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The Wasserstein distance has become increasingly important in machine learning and deep learning.
The speed of mean Glivenko-Cantelli convergence
Richard Mansfield Dudley · 1969
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Optimal transport: old and new
Cédric Villani · 2008
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Optimization algorithms on matrix manifolds
P-A Absil, Robert Mahony, and Rodolphe Sepulchre · 2009
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Adaptive subgradient methods for online learning and stochastic optimization
John Duchi, Elad Hazan, and Yoram Singer · 2011
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Wasserstein barycenter and its application to texture mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot · 2011
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Sliced and Radon Wasserstein barycenters of measures
Nicolas Bonneel, Julien Rabin, Gabriel Peyré, 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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Adam: A method for stochastic optimization
Diederik P. Kingma and Jimmy Lei Ba · 2015
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Convergence rates of parameter estimation for some weakly identifiable finite mixtures
Nhat Ho and XuanLong Nguyen · 2016
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Sliced Wasserstein kernels for probability distributions
Soheil Kolouri, Yang Zou, and Gustavo K Rohde · 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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A distributional perspective on reinforcement learning
Marc G Bellemare, Will Dabney, and Rémi Munos · 2017
Cited alongside, same era.
Bo Jiang, Shiqian Ma, Anthony Man-Cho So, and Shuzhong Zhang · 2017
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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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SGD without replacement: Sharper rates for general smooth convex functions
Dheeraj Nagaraj, Prateek Jain, and Praneeth Netrapalli · 2019
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Estimation of Wasserstein distances in the spiked transport model
Jonathan Niles-Weed and Philippe Rigollet · 2019
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Wasserstein dependency measure for representation learning
Sherjil Ozair, Corey Lynch, Yoshua Bengio, Aaron Van den Oord, Sergey Levine, and Pierre Sermanet · 2019
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Subspace robust Wasserstein distances
François-Pierre Paty and Marco Cuturi · 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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Advances in pre-training distributed word representations
Tomáš Mikolov, Édouard Grave, Piotr Bojanowski, Christian Puhrsch, and Armand Joulin · 2018
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Global rates of convergence for nonconvex optimization on manifolds
Nicolas Boumal, Pierre-Antoine Absil, and Coralia Cartis · 2019
Cited alongside, same era.
Max-sliced Wasserstein distance and its use for GANs
Ishan Deshpande, Yuan-Ting Hu, Ruoyu Sun, Ayis Pyrros, Nasir Siddiqui, Sanmi Koyejo, Zhizhen Zhao, David Forsyth, and Alexander G Schwing · 2019
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Riemannian adaptive stochastic gradient algorithms on matrix manifolds
Hiroyuki Kasai, Pratik Jawanpuria, and Bamdev Mishra · 2019
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Generalized sliced Wasserstein distances
Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, and Gustavo Rohde · 2019
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On efficient optimal transport: An analysis of greedy and accelerated mirror descent algorithms
Tianyi Lin, Nhat Ho, and Michael Jordan · 2019
Cited alongside, same era.
Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, and Tong Zhang · 2020
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Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces
Jing Lei · 2020
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Projection robust Wasserstein distance and Riemannian optimization
Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, and Michael Jordan · 2020
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Projection robust Wasserstein distance and Riemannian optimization
Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, and Michael Jordan · 2020
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On projection robust optimal transport: Sample complexity and model misspecification
Tianyi Lin, Zeyu Zheng, Elynn Y Chen, Marco Cuturi, and Michael I Jordan · 2020
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