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We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver.
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Maurice Fréchet · 1948
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Leonid Nisonovich Vaserstein · 1969
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Vladimir Mikhailovich Zolotarev · 1976
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Central limit theorems for the Wasserstein distance between the empirical and the true distributions
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The linpack benchmark: past, present and future
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Siegfried Graf and Harald Luschgy · 2007
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Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
Ian L Dryden, Alexey Koloydenko, and Diwei Zhou · 2009
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Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric Lie group actions
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A multiscale approach to optimal transport
Quentin Mérigot · 2011
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The phylogenetic Kantorovich–Rubinstein metric for environmental sequence samples
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A sharp estimate of the binomial mean absolute deviation with applications
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Sinkhorn distances: Lightspeed computation of optimal transport
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Brendan Pass · 2013
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On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
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Fast computation of Wasserstein barycenters
Marco Cuturi and Arnaud Doucet · 2014
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Decentralize and randomize: Faster algorithm for Wasserstein barycenters
Pavel Dvurechenskii, Darina Dvinskikh, Alexander Gasnikov, Cesar Uribe, and Angelia Nedich · 2018
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Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn’s algorithm
Pavel Dvurechensky, Alexander Gasnikov, and Alexey Kroshnin · 2018
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Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning
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Inference for empirical Wasserstein distances on finite spaces
Max Sommerfeld and Axel Munk · 2018
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A fixed-point approach to barycenters in Wasserstein space
Pedro C Álvarez-Esteban, E Del Barrio, JA Cuesta-Albertos, and C Matrán · 2016
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Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
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Computational optimal transport: With applications to data science
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Stabilized sparse scaling algorithms for entropy regularized transport problems
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Optimal transport: Fast probabilistic approximation with exact solvers
Max Sommerfeld, Jörn Schrieber, Yoav Zemel, and Axel Munk · 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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Fréchet means and Procrustes analysis in Wsserstein space
Yoav Zemel and Victor M Panaretos · 2019
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Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics
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