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Given a source and a target probability measure supported on $\mathbb{R}^d$, the Monge problem asks to find the most efficient way to map one distribution to the other.
Computational optimal transport
Gabriel Peyré and Marco Cuturi · 1935
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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Monotone operators and the proximal point algorithm
R Tyrrell Rockafellar · 1976
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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The geometry of optimal transportation
Wilfrid Gangbo and Robert J McCann · 1996
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The geometry of algorithms with orthogonality constraints
Alan Edelman, Tomás A Arias, and Steven T Smith · 1998
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Existence and stability results in the l1 theory of optimal transportation
Luigi Ambrosio and Aldo Pratelli · 2003
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Regularity of potential functions of the optimal transportation problem
Xi-Nan Ma, Neil S Trudinger, and Xu-Jia Wang · 2005
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Regularization and variable selection via the elastic net
Hui Zou and Trevor Hastie · 2005
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Amir Beck and Marc Teboulle · 2009
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Optimal transport: old and new , volume 338
Cédric Villani et al · 2009
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Mass transportation on sub-riemannian manifolds
Alessio Figalli and Ludovic Rifford · 2010
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On the ma–trudinger–wang curvature on surfaces
Alessio Figalli, Ludovic Rifford, and Cédric Villani · 2010
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Convex analysis and monotone operator theory in Hilbert spaces , volume 408
Heinz H Bauschke and Patrick L Combettes · 2011
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Projection-like retractions on matrix manifolds
P-A Absil and Jérôme Malick · 2012
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New examples satisfying ma–trudinger–wang conditions
Paul WY Lee and Jiayong Li · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Matrix computations
Gene H Golub and Charles F Van Loan · 2013
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Proximal algorithms
Neal Parikh, Stephen Boyd, et al · 2014
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Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
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Input Convex Neural Networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
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Unbalanced optimal transport: Dynamic and kantorovich formulations
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard · 2018
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Optimal entropy-transport problems and a new hellinger–kantorovich distance between positive measures
Matthias Liero, Alexander Mielke, and Giuseppe Savaré · 2018
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Scalable unbalanced optimal transport using generative adversarial networks
Karren D Yang and Caroline Uhler · 2018
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Interpolating between optimal transport and mmd using sinkhorn divergences
On projection robust optimal transport: Sample complexity and model misspecification
Tianyi Lin, Zeyu Zheng, Elynn Chen, Marco Cuturi, and Michael I Jordan · 2021
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Plugin estimation of smooth optimal transport maps
Tudor Manole, Sivaraman Balakrishnan, Jonathan Niles-Weed, and Larry Wasserman · 2021
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Near-optimal estimation of smooth transport maps with kernel sums-of-squares
Boris Muzellec, Adrien Vacher, Francis Bach, François-Xavier Vialard, and Alessandro Rudi · 2021
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Entropic estimation of optimal transport maps
Aram-Alexandre Pooladian and Jonathan Niles-Weed · 2021
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Optimal transport tools (ott): A jax toolbox for all things wasserstein
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Jean Feydy, Thibault Séjourné, François-Xavier Vialard, Shun-ichi Amari, Alain Trouvé, and Gabriel Peyré · 2019
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Wasserstein-2 generative networks
Alexander Korotin, Vage Egiazarian, Arip Asadulaev, Alexander Safin, and Evgeny Burnaev · 2019
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Subspace robust wasserstein distances
François-Pierre Paty and Marco Cuturi · 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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Projection robust wasserstein distance and riemannian optimization
Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, and Michael Jordan · 2020
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Optimal transport mapping via input convex neural networks
Ashok Makkuva, Amirhossein Taghvaei, Sewoong Oh, and Jason Lee · 2020
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Massively multiplex chemical transcriptomics at single-cell resolution
Sanjay R Srivatsan, José L McFaline-Figueroa, Vijay Ramani, Lauren Saunders, Junyue Cao, Jonathan Packer, Hannah A Pliner, Dana L Jackson, Riza M Daza, Lena Christiansen, et al · 2020
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Marco Cuturi, Laetitia Meng-Papaxanthos, Yingtao Tian, Charlotte Bunne, Geoff Davis, and Olivier Teboul · 2022
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An improved central limit theorem and fast convergence rates for entropic transportation costs
Eustasio del Barrio, Alberto Gonzalez-Sanz, Jean-Michel Loubes, and Jonathan Niles-Weed · 2022
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Optimal transport map estimation in general function spaces
Vincent Divol, Jonathan Niles-Weed, and Aram-Alexandre Pooladian · 2022
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Limit theorems for entropic optimal transport maps and the sinkhorn divergence
Ziv Goldfeld, Kengo Kato, Gabriel Rioux, and Ritwik Sadhu · 2022
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Rectified flow: A marginal preserving approach to optimal transport
Qiang Liu · 2022
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Estimation of wasserstein distances in the spiked transport model
Jonathan Niles-Weed and Philippe Rigollet · 2022
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On the sample complexity of entropic optimal transport
Philippe Rigollet and Austin J Stromme · 2022
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An introduction to optimization on smooth manifolds
Nicolas Boumal · 2023
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Learning single-cell perturbation responses using neural optimal transport
Charlotte Bunne, Stefan G. Stark, Gabriele Gut, Jacobo Sarabia del Castillo, Mitch Levesque, Kjong-Van Lehmann, Lucas Pelkmans, Andreas Krause, and Gunnar Rätsch · 2023
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Generative modeling through the semi-dual formulation of unbalanced optimal transport
Jaemoo Choi, Jaewoong Choi, and Myungjoo Kang · 2023
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Monge, bregman and occam: Interpretable optimal transport in high-dimensions with feature-sparse maps
Marco Cuturi, Michal Klein, and Pierre Ablin · 2023
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Computational optimal transport and filtering on riemannian manifolds
Daniel Grange, Mohammad Al-Jarrah, Ricardo Baptista, Amirhossein Taghvaei, Tryphon T Georgiou, Sean Phillips, and Allen Tannenbaum · 2023
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The elements of differentiable programming
Mathieu Blondel and Vincent Roulet · 2024
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Unbalancedness in neural monge maps improves unpaired domain translation
Luca Eyring, Dominik Klein, Théo Uscidda, Giovanni Palla, Niki Kilbertus, Zeynep Akata, and Fabian J Theis · 2024
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