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Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map $T$ between two probability distributions $P$ and $Q$ over $\mathbb{R}^d$ under certain regularity conditions.
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Luis A. Caffarelli · 1996
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Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, and Alexander Tsybakov · 1998
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Axel Munk and Claudia Czado · 1998
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Stéphane Mallat · 1999
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Vyacheslav S. Rychkov · 1999
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Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal · 2001
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Olivier Bousquet · 2002
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Mohammad Ghomi · 2002
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Sara van de Geer · 2002
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Cédric Villani · 2003
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Theory of Function Spaces III
Hans Triebel · 2006
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Joseph E Yukich · 2006
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Concentration Inequalities and Model Selection: Ecole d’Eté de Probabilités de Saint-Flour XXXIII - 2003
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Aad W. van der Vaart and Jon A. Wellner Wellner · 2007
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Introduction to nonparametric estimation
Alexandre B. Tsybakov · 2009
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Cédric Villani · 2009
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Lawrence C. Evans · 2010
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Holger Rauhut · 2010
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Claire Caillerie, Frédéric Chazal, Jérôme Dedecker, and Bertrand Michel · 2011
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Best constants in Poincaré inequalities for convex domains
Luca Esposito, Carlo Nitsch, and Cristina Trombetti · 2011
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On Hölder continuity-in-time of the optimal transport map towards measures along a curve
Nicola Gigli · 2011
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Oracle inequalities in empirical risk minimization and sparse recovery problems. École d’Été de Probabilités de Saint-Flour XXXVIII-2008
Vladimir Koltchinskii · 2011
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Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
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Guillermo Canas and Lorenzo Rosasco · 2012
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David Alvarez-Melis, Tommi S. Jaakkola, and Stefanie Jegelka · 2018
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Wasserstein coresets for lipschitz costs
Sebastian Claici and Justin Solomon · 2018
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Geodesic PCA versus log-pca of histograms in the wasserstein space
Elsa Cazelles, Vivien Seguy, Jérémie Bigot, Marco Cuturi, and Nicolas Papadakis · 2018
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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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Kevin P Murphy · 2012
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Marco Cuturi · 2013
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Jérôme Dedecker and Bertrand Michel · 2013
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Estimation of an embedding constant on Lipschitz domains using extension operators
Kazuaki Tanaka, Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, and Shin’ichi Oishi · 2013
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Domain adaptation with regularized optimal transport
Nicolas Courty, Rémi Flamary, and Devis Tuia · 2014
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Michel Talagrand · 2014
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Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel, Fred Maurice Ngolè Mboula, David Coeurjolly, Marco Cuturi, Gabriel Peyré, and Jean-Luc Starck · 2018
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High-Dimensional Probability: An Introduction with Applications in Data Science
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Autoencoder and optimal transport to infer single-cell trajectories of biological processes
Karren D Yang, Karthik Damodaran, Saradha Venkatchalapathy, Ali C Soylemezoglu, GV Shivashankar, and Caroline Uhler · 2018
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