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Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples and where the goal is to find the closest map to the ground truth OT map, unknown in practical settings.
Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Finitely generated cumulants
Giovanni Pistone and Henry P Wynn · 1999
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Monotonicity properties of optimal transportation
Luis A Caffarelli · 2000
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Hedonic price equilibria, stable matching, and optimal transport: Equivalence, topology, and uniqueness
Pierre-André Chiappori, Robert J. McCann, and Lars P. Nesheim · 2010
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Non-parametric estimation of convex bodies and convex polytopes
Victor-Emmanuel Brunel · 2014
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Decaf: A deep convolutional activation feature for generic visual recognition
Jeff Donahue, Yangqing Jia, Oriol Vinyals, Judy Hoffman, Ning Zhang, Eric Tzeng, and Trevor Darrell · 2014
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Adaptive color transfer with relaxed optimal transport
Julien Rabin, Sira Ferradans, and Nicolas Papadakis · 2014
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Optimal transport methods in economics
Alfred Galichon · 2016
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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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Input convex neural networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
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Optimal transport for domain adaptation
Nicolas Courty, Rémi Flamary, Devis Tuia, and Alain Rakotomamonjy · 2017
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Optimal transport for diffeomorphic registration
Jean Feydy, Benjamin Charlier, François-Xavier Vialard, and Gabriel Peyré · 2017
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Gromov-wasserstein alignment of word embedding spaces
David Alvarez-Melis and Tommi Jaakkola · 2018
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The Sinkhorn algorithm, parabolic optimal transport and geometric monge-amp \ \backslash ere equations
Robert J Berman · 2018
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Large-scale optimal transport and mapping estimation
Vivien. Seguy, Bharath B. Damodaran, Remi Flamary, Nicolas Courty, Antoine Rolet, and Mathieu Blondel · 2018
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Spot: Sliced partial optimal transport
Nicolas Bonneel and David Coeurjolly · 2019
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Improving sequence-to-sequence learning via optimal transport
Liqun Chen, Yizhe Zhang, Ruiyi Zhang, Chenyang Tao, Zhe Gan, Haichao Zhang, Bai Li, Dinghan Shen, Changyou Chen, and Lawrence Carin · 2019
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Optimal transport for multi-source domain adaptation under target shift
Ievgen Redko, Nicolas Courty, Rémi Flamary, and Devis Tuia · 2019
Regularity as regularization: Smooth and strongly convex brenier potentials in optimal transport
François-Pierre Paty, Alexandre d’Aspremont, and Marco Cuturi · 2020
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Optimal transport driven cyclegan for unsupervised learning in inverse problems
Byeongsu Sim, Gyutaek Oh, Jeongsol Kim, Chanyong Jung, and Jong Chul Ye · 2020
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Trajectorynet: A dynamic optimal transport network for modeling cellular dynamics
Alexander Tong, Jessie Huang, Guy Wolf, David Van Dijk, and Smita Krishnaswamy · 2020
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Reliable weighted optimal transport for unsupervised domain adaptation
Renjun Xu, Pelen Liu, Liyan Wang, Chao Chen, and Jindong Wang · 2020
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Quantitative stability of optimal transport maps under variations of the target measure
Alex Delalande and Quentin Merigot · 2021
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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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Generalized self-concordant functions: a recipe for newton-type methods
Tianxiao Sun and Quoc Tran-Dinh · 2019
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2-wasserstein approximation via restricted convex potentials with application to improved training for gans
Amirhossein Taghvaei and Amin Jalali · 2019
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Log-sum-exp neural networks and posynomial models for convex and log-log-convex data
Giuseppe Carlo Calafiore, Stéphane Gaubert, and Corrado Possieri · 2020
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A fast approach to optimal transport: the back-and-forth method
M. Jacobs and F. Léger · 2020
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Optimal transport mapping via input convex neural networks
Ashok Makkuva, Amirhossein Taghvaei, Sewoong Oh, and Jason Lee · 2020
Cited alongside, same era.
Jan-Christian Hütter and Philippe Rigollet · 2021
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Do neural optimal transport solvers work? a continuous wasserstein-2 benchmark
Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Alexander Filippov, and Evgeny Burnaev · 2021
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Plugin estimation of smooth optimal transport maps, 2021
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, 2021
Boris Muzellec, Adrien Vacher, Francis Bach, François-Xavier Vialard, and Alessandro Rudi · 2021
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Entropic estimation of optimal transport maps, 2021
Aram-Alexandre Pooladian and Jonathan Niles-Weed · 2021
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Wasserstein gans work because they fail (to approximate the wasserstein distance)
Jan Stanczuk, Christian Etmann, Lisa Maria Kreusser, and Carola-Bibiane Schönlieb · 2021
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A dimension-free computational upper-bound for smooth optimal transport estimation
Adrien Vacher, Boris Muzellec, Alessandro Rudi, Francis Bach, and Francois-Xavier Vialard · 2021
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