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Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown.
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Patrick Billingsley · 1999
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Eustasio del Barrio, Evarist Gin\’e and Carlos Matr\’an · 1999
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Vladimir Levin · 1999
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Yossi Rubner, Carlo Tomasi and Leonidas. Guibas · 2000
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Paolo Albano · 2002
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C\’edric Villani · 2003
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“Asymptotics for L 2 {L}_{2} functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances”
Eustasio del Barrio, Evarist Gin\’e and Frederic Utzet · 2005
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Werner R\"omisch · 2006
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Aad. van der Vaart and Jon. Wellner · 2007
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Francois Bolley · 2008
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C\’edric Villani · 2008
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Najma Ahmad, Hwa Kim and Robert. McCann · 2011
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Steven Evans and Frederick Matsen · 2012
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“Sliced and Radon Wasserstein Barycenters of measures”
Nicolas Bonneel, Julien Rabin, Gabriel Peyr\’e and Hanspeter Pfister · 2015
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“On the rate of convergence in Wasserstein distance of the empirical measure”
Nicolas Fournier and Arnaud Guillin · 2015
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“Optimal Transport for Applied Mathematicians” 87
Filippo Santambrogio · 2015
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“High-dimensional statistics: A non-asymptotic viewpoint” 48
Martin. Wainwright · 2019
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“Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance”
Jonathan Weed and Francis Bach · 2019
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“Directional differentiability for supremum-type functionals: Statistical applications”
Javier C\’arcamo, Antonio Cuevas and Luis-Alberto Rodr\’guez · 2020
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“A Wasserstein-type distance in the space of Gaussian mixture models”
Julie Delon and Agnes Desolneux · 2020
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“Central limit theorems for general transportation costs”
Eustasio del Barrio, Alberto Gonz\’alez-Sanz and Jean-Michel Loubes · 2021
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“Mathematical foundations of infinite-dimensional statistical models”
Evarist Gin\’e and Richard Nickl · 2016
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“A weighted approximation approach to the study of the empirical Wasserstein distance”
David. Mason · 2016
Cited alongside, same era.
“The intrinsic dynamics of optimal transport”
Robert. McCann and Ludovic Rifford · 2016
Cited alongside, same era.
“Wasserstein generative adversarial networks”
Martin Arjovsky, Soumith Chintala and L\’eon Bottou · 2017
Cited alongside, same era.
“Monge–Kantorovich depth, quantiles, ranks and signs”
Victor Chernozhukov, Alfred Galichon, Marc Hallin and Marc Henry · 2017
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“Minimax distribution estimation in Wasserstein distance”
Shashank Singh and Barnab\’as P\’oczos · 2018
Cited alongside, same era.
“Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach”
Marc Hallin, Eustasio del Barrio, Juan Cuesta-Albertos and Carlos Matr\’an · 2021
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“Multivariate goodness-of-fit tests based on Wasserstein distance”
Marc Hallin, Gilles Mordant and Johan Segers · 2021
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“Two-sided Wasserstein Procrustes analysis”
Kun Jin, Chaoyue Liu and Cathy Xia · 2021
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“Central limit theorem over non-linear functionals of empirical measures with applications to the mean-field fluctuation of interacting diffusions”
Benjamin Jourdain and Alvin Tse · 2021
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“Sharp convergence rates for empirical optimal transport with smooth costs”
Tudor Manole and Jonathan Niles-Weed · 2021
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“Transport dependency: Optimal transport based dependency measures”
Thomas Nies, Thomas Staudt and Axel Munk · 2021
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“Colocalization for super-resolution microscopy via optimal transport”
Carla Tameling et al · 2021
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“An optimal transport approach to causal inference”
William Torous, Florian Gunsilius and Philippe Rigollet · 2021
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“The sketched Wasserstein distance for mixture distributions”
Xin Bing, Florentina Bunea and Jonathan Niles-Weed · 2022
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“Central limit theorems for semidiscrete Wasserstein distances”
Eustasio del Barrio, Alberto Gonz\’alez-Sanz and Jean-Michel Loubes · 2022
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“Statistical inference with regularized optimal transport”
Ziv Goldfeld, Kengo Kato, Gabriel Rioux and Ritwik Sadhu · 2022
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“A unifying approach to distributional limits for empirical optimal transport”
Shayan Hundrieser, Marcel Klatt, Thomas Staudt and Axel Munk · 2022
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“Empirical optimal transport between different measures adapts to lower complexity”
Shayan Hundrieser, Thomas Staudt and Axel Munk · 2022
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“Limit Laws for Empirical Optimal Solutions in Stochastic Linear Programs”
Marcel Klatt, Axel Munk and Yoav Zemel · 2022
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“Minimax confidence intervals for the sliced Wasserstein distance”
Tudor Manole, Sivaraman Balakrishnan and Larry Wasserman · 2022
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“Measuring dependence between random vectors via optimal transport”
Gilles Mordant and Johan Segers · 2022
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“On the uniqueness of Kantorovich potentials”
Thomas Staudt, Shayan Hundrieser and Axel Munk · 2022
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“Distribution of distances based object matching: asymptotic inference”
Christoph Weitkamp, Katharina Proksch, Carla Tameling and Axel Munk · 2022
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“Measuring association with Wasserstein distances”
Johannes.W. Wiesel · 2022
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“Distributional convergence of the sliced Wasserstein process”
Jiaqi Xi and Jonathan Niles-Weed · 2022
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Xianliang Xu and Zhongyi Huang · 2022
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