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Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems.
Lebesgue spaces of differentiable functions and distributions
Alberto P Calderón · 1961
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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Information-type measures of difference of probability distributions and indirect observation
Imre Csiszár · 1967
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The speed of mean Glivenko-Cantelli convergence
Richard M. Dudley · 1969
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On the convergence of Halley’s method
Georg Alefeld · 1981
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Kantorovich–Rubinstein norm and its application in the theory of Lipschitz spaces
Leonid G Hanin · 1992
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Entropic proximal mappings with applications to nonlinear programming
Marc Teboulle · 1992
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On the Lambert-W function
Robert M Corless, Gaston H Gonnet, David EG Hare, David J Jeffrey, and Donald E Knuth · 1996
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A multivariate Faa di Bruno formula with applications
Gregory M. Constantine and Thomas H. Savits · 1996
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An extension of the Kantorovich norm
Leonid G Hanin · 1999
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Three-dimensional scene flow
Sundar Vedula, Simon Baker, Peter Rander, Robert Collins, and Takeo Kanade · 1999
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Convergence of a block coordinate descent method for nondifferentiable minimization
Paul Tseng · 2001
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Rademacher and Gaussian complexities: Risk bounds and structural results
Peter L Bartlett and Shahar Mendelson · 2002
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A kernel method for the two-sample-problem
Arthur Gretton, Karsten Borgwardt, Malte Rasch, Bernhard Schölkopf, and Alex Smola · 2006
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A guide to numpy, 2006
Travis Oliphant · 2006
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Matplotlib: A 2D graphics environment
J. D. Hunter · 2007
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Variational analysis
R Tyrrell Rockafellar and Roger J-B Wets · 2009
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The optimal partial transport problem
Alessio Figalli · 2010
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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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Nonlinear Perron-Frobenius Theory
Bas Lemmens and Roger Nussbaum · 2012
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Moreau’s decomposition in Banach spaces
Patrick L Combettes and Noli N Reyes · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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A symmetry preserving algorithm for matrix scaling
Philip A Knight, Daniel Ruiz, and Bora UCcar · 2014
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Unbalanced optimal transport: geometry and Kantorovich formulation
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and FranCcois-Xavier Vialard · 2015
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Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures
Matthias Liero, Alexander Mielke, and Giuseppe Savaré · 2015
Improving GANs using optimal transport
Tim Salimans, Han Zhang, Alec Radford, and Dimitris Metaxas · 2018
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Scalable unbalanced optimal transport using generative adversarial networks
Karren D Yang and Caroline Uhler · 2018
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Sparse optimization on measures with over-parameterized gradient descent
Lenaic Chizat · 2019
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Interpolating between optimal transport and MMD using Sinkhorn divergences
Jean Feydy, Thibault Séjourné, FranCcois-Xavier Vialard, Shun-ichi Amari, Alain Trouvé, and Gabriel Peyré · 2019
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Sample complexity of Sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2019
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Object scene flow for autonomous vehicles
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Optimal Transport for applied mathematicians
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A new optimal transport distance on the space of finite Radon measures
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FlowNet3D: Learning scene flow in 3D point clouds
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Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
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Global convergence of neuron birth-death dynamics
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Faster Wasserstein distance estimation with the Sinkhorn divergence
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Accurate point cloud registration with robust optimal transport
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