40834125 Published: DEC 2017
Abstract: We introduce a new technique, which we call the boundary method, for solving the
semidiscrete optimal transport problem, a special, but quite general, type of optimal
transportation. We provide mathematical justification, convergence analysis, algorithmic
J Weed, F Bach  arXiv preprint arXiv:1707.00087, 2017  arxiv.org
We study the Wasserstein distance between two measures µ, ν which are mutually singular.
In particular, we are interested in minimization problems of the form W (µ, A)= inf W (µ, ν): ν∈
A where µ is a given probability and A is contained in the class µ⊥ of probabilities that are
This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs
between two distinct continuous distributions $ F $ and $ G $ on $\mathbb R $. The
estimator is based on the order statistics of (possibly dependent) samples of $ F $ resp. $ G
E Bernton, PE Jacob, M Gerber, CP Robert  arXiv preprint arXiv …, 2017  arxiv.org
Abstract: In purely generative models, one can simulate data given parameters but not
necessarily evaluate the likelihood. We use Wasserstein distances between empirical
distributions of observed data and empirical distributions of synthetic data drawn from such
Abstract: In this paper, we introduce a new CT image denoising method based on the
generative adversarial network (GAN) with Wasserstein distance and perceptual similarity.
The Wasserstein distance is a key concept of the optimal transform theory, and promises to
… In this article, we advocate for a different approach, which is to consider generic optimal transport
(OT) metrics which can be used over general spaces X (not just the Euclidean space Rd and
not only the 1Wasserstein distance). The OT metric between two probability …
A Mallasto, A Feragen  Advances in Neural Information Processing …, 2017  papers.nips.cc
Abstract We introduce a novel framework for statistical analysis of populations of non
degenerate Gaussian processes (GPs), which are natural representations of uncertain
curves. This allows inherent variation or uncertainty in functionvalued data to be properly
Y Yang, B Engquist, J Sun, BD Froese  Geophysics, 2017  library.seg.org
Conventional fullwaveform inversion (FWI) using the leastsquares norm as a misfit function
is known to suffer from cycleskipping issues which increases the risk of computing a local
rather than the global minimum of the misfit. The quadratic Wasserstein metric has been
M Agueh, G Carlier  COMPTES …, 2017  ELSEVIER FRANCEEDITIONS …
Volume 355, Issue 7, July 2017, Pages 812818
J Lott  arXiv preprint arXiv:1701.02297, 2017  arxiv.org
Abstract: If M is a smooth compact connected Riemannian manifold, let P (M) denote the
Wasserstein space of probability measures on M. We describe a geometric construction of
parallel transport of some tangent cones along geodesics in P (M). We show that when
E Cazelles, J Bigot, N Papadakis  International Conference on Geometric …, 2017  Springer
Abstract This paper is an overview of results that have been obtain in 2 on the convex
regularization of Wasserstein barycenters for random measures supported on\mathbb R^ d.
We discuss the existence and uniqueness of such barycenters for a large class of
J Lott  Proceedings of the American Mathematical Society, 2017  ams.org
Abstract: If $ M $ is a smooth compact Riemannian manifold, let $ P (M) $ denote the
Wasserstein space of probability measures on $ M $. If $ S $ is an embedded submanifold of
$ M $, and $\mu $ is an absolutely continuous measure on $ S $, then we compute the
K Kang, HK Kim  SIAM Journal on Mathematical Analysis, 2017  SIAM
We consider a coupled system of KellerSegeltype equations and the incompressible
NavierStokes equations in spatial dimension two and three. We first establish the existence
of a weak solution of a FokkerPlank equation in the Wasserstein space under the
J Mifdal, B Coll, N Courty, J Froment…  IGARSS …, 2017  hal.archivesouvertes.fr
… Index Terms— Image Fusion, Optimal Transport, Wasser stein Barycenter 1. INTRODUCTION …
This regularization is carried out by penalizing the entropy of the joint coupling φ … Convolutional
wasserstein distances: Efficient optimal transportation on geometric do mains …
J Tong, X Jin, Z Zhang  Potential Analysis, 2017  Springer
… Keywords Exponential ergodicity · Symmetric αstable process · Markovian switching · Mmatrix ·
Wasserstein distance · Coupling method … To get the exponential ergodicity in Wasserstein
distances, we use the coupling method to deal with the Markov chain …
arXiv:1712.07528 [pdf, ps, other]
Harmonic mappings valued in the Wasserstein space
Hugo Lavenant (LMOrsay)
Subjects: Analysis of PDEs (math.AP)
arXiv:1712.07185 [pdf, ps, other]
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Pierre H. Richemond, Brendan Maginnis
Subjects: Learning (cs.LG)
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Clément Cancès, Daniel Matthes, Flore Nabet
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (mathph)
Wasserstein Distributional Robustness and Regularization in Statistical Learning
Rui Gao, Xi Chen, Anton J. Kleywegt
Subjects: Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)
A central question in statistical learning is to design algorithms that not only perform well on training data, but also generalize to new and unseen data. In...
arXiv:1712.05923 [pdf, ps, other]
Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces
José A. Carrillo, YoungPil Choi, Oliver Tse
Subjects: Analysis of PDEs (math.AP)
On reproduction of On the regularization of Wasserstein GANs
Comments: 9 pages, 9 figures, ICLR 2018 reproducibility challenge
Subjects: Learning (cs.LG); Machine Learning (stat.ML)
Wasserstein Generative Adversarial Networks
[edit]Martin Arjovsky, Soumith Chintala, Léon Bottou ;
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:214223, 2017.
Abstract We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to different distances between distributions.
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Wasserstein Distributional Robustness and Regularization in Statistical Learning
by R Gao Xi Chen Anton J. Kleywegt 2017
arXiv:1712.06050 [cs.LG]
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Dec 22, 2016  We investigate a definition of quantum Wasserstein distance of two states based on their couplings on the product algebra as in the classical case. A detailed analysis of the two qubit model leads to a formal definition fulfilling some minimal requirements. It also shows that a clearcut definition, by direct ...
Finding the closest probabilistic Parseval frame in the 2Wasserstein metric spie
by D Cheng  2017
It is known in the standard l^{2} distance that the closest Parseval frame to a given frame {Φi}^{m}i=1 ⊂ ℜ ^{d} is {S^{1/2}(Φi)}^{m}i=1 where S is the frame operator of the original frame. We show this is also the case for probabilistic frames in the 2Wasserstein distance. In the process we develop some regularity properties for the map ...
By: Cheng, Desai; Okoudjou, Kasso A.
Edited by: Lu, YM; VanDeVille, D; Papadakis, M
Conference: Conference on Wavelets and Sparsity XVII Location: San Diego, CA Date: AUG 0609, 2017
Sponsor(s): SPIE
WAVELETS AND SPARSITY XVII Book Series: Proceedings of SPIE Volume: 10394 Article Number: 103940N Published: 2017
Wasserstein Dictionary Learning: Optimal Transportbased unsupervised nonlinear dictionary learning arXiv
MA Schmitz, M Heitz, N Bonneel, FMN Mboula…  arXiv preprint arXiv …, 2017
Abstract: This article introduces a new nonlinear dictionary learning method for histograms
in the probability simplex. The method leverages optimal transport theory, in the sense that
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Wasserstein barycenters over Riemannian manifolds  ScienceDirect
Volume 307, 5 February 2017, Pages 640683. Advances in Mathematics. Wasserstein barycenters over Riemannian manifolds☆.
This paper is dedicated to the fond memory of our colleague and friend Martial Agueh, one of the originators of the theory of Wasserstein barycenters. Author links open overlay ...
Abstract We study barycenters in the space of probability measures on a Riemannian
manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we
establish absolute continuity of the barycenter of general measures Ω∈ P (P (M)) on
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Zbl 06817170 Al Reda, F.; Maury, B.
Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 9783110439267/hbk; 9783110430417/ebook). Radon Series on Computational and Applied Mathematics 17, 400416 (2017).
MSC: 60J60 94C15 35K05 35K08 65N08 60J27 60J28
Wasserstein blue noise sampling ACM
by Qin, Hongxing; Chen, Yi; He, Jinlong; More...
ACM Transactions on Graphics (TOG), 10/2017, Volume 36, Issue 5 07/2017, Volume 36, Issue 4
In this article, we present a multiclass blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density...
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non convex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions: NONCONVEX GRADIENT FLOW IN THE WASSERSTEIN METRIC
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by Arjovsky, Martin; Chintala, Soumith; Bottou, Léon
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Abstract: We introduce a new algorithm named WGAN, an alternative to traditional GAN
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by Su, Bing; Hua, Gang Page(s):2906  2914
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Entropy, 01/2017, Volume 19, Issue 2
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Mathematical Programming, 2017
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Wasserstein Introspective Neural Networks arXiv
by Lee, Kwonjoon; Xu, Weijian; Fan, Fan; More...
11/2017
We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant...
by Tolstikhin, Ilya; Bousquet, Olivier; Gelly, Sylvain; More...
11/2017
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Wasserstein Identity Testing  arXiv
by Deng, Shichuan; Li, Wenzheng; Wu, Xuan
10/2017
Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing...
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Learning Wasserstein Embeddings arXiv
by Courty, Nicolas; Flamary, Rémi; Ducoffe, Mélanie
10/2017
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing...
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Nuit Blanche: Wasserstein GAN  implementation 
Feb 7, 2017  My name is Igor Carron ... Here is an implementation of it that I found on GitXiv, the most awesomest website on the interweb: https://github.com/martinarjovsky/WassersteinGAN. ... It's a problem when the critic fails to be close to optimum, and hence it's error stops being a good Wasserstein estimate. Known ...
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Apr 4, 2017  Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes significant progress toward stable training of GANs, but can still generate lowquality samples or fail to converge in some settings. We find ...
by Igor Carron
Nuit Blanche, 04/2017
Thanks Alex for the headsup ! We propose an alternative method for enforcing the Lipschitz constraint: instead of clipping weights, penalize the norm of the...
Nuit Blanche: Wasserstein GAN / Towards Principled Methods for ...
Jan 30, 2017  We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore ...
Multilevel Clustering via Wasserstein Means arXiv
by Ho, Nhat; Nguyen, XuanLong; Yurochkin, Mikhail; More...
06/2017
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns...
Improved Training of Wasserstein GANs arXiv
by Gulrajani, Ishaan; Ahmed, Faruk; Arjovsky, Martin; More...
03/2017
Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes...
Abstract Generative Adversarial Networks (GANs) are powerful generative models, but suffer
from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress
toward stable training of GANs, but sometimes can still generate only poor samples or fail to
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by 曹小鹿 辛云宏
计算机应用, 2017, Volume 37, Issue 10
Visual Feature Attribution using Wasserstein GANs arXiv
by Baumgartner, Christian F; Koch, Lisa M; Tezcan, Kerem Can; More...
11/2017
Attributing the pixels of an input image to a certain category is an important and wellstudied problem in computer vision, with applications ranging from...
Correcting Nuisance Variation using Wasserstein Distance arXiv
by Tabak, Gil; Fan, Minjie; Yang, Samuel J; More...
11/2017
Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One...
On the regularization of Wasserstein GANs
by Petzka, Henning; Fischer, Asja; Lukovnicov, Denis
09/2017
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data....
Dimensionfree Wasserstein contraction of nonlinear filters  arXiv
by Whiteley, Nick
08/2017
For a class of partially observed diffusions, sufficient conditions are given for the map from initial condition of the signal to filtering distribution to be...
Sliced Wasserstein Kernel for Persistence Diagrams arXiv
by Carrière, Mathieu; Cuturi, Marco; Oudot, Steve
06/2017
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of...
sliced Wasserstein estimation of mixtures rb;oggers
by Christian P. Robert
Xi'an's Og, 11/2017
A paper by Soheil Kolouri and coauthors was arXived last week about using Wasserstein distance for inference on multivariate Gaussian mixtures. The basic...
sliced Wasserstein estimation of mixtures  Xi'an's Og
Relaxed Wasserstein with Applications to GANs nuitblanche
May 26, 2017  Generative Adversarial Networks (GANs) provide a versatile class of models for generative modeling. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Wasserstein distance rather than JensenShannon
Relaxed Wasserstein with Applications to GANs arXiv
by X Guo  2017  Cited by 4  Related articles
May 19, 2017  In comparison to the existing literature in GANs, which are adhoc in the choices of cost functions, this new conceptual framework not only provides great flexibility in designing general cost functions, e.g., for applications to GANs, but also allows different cost functions implemented and compared under a ...
Relaxed Wasserstein with Applications to GANs  Semantic Scholar
We propose a novel class of statistical divergences called Relaxed Wasserstein (RW) divergence. RW divergence generalizes Wasserstein distance and is parametrized by strictly convex, differentiable functions. We establish for RW several key probabilistic properties, which are critical for the success of Wasserstein ...
Xin Guo, Johnny Hong, Tianyi Lin, Nan Yang
Relaxed Wasserstein with Applications to GANs  ResearchGate
https://www.researchgate.net/.../317062321_Relaxed_Wasserstein_with_Applications_to...
Request (PDF)  Relaxed Wasserstein...  Generative Adversarial Networks (GANs) provide a versatile class of models for generative modeling. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Wasserstein distance rather than ...
Xin Guo
Face SuperResolution Through Wasserstein GANs arXiv
by Z Chen  2017  Cited by 1  Related articles
May 6, 2017  Face SuperResolution Through Wasserstein GANs. Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide range of problems. Despite its great potential, GANs are difficult to train.
by Chen, Zhimin; Tong, Yuguang
05/2017
Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide...
Strongly Polynomial 2Approximations of Discrete Wasserstein Barycenters arXiv
by S Borgwardt  2017  Related articles
Apr 18, 2017  We discuss approximation algorithms that trade a small error for a significant reduction in computational effort. ... After a finite number of iterations, it terminates with a 2approximation that retains the favorable properties of a barycenter, namely a sparse support and no mass split at the
Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals. These arise in applications from economics to...
A canonical barycenter via Wasserstein regularization arXiv
by Kim, YoungHeon; Pass, Brendan
03/2017
We introduce a weak notion of barycenter of a probability measure \mu on a metric measure space (X, d, {\bf m}), with the metric d and reference measure {\bf...
Extremal flows on Wasserstein space arXiv
by Conforti, Giovanni; Pavon, Michele
12/2017
We develop an intrinsic geometric approach to calculus of variations on Wasserstein space. We show that the flows associated to the Schroedinger bridge with...
Inference in generative models using the Wasserstein distance arXiv
by Christian P. Robert
Xi'an's Og, 01/2017
Today, Pierre Jacob posted on arXiv a paper of ours on the use of the Wasserstein distance in statistical inference, which main focus is exploiting this...
Nuit Blanche: Wasserstein Training of Restricted Boltzmann Machines nuitblanche.
Feb 1, 2017  We propose in this work a novel approach for Boltzmann machine training which assumes that a meaningful metric between observations is given. This metric can be represented by the Wasserstein distance between distributions, for which we derive a gradient with respect to the model
基于LBP特征和熵正则化Wasserstein距离的人脸表情识别 [Facial Expression Recognition Based on LBP Features and Entropy Regularized Wasserstein Distance
Facial Expression Recognition Based on LBP Features and Entropyregularized Wasserstein Distance]
by 郑昌金 章登义 苏科华 武小平 洪程
计算机与数字工程, 2017, Volume 45, Issue 2
On the BuresWasserstein distance between positive definite matrices arXiv
by Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo
12/2017
The metric d(A,B)=\left[ \tr\, A+\tr\, B2\tr(A^{1/2}BA^{1/2})^{1/2}\right]^{1/2} on the manifold of n\times n positive definite matrices arises in various...
Manifoldvalued Image Generation with Wasserstein Adversarial Networks arXiv
by Huang, Zhiwu; Wu, Jiqing; Van Gool, Luc
12/2017
Unsupervised image generation has recently received an increasing amount of attention thanks to the great success of generative adversarial networks (GANs),...
The Pontryagin Maximum Principle in the Wasserstein Space arXiv
by Bonnet, Benoît; Rossi, Francesco
11/2017
We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation...
Sliced Wasserstein Distance for Learning Gaussian Mixture Models grabdAI
Sliced Wasserstein Distance for Learning Gaussian Mixture Models arXiv
by Kolouri, Soheil; Rohde, Gustavo K; Hoffmann, Heiko
11/2017
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is...
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Aggregated Wasserstein Metric and State Registration for Hidden Markov Models arXiv
by Chen, Yukun; Ye, Jianbo; Li, Jia
11/2017
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional...
Unsupervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning
by Zhang, Ning; Yan, Junchi; Zhou, Yuchen
11/2017
Separating audio mixtures into individual tracks has been a long standing challenging task. We introduce a novel unsupervised audio source separation approach...
Abstract: Separating audio mixtures into individual instrument tracks has been a long
standing challenging task. We introduce a novel unsupervised audio source separation
approach based on deep adversarial learning. Specifically, our loss function adopts the
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by Adler, Jonas; Ringh, Axel; Öktem, Ozan; More...
10/2017
We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primaldual reconstruction scheme for illposed...
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by J Chen  2017
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by Grimm, Christopher; Song, Yuhang; Littman, Michael L
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Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problemsusing data to assess how likely...
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09/2017
We introduce a family of reversible fragmentatingcoagulating processes of particles of varying sizescaled diffusivity with strictly local interaction on th
Cadlag stability and approximation of reversible coalescingfragmentating Wasserstein dynamics arXiv
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by Adler, Jonas; Ringh, Axel; Öktem, Ozan; More...
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The quadratic Wasserstein metric for earthquake location arXiv
by Chen, Jing; Chen, Yifan; Wu, Hao; More...
10/2017
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A new approach for the construction of a Wasserstein diffusion arXiv
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by Konarovskyi, Vitalii; von Renesse, Max
09/2017
We introduce a family of reversible fragmentatingcoagulating processes of particles of varying sizescaled diffusivity with strictly local interaction on the...
Wasserstein CNN: Learning Invariant Features for NIRVIS Face Recognition arXiv
by He, Ran; Wu, Xiang; Sun, Zhenan; More...
08/2017
Heterogeneous face recognition (HFR) aims to match facial images acquired from different sensing modalities with missioncritical applications in forensics,...
Wasserstein Distance Guided Representation Learning for Domain Adaptation arXiv
by Shen, Jian; Qu, Yanru; Zhang, Weinan; More...
07/2017
Domain adaptation aims at generalizing a highperformance learner on a target domain via utilizing the knowledge distilled from a source domain which has a...
Outlier Detection Using Distributionally Robust Optimization under the Wasserstein Metric arXiv
by Chen, Ruidi; Paschalidis, Ioannis Ch
06/2017
We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability...
The Cramer Distance as a Solution to Biased Wasserstein Gradients arXiv
by Bellemare, Marc G; Danihelka, Ivo; Dabney, Will; More...
05/2017
The Wasserstein probability metric has received much attention from the machine learning community. Unlike the KullbackLeibler divergence, which strictly...
… the Cramér distance is not a metric proper. However, its square root is, and is a member of the
lp family of metrics lp(P, Q) := (∫ FP (x) − FQ(x)pdx )1/p . The lp and Wasserstein metrics are
identical at p = 1, but are otherwise distinct. Like the Wasser stein metrics, the lp …
Convergence of the Population Dynamics algorithm in the Wasserstein metric arXiv
by OlveraCravioto, Mariana
05/2017
We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates...
Minimax Statistical Learning and Domain Adaptation with Wasserstein Distances arXiv
by Lee, Jaeho; Raginsky, Maxim
05/2017
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worstcase risk over a larger ambiguity set...
Ambiguity set and learning via Bregman and Wasserstein arXiv
by Guo, Xin; Hong, Johnny; Yang, Nan
05/2017
Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing...
Wasserstein Learning of Deep Generative Point Process Models arXiv
by Xiao, Shuai; Farajtabar, Mehrdad; Ye, Xiaojing; More... Cited by 3 
05/2017
Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a...
Optimal Ballistic Transport and HopfLax Formulae on Wasserstein Space arXiv
by Ghoussoub, Nassif
05/2017
Abstract: We investigate the optimal mass transport problem associated to the following"
ballistic" cost functional on phase space $ M\times M^* $, b_T (v, x):=\inf\{\langle v,\gamma
(0)\rangle+\int_0^ TL (\gamma (t),{\dot\gamma}(t))\, dt;\gamma\in C^ 1 ([0, T), M);\gamma
Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric arXiv
by Luo, Fengqiao; Mehrotra, Sanjay
04/2017
We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO...
e in generative models using the Wasserstein distance arXiv
by Bernton, Espen; Jacob, Pierre E; Gerber, Mathieu; More...
01/2017
A growing range of generative statistical models are such the numerical evaluation of their likelihood functions is intractable. Approximate Bayesian...
Fr\'echet Means and Procrustes Analysis in Wasserstein Space arXiv
by Zemel, Yoav; Panaretos, Victor M
01/2017
We consider two statistical problems at the intersection of functional and nonEuclidean data analysis: the determination of a Fr\'echet mean in the...
Wasserstein and Kolmogorov error bounds for variancegamma approximation via Stein's method I arXiv
by Gaunt, Robert E
11/2017
The variancegamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions....
A partial Laplacian as an infinitesimal generator on the Wasserstein space ResearchGate
A partial Laplacian as an infinitesimal generator on the Wasserstein space arXiv
by Chow, Yat Tin; Gangbo, Wilfrid
10/2017
We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion...
A Central Limit Theorem for Wasserstein type distances between two different laws arXiv
by Berthet, Philippe; Fort, JeanClaude; Klein, Thierry
10/2017
This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions F and G on \mathbb R....
by Li, Songzi; Li, XiangDong
10/2017
Abstract: In this survey paper, we give an overview of our recent works on the study of the $
W $entropy for the heat equation associated with the Witten Laplacian on superRicci flows
and the Langevin deformation on Wasserstein space over Riemannian manifolds. Inspired
Wasserstein and total variation distance between marginals of L\'evy processes arXiv
by Mariucci, Ester; Reiß, Markus
10/2017
We present upper bounds for the Wasserstein distance of order p between the marginals of L\'evy processes, including Gaussian approximations for jumps of...
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Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment arXiv
by Hühnerbein, Ruben; Savarino, Fabrizio; Åström, Freddie; More...
10/2017
We introduce a novel approach to Maximum A Posteriori inference based on discrete graphical models. By utilizing local Wasserstein distances for co
by Amari, Shunichi; Karakida, Ryo; Oizumi, Masafumi
09/2017
Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is...
Journal Article:
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LogPCA versus Geodesic PCA of histograms in the Wasserstein space arXiv
by Cazelles, Elsa; Seguy, Vivien; Bigot, Jérémie; More...
08/2017
This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation...
Journal Article:
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by Mora, Maria Giovanna; Peletier, Mark; Scardia, Lucia
08/2017
We consider systems of n parallel edge dislocations in a single slip system, represented by points in a twodimensional domain; the elastic medium is modelled...
Wasserstein stability of the entropy power inequality for logconcave random vectors IEEE
by Thomas A. Courtade; Max Fathi; Ashwin Pananjady
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings, 01/2017
Conference Title: 2017 IEEE International Symposium on Information Theory (ISIT) Conference Start Date: 2017, June 25 Conference End Date: 2017, June 30...
Conference Proceeding:
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Wasserstein Stability of the Entropy Power Inequality for LogConcave Densities arXiv
by TA Courtade  2016  Cited by 5  Related articles
Oct 25, 2016  Wasserstein Stability of the Entropy Power Inequality for LogConcave Densities. ... As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein distance when densities are uniformly logconcave on sets of measure arbitrarily close to one.
by Wen Zhang; Jie Shi; Jun Yu; More...
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Conference Proceedings, 01/2017
Conference Title: 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017) Conference Start Date: 2017, April 18 Conference End Date: 2017,...
Conference Proceeding:
By: Zhang, Wen; Shi, Jie; Yu, Jun; et al.
Book Group Author(s): IEEE
Conference: IEEE 14th International Symposium on Biomedical Imaging (ISBI)  From Nano to Macro Location: Melbourne, AUSTRALIA Date: APR 1821, 2017
Sponsor(s): IEEE; EMB; IEEE Signal Proc Soc
2017 IEEE 14TH INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING (ISBI 2017) Pages: 520524 Published: 2017
Zbl 06817167 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. (English) Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 9783110439267/hbk; 9783110430417/ebook). Radon Series on Computational and Applied Mathematics 17, 304332 (2017).
Topological Optimization and Optimal Transport, 2017
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indings in Computer Graphics Reported from Shandong ...
(20171129), Findings in Computer Graphics Reported from Shandong University (Wasserstein Blue Noise Sampling), Computer Weekly News , 279, ISSN: 19441606, BUTTER® ID: 014750427 DOI Information The direct object identifier (DOI) for that additional information is: https://doi.org/10.1145
Journal of Technology & Science, Oct 8, 2017, 523
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Mathematics  Calculus; Findings on Calculus from M. Kell and Colleagues Provide New Insights (On interpolation and curvature via Wasserstein geodesics)
Mathematics Week, May 9, 2017, 4
According to news reporting out of Leipzig, Germany, by VerticalNews editors, the research stated, "In this article, a proof of the interpolation inequality...
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Patent US20170083608  Accelerated discrete distribution clustering under wasserstein distance  Google patents
Accelerated discrete distribution clustering under wasserstein distance. US 20170083608 A1. Abstract. Computationally efficient accelerated D2clustering algorithms are disclosed for clustering discrete distributions under the Wasserstein distance with improved scalability. Three firstorder methods include subgradient ...
Accelerated Discrete Distribution Clustering under Wasserstein Distance ResearchGate
In a variety of research areas, the bag of weighted vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2clustering pursues the minimum total withincluster variation for a set of discrete distributions subject to the KantorovichWasserstein metric.
Global IP News. Software Patent News, Mar 23, 2017
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Accelerated Discrete Distribution Clustering under Wasserstein Distance slides
O We have developed and compared three rstorder methods for optimizing the Wasserstein centroids in. D clustering. We refer to the modi ed Bregman ADMM as the main algorithm. O The new methods, collectively called AD clustering, improve scalability signi cantly. We have also developed a parallel algorithm for the ...
Journal of Technology & Science, Nov 12, 2017, 223
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By: Hiai, Fumio; Lim, Yongdo
LINEAR ALGEBRA AND ITS APPLICATIONS Volume: 533 Pages: 118131 Published: NOV 15 2017
Abstract: We introduce a class of flows on the Wasserstein space of probability measures
with finite first moment on the CartanHadamard Riemannian manifold of positive definite
matrices, and consider the problem of differentiability of the corresponding Cartan
Energy Volume 135, 15 September 2017, Pages 153170 XueqianFu^{a}QinglaiGuo^{a}HongbinSun^{a}ZhaoguangPan^{a}WenXiong^{b}LiWang^{b}
Abstract The stochastic fluctuation characteristics of intermittent renewable energy sources
and energy loads, as well as their multienergy interactions and dependencies, have
negligible effects on the operation and analyses of integrated energy systems. Determining
Detecting changes in forced climate attractors with Wasserstein distance
by Y Robin  2017  Related articles
NONLINEAR PROCESSES IN GEOPHYSICS Volume: 24 Issue: 3 Pages: 393405 Published: JUL 31 2017
Jul 31, 2017  Citation: Robin, Y., Yiou, P., and Naveau, P.: Detecting changes in forced climate attractors with Wasserstein distance, Nonlin. ... If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified.
Climate Change; Data on Climate Change Discussed by Researchers at National Center for Scientific Research (CNRS) (Detecting changes in forced climate attractors with Wasserstein...
Global Warming Focus, Aug 28, 2017, 36
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[pdf] Detecting changes in forced climate attractors with Wasserstein distance
Journal of Technology & Science, Aug 27, 2017, 140
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Journal of Engineering, Jun 26, 2017, 1098
According to news originating from Beijing, People's Republic of China, by VerticalNews correspondents, research stated, "In this paper a nonparametric model...
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According to news reporting originating from Orsay, France, by VerticalNews editors, the research stated, "This is an expository paper on the theory of...
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According to news reporting originating from Paris, France, by VerticalNews correspondents, research stated, "The time discretization of gradient flows in...
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According to news reporting originating from Berkeley, California, by VerticalNews correspondents, research stated, "Nonparametric twosample or homogeneity...
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According to news reporting originating from Talence, France, by VerticalNews correspondents, research stated, "We introduce the method of Geodesic Principal...
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According to news reporting originating in Pavia, Italy, by VerticalNews editors, the research stated, "Nonlinear sigma models are quantum field theories...
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Wasserstein GAN / Towards Principled Methods for Training Generative Adversarial Networks Nuit Blanche,
by Igor Carron
Nuit Blanche, 01/2017
We mentioned GANs before. Here are contributions on how to use Earth Mover's distances to improve their training (Cedric Villani is mentioned in the references...
GromovHausdorff limit of Wasserstein spaces on point clouds arXiv
by NG Trillos  2017  Related articles
Feb 11, 2017 We show that as long as decays towards zero slower than an explicit rate depending on the level of uniformity of , then the space converges in the GromovHausdorff sense towards the space of probability measures on endowed with the Wasserstein distance.
by Trillos, Nicolas Garcia
We consider a point cloud X_n := \{ x_1, \dots, x_n \} uniformly distributed on the flat torus \mathbb{T}^d : = \mathbb{R}^d / \mathbb{Z}^d , and construct a...
A Wasserstein gradient flow approach to Poisson− Nernst− Planck equations ISAIM
D Kinderlehrer, L Monsaingeon, X Xu  … : Control, Optimisation and …, 2017  esaimcocv.org
Abstract The Poisson− Nernst− Planck system of equations used to model ionic transport is
interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of
probability measures with finite second moment. A variational scheme is then set up and is
2018 Wasserstein without MR 33 items
Inference for empirical Wasserstein distances on finite spaces
By: Sommerfeld, Max; Munk, Axel
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES BSTATISTICAL METHODOLOGY Volume: 80 Issue: 1 Pages: 219238 Published: JAN 2018
Summary The Wasserstein distance is an attractive tool for data analysis but statistical
inference is hindered by the lack of distributional limits. To overcome this obstacle, for
probability measures supported on finitely many points, we derive the asymptotic distribution
[pdf] Inference for Empirical Wasserstein Distances on Finite ... arXiv
Findings on Statistics Reported by A. Munk et al (Inference for empirical Wasserstein distances on finite spaces)
Journal of Technology & Science, 01/2018
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On the BuresWasserstein distance between positive definite matrices
R Bhatia, T Jain, Y Lim  Expositiones Mathematicae, 2018  Elsevier
d (A, B)= tr A+ tr B− 2 tr (A 1∕ 2 BA 1∕ 2) 1∕ 2 1∕ 2 on the manifold of n× nn× n positive
definite matrices arises in various optimisation problems, in quantum information and in the
theory of optimal transport. It is also related to Riemannian geometry. In the first part of this
Cited by 2 Related articles All 3 versions
Second order models for optimal transport and cubic splines on the Wasserstein space
JD Benamou, T Gallouët, FX Vialard  arXiv preprint arXiv:1801.04144, 2018  arxiv.org
Abstract: On the space of probability densities, we extend the Wasserstein geodesics to the
case of higherorder interpolation such as cubic spline interpolation. After presenting the
natural extension of cubic splines to the Wasserstein space, we propose simpler approach,
Related articles All 3 versions
H Wu, PC Ma, Y Lv, M Ihme  2018 AIAA Aerospace Sciences Meeting, 2018  arc.aiaa.org
The objective of this work is to address the need for assessing the quality of largeeddy
simulations with particular application to turbulent reacting flows. Such assessments include
the consideration of resolution requirements and the quantitative evaluation of the accuracy
Related articles All 4 versions
WassersteinRiemannian Geometry of Positivedefinite Matrices
L Malagò, L Montrucchio, G Pistone  arXiv preprint arXiv:1801.09269, 2018  arxiv.org
Abstract: The Wasserstein distance on multivariate nondegenerate Gaussian densities is a
Riemannian distance. After reviewing the properties of the distance and the metric geodesic,
we derive an explicit form of the Riemannian metrics on positivedefinite matrices and
A MalliavinStein approach for multivariate approximations in Wasserstein distance
X Fang, QM Shao, L Xu  arXiv preprint arXiv:1801.07815, 2018  arxiv.org
Abstract: Stein's method has been widely used for probability approximations. However, in
the multidimensional setting, most of the results are for multivariate normal approximation or
for test functions with bounded secondor higherorder derivatives. For a class of multivariate
All 2 versions [PDF] arxiv.org
Y Liu  arXiv preprint arXiv:1801.06148, 2018  arxiv.org
Abstract: We establish the condition for probability measure characterization by $ L^{p} $
quantization error function in $\mathbb {R}^{d} $. There are two types of characterization: the
static characterization for the identity of two probability measures, and the characterization
Related articles All 2 versions [PDF] crest.science
M HEITZ, N BONNEEL, F NGOLÈ, D COEURJOLLY…  crest.science
Abstract. This article introduces a new nonlinear dictionary learning method for histograms
in the probability simplex. The method leverages optimal transport theory, in the sense that
our aim is to reconstruct histograms using so called displacement interpolations (aka
Related articles [PDF] crest.science
[PDF] Sliced Wasserstein Kernel for Persistence Diagrams M. CARRIÈRE M. CUTURI 2
S OUDOT  crest.science
Abstract Persistence diagrams play a key role in topological data analysis (TDA), in which
they are routinely used to describe topological properties of complicated shapes.
persistence diagrams enjoy strong stability properties and have proven their utility in various
Datadriven riskaverse stochastic optimization with Wasserstein metric
C Zhao, Y Guan  Operations Research Letters, 2018  Elsevier
Abstract In this paper, we study a datadriven riskaverse stochastic optimization approach
with Wasserstein Metric for the general distribution case. By using the Wasserstein Metric,
we can successfully reformulate the riskaverse twostage stochastic optimization problem
[PDF] Semisupervised Biomedical Translation with Cycle Wasserstein Regression GANs
MBA McDermott, T Yan, T Naumann, N Hunt, H Suresh…  2018  marzyehghassemi.com
Abstract The biomedical field offers many learning tasks that share unique challenges: large
amounts of unpaired data, and a high cost to generate labels. In this work, we develop a
method to address these issues with semisupervised learning in regression tasks (eg,
M Erdmann, L Geiger, J Glombitza…  arXiv preprint arXiv …, 2018  arxiv.org
Abstract: We use adversarial network architectures together with the Wasserstein distance to
generate or refine simulated detector data. The data reflect twodimensional projections of
spatially distributed signal patterns with a broad spectrum of applications. As an example,
All 4 versions [PDF] arxiv.org
Distributionally Robust ChanceConstrained Approximate ACOPF with Wasserstein Metric
C Duan, W Fang, L Jiang, L Yao…  IEEE Transactions on …, 2018  ieeexplore.ieee.org
Chance constrained optimal power flow (OPF) has been recognized as a promising
framework to manage the risk from variable renewable energy (VRE). In presence of VRE
uncertainties, this paper discusses a distributionally robust chance constrained approximate
Solving Approximate Wasserstein GANs to Stationarity
M Sanjabi, J Ba, M Razaviyayn, JD Lee  arXiv preprint arXiv:1802.08249, 2018  arxiv.org
Abstract: Generative Adversarial Networks (GANs) are one of the most practical strategies to
learn data distributions. A popular GAN formulation is based on the use of Wasserstein
distance as a metric between probability distributions. Unfortunately, minimizing the
All 2 versions [PDF] arxiv.org
Y Han, J Jiao, T Weissman  arXiv preprint arXiv:1802.08405, 2018  arxiv.org
Abstract: We present\emph {Local Moment Matching (LMM)}, a unified methodology for
symmetric functional estimation and distribution estimation under Wasserstein distance. We
construct an efficiently computable estimator that achieves the minimax rates in estimating
All 2 versions [PDF] arxiv.org
Application of optimal transport and the quadratic Wasserstein metric to fullwaveform inversion
Y Yang, B Engquist, J Sun, BF Hamfeldt  Geophysics, 2018  library.seg.org
ABSTRACT Conventional fullwaveform inversion (FWI) using the leastsquares norm as a
misfit function is known to suffer from cycleskipping issues that increase the risk of
computing a local rather than the global minimum of the misfit. The quadratic Wasserstein
Cited by 7 Related articles All 5 versions [PDF] openreview.net
[PDF] Learning Disentangled Representations with Wasserstein AutoEncoders
PK Rubenstein, B Schoelkopf, I Tolstikhin  2018  openreview.net
Page 1. Workshop track  ICLR 2018 LEARNING DISENTANGLED REPRESENTATIONS WITH
WASSERSTEIN AUTOENCODERS Paul Rubenstein∗, Bernhard Schölkopf, Ilya Tolstikhin
Empirical Inference Max Planck Institute for Intelligent Systems, Tübingen 1paul.rubenstein,bs,
Free complete Wasserstein algebras
R Mardare, P Panangaden, GD Plotkin  arXiv preprint arXiv:1802.07366, 2018  arxiv.org
Abstract: We present an algebraic account of the Wasserstein distances $ W_p $ on
complete metric spaces. This is part of a program of a quantitative algebraic theory of effects
in programming languages. In particular, we give axioms, parametric in $ p $, for algebras
All 2 versions [PDF] arxiv.org
A Fast Proximal Point Method for Wasserstein Distance
Y Xie, X Wang, R Wang, H Zha  arXiv preprint arXiv:1802.04307, 2018  arxiv.org
Abstract: Wasserstein distance plays increasingly important roles in machine learning,
stochastic programming and image processing. Major efforts have been under way to
address its high computational complexity, some leading to approximate or regularized
J Ekanayake, N Kitchen, S Ourselin…  … Sclerosis, Stroke and …, 2018  books.google.com
Abstract. The Dice score is widely used for binary segmentation due to its robustness to
class imbalance. Soft generalisations of the Dice score allow it to be used as a loss function
for training convolutional neural networks (CNN). Although CNNs trained using meanclass
Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect
X Wei, B Gong, Z Liu, W Lu, L Wang  2018  openreview.net
Abstract: Despite being impactful on a variety of problems and applications, the generative
adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed
by\cite {arjovsky2017towards}, who also propose an alternative direction to avoid the
Distributionally Robust MeanVariance Portfolio Selection with Wasserstein Distances
J Blanchet, L Chen, XY Zhou  arXiv preprint arXiv:1802.04885, 2018  arxiv.org
Abstract: We revisit Markowitz's meanvariance portfolio selection model by considering a
distributionally robust version, where the region of distributional uncertainty is around the
empirical measure and the discrepancy between probability measures is dictated by the so
All 2 versions [PDF] arxiv.org
The existence of geodesics in Wasserstein spaces over path groups and loop groups
J Shao  arXiv preprint arXiv:1802.10226, 2018  arxiv.org
Abstract: In this work we prove the existence and uniqueness of the optimal transport map
for $ L^ p $Wasserstein distance with $ p> 1$, and particularly present an explicit
expression of the optimal transport map for the case $ p= 2$. As an application, we show the
All 2 versions [PDF] arxiv.org
Minimax Distribution Estimation in Wasserstein Distance
S Singh, B Póczos  arXiv preprint arXiv:1802.08855, 2018  arxiv.org
Abstract: The Wasserstein metric is an important measure of distance between probability
distributions, with several applications in machine learning, statistics, probability theory, and
data analysis. In this paper, we upper and lower bound minimax rates for the problem of
All 2 versions [PDF] semanticscholar.org
Wasserstein Geometry of Quantum States and Optimal Transport of MatrixValued Measures
Y Chen, TT Georgiou, A Tannenbaum  Emerging Applications of Control …, 2018  Springer
Abstract We overview recent results on generalizations of the Wasserstein 2metric,
originally defined on the space of scalar probability densities, to the space of Hermitian
matrices and of matrixvalued distributions, as well as some extensions of the theory to
Related articles All 2 versions [PDF] arxiv.org
Stochastic Wasserstein Barycenters
S Claici, E Chien, J Solomon  arXiv preprint arXiv:1802.05757, 2018  arxiv.org
Abstract: We present a stochastic algorithm to compute the barycenter of a set of probability
distributions under the Wasserstein metric from optimal transport. Unlike previous
approaches, our method extends to continuous input distributions and allows the support of
All 2 versions [PDF] arxiv.org
Wasserstein Distance Measure Machines
A Rakotomamonjy, A Traore, M Berar…  arXiv preprint arXiv …, 2018  arxiv.org
Abstract: This paper presents a distancebased discriminative framework for learning with
probability distributions. Instead of using kernel mean embeddings or generalized radial
basis kernels, we introduce embeddings based on dissimilarity of distributions to some
All 5 versions [PDF] openreview.net
Wasserstein AutoEncoders: Latent Dimensionality and Random Encoders
PK Rubenstein, B Schoelkopf, I Tolstikhin  2018  openreview.net
Paul Rubenstein∗, Bernhard Schölkopf, Ilya Tolstikhin Empirical Inference Max Planck Institute
for Intelligent Systems, Tübingen {paul.rubenstein,bs,ilya}@tuebingen.mpg.de … We study the
role of latent space dimensionality in Wasserstein autoencoders (WAEs). Through experimentation
MA Abdullah, A Pacchiano, M Draief  arXiv preprint arXiv:1802.03976, 2018  arxiv.org
Abstract: In this note we describe an application of Wasserstein distance to Reinforcement
Learning. The Wasserstein distance in question is between the distribution of mappings of
trajectories of a policy into some metric space, and some other fixed distribution (which may,
All 2 versions [PDF] arxiv.org
On the Latent Space of Wasserstein AutoEncoders
PK Rubenstein, B Schoelkopf, I Tolstikhin  arXiv preprint arXiv …, 2018  arxiv.org
Abstract: We study the role of latent space dimensionality in Wasserstein autoencoders
(WAEs). Through experimentation on synthetic and real datasets, we argue that random
encoders should be preferred over deterministic encoders. We highlight the potential of
All 2 versions [PDF] arxiv.org
Discrete Wasserstein Generative Adversarial Networks (DWGAN)
R Fathony, N Goela  2018  openreview.net
Abstract: Generating complex discrete distributions remains as one of the challenging
problems in machine learning. Existing techniques for generating complex distributions with
high degrees of freedom depend on standard generative models like Generative Adversarial
On Wasserstein isometries of probability measures on unit spheres
D Virosztek  arXiv preprint arXiv:1802.03305, 2018  arxiv.org
Abstract: We consider the space of all Borel probability measures on the unit sphere of a
Euclidean space endowed with the Wasserstein metric $ W_p $ for arbitrary $ p\geq 1. $ Our
goal is to describe the isometry group of this metric space. We make some progress in the
——————————————————
138 items + 41 (2011) + 39 (2012) + 54 (2013) + 53 (2014) + 60 (2015) + 65 (2016)
+ 155 (2017) + 33 (2018) = 651 items

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