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Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning.
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On the surprising behavior of distance metrics in high dimensional space
Charu C. Aggarwal, Alexander Hinneburg, and Daniel A. Keim · 2001
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On the euclidean distance of images
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Measure Theory , volume 1
Vladimir Bogachev · 2007
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Probability Theory: A Comprehensive Course
Achim Klenke · 2008
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Displacement interpolation using lagrangian mass transport
Nicolas Bonneel, Michiel van de Panne, Sylvain Paris, and Wolfgang Heidrich · 2011
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Gromov–wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
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Scikit-learn: Machine learning in python
Fabian Pedregosa et al · 2011
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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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Lecture 6.5-rmsprop: Divide the gradient by a running average of its recent magnitude
Tijmen Tieleman and Geoffrey Hinton · 2012
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Unidimensional and Evolution Methods for Optimal Transportation
Nicolas Bonnotte · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Regularized discrete optimal transport
Sira Ferradans, Nicolas Papadakis, Julien Rabin, Gabriel Peyré, and Jean-François Aujol · 2013
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Accelerating stochastic gradient descent using predictive variance reduction
Rie Johnson and Tong Zhang · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Auto-encoding variational bayes
Diederik P. Kingma and Max Welling · 2014
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Learning with a wasserstein loss
Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya, and Tomaso A Poggio · 2015
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Adam: A method for stochastic optimization
Diederik P. Kingma and Jimmy Ba · 2015
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Deep learning face attributes in the wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Sgd algorithms based on incomplete u-statistics: Large-scale minimization of empirical risk
Guillaume Papa, Stéphan Clémençon, and Aurélien Bellet · 2015
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Entropic approximation of wasserstein gradient flows
G. Peyré · 2015
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Optimal transport for applied mathematicians, 2015
Filippo Santambrogio · 2015
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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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Scaling-up empirical risk minimization: Optimization of incomplete u u -statistics
Stephan Clémençon, Igor Colin, and Aurélien Bellet · 2016
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Optimal transport for domain adaptation
N. Courty, R. Flamary, D. Tuia, and A. Rakotomamonjy · 2016
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Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
Sliced wasserstein distance for learning gaussian mixture models
Soheil Kolouri, Gustavo Kunde Rohde, and Heiko Hoffmann · 2018
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Analysis of nonsmooth stochastic approximation: the differential inclusion approach
Szymon Majewski, Błażej Miasojedow, and Eric Moulines · 2018
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Improving GANs using optimal transport
Tim Salimans, Han Zhang, Alec Radford, and Dimitris Metaxas · 2018
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Large scale optimal transport and mapping estimation
Vivien Seguy, Bharath Bhushan Damodaran, Remi Flamary, Nicolas Courty, Antoine Rolet, and Mathieu Blondel · 2018
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Wasserstein auto-encoders
Ilya Tolstikhin, Olivier Bousquet, Sylvain Gelly, and Bernhard Schoelkopf · 2018
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Towards optimal transport with global invariances
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Sliced wasserstein kernels for probability distributions
Soheil Kolouri, Yang Zou, and Gustavo K Rohde · 2016
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Gromov-wasserstein averaging of kernel and distance matrices
Gabriel Peyré, Marco Cuturi, and Justin Solomon · 2016
Cited alongside, same era.
Entropic metric alignment for correspondence problems
Justin Solomon, Gabriel Peyré, Vladimir G. Kim, and Suvrit Sra · 2016
Cited alongside, same era.
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.
The cramer distance as a solution to biased wasserstein gradients
Marc G. Bellemare, Ivo Danihelka, Will Dabney, Shakir Mohamed, Balaji Lakshminarayanan, Stephan Hoyer, and Rémi Munos · 2017
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David Alvarez-Melis, Stefanie Jegelka, and Tommi S. Jaakkola · 2019
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On parameter estimation with the wasserstein distance
Espen Bernton, Pierre E Jacob, Mathieu Gerber, and Christian P Robert · 2019
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Learning generative models across incomparable spaces
Charlotte Bunne, David Alvarez-Melis, Andreas Krause, and Stefanie Jegelka · 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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Entropy-Regularized Optimal Transport for Machine Learning
Aude Genevay · 2019
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Sample complexity of sinkhorn divergences
Aude Genevay, Lénaïc Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2019
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U-statistics : theory and practice / a. j. lee
A J Lee · 2019
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A short note on concentration inequalities for random vectors with subgaussian norm
Chi Jin, Praneeth Netrapalli, R. Ge, Sham M. Kakade, and Michael I. Jordan · 2019
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Tree-sliced variants of wasserstein distances
Tam Le, Makoto Yamada, Kenji Fukumizu, and Marco Cuturi · 2019
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Hierarchical optimal transport for multimodal distribution alignment
John Lee, Max Dabagia, Eva Dyer, and Christopher Rozell · 2019
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Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
Antoine Liutkus, Umut Simsekli, Szymon Majewski, Alain Durmus, and Fabian-Robert Stöter · 2019
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Sinkhorn autoencoders
Giorgio Patrini, Marcello Carioni, Patrick Forré, Samarth Bhargav, Max Welling, Rianne van den Berg, Tim Genewein, and Frank Nielsen · 2019
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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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Sliced gromov-wasserstein
Titouan Vayer, Rémi Flamary, Nicolas Courty, Romain Tavenard, and Laetitia Chapel · 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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Wasserstein adversarial examples via projected Sinkhorn iterations
Eric Wong, Frank Schmidt, and Zico Kolter · 2019
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Sliced wasserstein generative models
Jiqing Wu, Zhiwu Huang, Dinesh Acharya, Wen Li, Janine Thoma, Danda Pani Paudel, and Luc Van Gool · 2019
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Stochastic optimization for regularized wasserstein estimators
Marin Ballu, Quentin Berthet, and Francis R. Bach · 2020
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Stochastic subgradient method converges on tame functions
Damek Davis, Dmitriy Drusvyatskiy, Sham Kakade, and Jason D Lee · 2020
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Learning with minibatch wasserstein: asymptotic and gradient properties
Kilian Fatras, Younes Zine, Rémi Flamary, Rémi Gribonval, and Nicolas Courty · 2020
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Convergence of a stochastic gradient method with momentum for nonsmooth nonconvex optimization
Vien V Mai and Mikael Johansson · 2020
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