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Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects.
The hungarian method for the assignment problem
Harold W Kuhn · 1955
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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On minimum kantorovich distance estimators
Federico Bassetti, Antonella Bodini, and Eugenio Regazzini · 2006
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On the translocation of masses
Leonid V Kantorovich · 2006
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Optimal transport: old and new , volume 338
Cédric Villani · 2008
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Barycenters in the wasserstein space
Martial Agueh and Guillaume Carlier · 2011
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Sublinear optimization for machine learning
Kenneth L. Clarkson, Elad Hazan, and David P Woodruff · 2012
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A kernel two-sample test
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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Ohad Shamir and Tong Zhang · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Fast computation of wasserstein barycenters
Marco Cuturi and Arnaud Doucet · 2014
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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Justin Solomon, Fernando De Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas · 2015
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Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
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Near-linear time approximation algorithms for optimal transport via sinkhorn iteration
Jason Altschuler, Jonathan Niles-Weed, and Philippe Rigollet · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
Cited alongside, same era.
Optimal transport for diffeomorphic registration
Jean Feydy, Benjamin Charlier, François-Xavier Vialard, and Gabriel Peyré · 2017
Cited alongside, same era.
Learning generative models with sinkhorn divergences
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2017
Cited alongside, same era.
Parallel streaming wasserstein barycenters
Matthew Staib, Sebastian Claici, Justin M Solomon, and Stefanie Jegelka · 2017
Cited alongside, same era.
Structured optimal transport
David Alvarez-Melis, Tommi Jaakkola, and Stefanie Jegelka · 2018
Cited alongside, same era.
Stochastic wasserstein barycenters
Sebastian Claici, Edward Chien, and Justin Solomon · 2018
Cited alongside, same era.
Maximum mean discrepancy gradient flow
Michael Arbel, Anna Korba, Adil Salim, and Arthur Gretton · 2019
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Statistical windows in testing for the initial distribution of a reversible markov chain
Quentin Berthet and Varun Kanade · 2019
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Private learning and regularized optimal transport
Etienne Boursier and Vianney Perchet · 2019
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optimalflow: Optimal-transport approach to flow cytometry gating and population matching
Eustasio del Barrio, Hristo Inouzhe, Jean-Michel Loubes, Carlos Matrán, and Agustín Mayo-Íscar · 2019
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Interpolating between optimal transport and mmd using sinkhorn divergences
Jean Feydy, Thibault Séjourné, François-Xavier Vialard, Shun-ichi Amari, Alain Trouve, and Gabriel Peyré · 2019
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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
Cited alongside, same era.
Wasserstein discriminant analysis
Rémi Flamary, Marco Cuturi, Nicolas Courty, and Alain Rakotomamonjy · 2018
Cited alongside, same era.
Dynamical optimal transport on discrete surfaces
Hugo Lavenant, Sebastian Claici, Edward Chien, and Justin Solomon · 2018
Cited alongside, same era.
Differential properties of sinkhorn approximation for learning with wasserstein distance
Giulia Luise, Alessandro Rudi, Massimiliano Pontil, and Carlo Ciliberto · 2018
Cited alongside, same era.
Entropic optimal transport is maximum-likelihood deconvolution
Philippe Rigollet and Jonathan Weed · 2018
Cited alongside, same era.
Fréchet means and procrustes analysis in wasserstein space
Yoav Zemel, Victor M Panaretos, et al · 2018
Cited alongside, same era.
Sample complexity of sinkhorn divergences
Aude Genevay, Lénaïc Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2019
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Obtaining fairness using optimal transport theory
Paula Gordaliza, Eustasio Del Barrio, Gamboa Fabrice, and Jean-Michel Loubes · 2019
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Unsupervised alignment of embeddings with wasserstein procrustes
Edouard Grave, Armand Joulin, and Quentin Berthet · 2019
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Sinkhorn barycenters with free support via frank-wolfe algorithm
Giulia Luise, Saverio Salzo, Massimiliano Pontil, and Carlo Ciliberto · 2019
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Computational optimal transport
Gabriel Peyré, Marco Cuturi, et al · 2019
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Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming
Geoffrey Schiebinger, Jian Shu, Marcin Tabaka, Brian Cleary, Vidya Subramanian, Aryeh Solomon, Joshua Gould, Siyan Liu, Stacie Lin, Peter Berube, et al · 2019
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Nonparametric density estimation & convergence rates for gans under besov ipm losses
Ananya Uppal, Shashank Singh, and Barnabas Poczos · 2019
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in wasserstein distance
Jonathan Weed, Francis Bach, et al · 2019
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