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In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent.
Reaching a consensus
Morris H. DeGroot · 1974
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On a formula for the L 2 L^{2} Wasserstein metric between measures on Euclidean and Hilbert spaces
Matthias Gelbrich · 1990
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On a generalization of cyclic monotonicity and distances among random vectors
Martin Knott and Cyril S. Smith · 1994
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A Course in Probability Theory
Kai Lai Chung · 2001
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On the n n -coupling problem
Ludger Rüschendorf and Ludger Uckelmann · 2002
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Topics in Optimal Transportation , volume 58 of Graduate Studies in Mathematics
Cédric Villani · 2003
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Gradient Flows: In Metric Spaces and in the Space of Probability Measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2005
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Towards a coherent statistical framework for dense deformable template estimation
Stéphanie Allassonnière, Yali Amit, and Alain Trouvé · 2007
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Quantitative concentration inequalities for empirical measures on non-compact spaces
François Bolley, Arnaud Guillin, and Cédric Villani · 2007
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Ambiguity in portfolio selection
Georg Pflug and David Wozabal · 2007
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Optimal Transport: Old and New , volume 338
Cédric Villani · 2009
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Distributionally robust optimization under moment uncertainty with application to data-driven problems
Erick Delage and Yinyu Ye · 2010
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Distributionally robust optimization and its tractable approximations
Joel Goh and Melvyn Sim · 2010
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Barycenters in the Wasserstein space
Martial Agueh and Guillaume Carlier · 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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Statistical models for deformable templates in image and shape analysis
Stéphanie Allassonnière, Jérémie Bigot, Joan Alexis Glaunès, Florian Maire, and Frédéric J.P. Richard · 2013
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Robust solutions of optimization problems affected by uncertain probabilities
Aharon Ben-Tal, Dick Den Hertog, Anja De Waegenaere, Bertrand Melenberg, and Gijs Rennen · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Information fusion via the Wasserstein barycenter in the space of probability measures: Direct fusion of empirical measures and Gaussian fusion with unknown correlation
Adrian N. Bishop · 2014
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Fast computation of Wasserstein barycenters
Marco Cuturi and Arnaud Doucet · 2014
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Distributionally robust convex optimization
Wolfram Wiesemann, Daniel Kuhn, and Melvyn Sim · 2014
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Distribution’s template estimate with Wasserstein metrics
Emmanuel Boissard, Thibaut Le Gouic, and Jean-Michel Loubes · 2015
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Sliced and Radon Wasserstein barycenters of measures
Nicolas Bonneel, Julien Rabin, Gabriel Peyré, and Hanspeter Pfister · 2015
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Numerical methods for matching for teams and Wasserstein barycenters
Guillaume Carlier, Adam Oberman, and Edouard Oudet · 2015
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On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier and Arnaud Guillin · 2015
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Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling , volume 87 of Progress in Nonlinear Differential Equations and Their Applications
Filippo Santambrogio · 2015
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Distributionally robust logistic regression
Soroosh Shafieezadeh-Abadeh, Peyman Mohajerin Esfahani, and Daniel Kuhn · 2015
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A fixed-point approach to barycenters in Wasserstein space
Pedro C. Álvarez-Esteban, E. Del Barrio, J.A. Cuesta-Albertos, and C. Matrán · 2016
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Distributionally robust stochastic optimization with Wasserstein distance
Rui Gao and Anton J. Kleywegt · 2016
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Gromov-Wasserstein averaging of kernel and distance matrices
Gabriel Peyré, Marco Cuturi, and Justin Solomon · 2016
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Wasserstein distributionally robust optimization and variation regularization
Rui Gao, Xi Chen, and Anton J. Kleywegt · 2017
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Existence and consistency of Wasserstein barycenters
Thibaut Le Gouic and Jean-Michel Loubes · 2017
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Communication-efficient learning of deep networks from decentralized data
H. Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Agüera y Arcas · 2017
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On Wasserstein two-sample testing and related families of nonparametric tests
Aaditya Ramdas, Nicolás García Trillos, and Marco Cuturi · 2017
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Wide consensus aggregation in the Wasserstein space. Application to location-scatter families
Pedro C. Álvarez-Esteban, Eustasio del Barrio, Juan A. Cuesta-Albertos, and Carlos Matrán · 2018
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Bayesian learning with Wasserstein barycenters
Julio Backhoff-Veraguas, Joaquin Fontbona, Gonzalo Rios, and Felipe Tobar · 2018
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Data-driven robust optimization
Dimitris Bertsimas, Vishal Gupta, and Nathan Kallus · 2018
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Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
Jérémie Bigot and Thierry Klein · 2018
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Semidual regularized optimal transport
Marco Cuturi and Gabriel Peyré · 2018
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Decentralize and randomize: Faster algorithm for Wasserstein barycenters
Pavel Dvurechenskii, Darina Dvinskikh, Alexander Gasnikov, Cesar Uribe, and Angelia Nedich · 2018
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Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations
Peyman Mohajerin Esfahani and Daniel Kuhn · 2018
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Learning generative models with Sinkhorn divergences
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2018
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Does distributionally robust supervised learning give robust classifiers?
Weihua Hu, Gang Niu, Issei Sato, and Masashi Sugiyama · 2018
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A canonical barycenter via Wasserstein regularization
Young-Heon Kim and Brendan Pass · 2018
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Fréchet barycenters in the Monge-Kantorovich spaces
Entropic optimal transport: Geometry and large deviations
Espen Bernton, Promit Ghosal, and Marcel Nutz · 2021
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Network consensus in the Wasserstein metric space of probability measures
Adrian N. Bishop and Arnaud Doucet · 2021
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Sample out-of-sample inference based on Wasserstein distance
Jose Blanchet and Yang Kang · 2021
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Entropic-Wasserstein barycenters: PDE characterization, regularity, and CLT
Guillaume Carlier, Katharina Eichinger, and Alexey Kroshnin · 2021
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A novel notion of barycenter for probability distributions based on optimal weak mass transport
Elsa Cazelles, Felipe Tobar, and Joaquin Fontbona · 2021
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Boosting with multiple sources
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Alexey Kroshnin · 2018
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Generalizing point embeddings using the Wasserstein space of elliptical distributions
Boris Muzellec and Marco Cuturi · 2018
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Wasserstein dictionary learning: Optimal transport-based unsupervised nonlinear dictionary learning
Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel, Fred Ngole, David Coeurjolly, Marco Cuturi, Gabriel Peyré, and Jean-Luc Starck · 2018
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Wasserstein distributionally robust Kalman filtering
Soroosh Shafieezadeh-Abadeh, Viet Anh Nguyen, Daniel Kuhn, and Peyman Mohajerin Esfahani · 2018
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Scalable Bayes via barycenter in Wasserstein space
Sanvesh Srivastava, Cheng Li, and David B. Dunson · 2018
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On the Bures–Wasserstein distance between positive definite matrices
Rajendra Bhatia, Tanvi Jain, and Yongdo Lim · 2019
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Optimal uncertainty size in distributionally robust inverse covariance estimation
Jose Blanchet and Nian Si · 2019
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Corinna Cortes, Mehryar Mohri, Dmitry Storcheus, and Ananda Theertha Suresh · 2021
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Sampling from the Wasserstein barycenter
Chiheb Daaloul, Thibaut Le Gouic, Jacques Liandrat, and Magali Tournus · 2021
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Learning models with uniform performance via distributionally robust optimization
John C. Duchi and Hongseok Namkoong · 2021
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Statistics of robust optimization: A generalized empirical likelihood approach
John C. Duchi, Peter W. Glynn, and Hongseok Namkoong · 2021
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An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
Alessio Figalli and Federico Glaudo · 2021
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Barycenters for the Hellinger–Kantorovich distance over ℝ d \mathbb{R}^{d}
Gero Friesecke, Daniel Matthes, and Bernhard Schmitzer · 2021
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Stability of entropic optimal transport and Schrödinger bridges
Promit Ghosal, Marcel Nutz, and Espen Bernton · 2021
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Non-convex distributionally robust optimization: Non-asymptotic analysis
Jikai Jin, Bohang Zhang, Haiyang Wang, and Liwei Wang · 2021
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Advances and open problems in federated learning
Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G. L. D’Oliveira, Hubert Eichner, Salim El Rouayheb, David Evans, Josh Gardner, Zachary Garrett, Adrià Gascón, Badih Ghazi, Phillip B. Gibbons, Marco Gruteser, Zaid Harchaoui, Chaoyang He, Lie He, Zhouyuan Huo, Ben Hutchinson, Justin Hsu, Martin Jaggi, Tara Javidi, Gauri Joshi, Mikhail Khodak, Jakub Konecný, Aleksandra Korolova, Farinaz Koushanfar, Sanmi Koyejo, Tancrède Lepoint, Yang Liu, Prateek Mittal, Mehryar Mohri, Richard Nock, Ayfer Özgür, Rasmus Pagh, Hang Qi, Daniel Ramage, Ramesh Raskar, Mariana Raykova, Dawn Song, Weikang Song, Sebastian U. Stich, Ziteng Sun, Ananda Theertha Suresh, Florian Tramèr, Praneeth Vepakomma, Jianyu Wang, Li Xiong, Zheng Xu, Qiang Yang, Felix X. Yu, Han Yu, and Sen Zhao · 2021
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Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
Thibaut Le Gouic, Quentin Paris, Philippe Rigollet, and Austin J. Stromme · 2021
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Distributionally robust optimization with Markovian data
Mengmeng Li, Tobias Sutter, and Daniel Kuhn · 2021
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Entropy-regularized 2 2 -Wasserstein distance between Gaussian measures
Anton Mallasto, Augusto Gerolin, and Hà Quang Minh · 2021
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A theory of multiple-source adaptation with limited target labeled data
Yishay Mansour, Mehryar Mohri, Jae Ro, Ananda Theertha Suresh, and Ke Wu · 2021
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Introduction to Entropic Optimal Transport
Marcel Nutz · 2021
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Entropic optimal transport: Convergence of potentials
Marcel Nutz and Johannes Wiesel · 2021
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Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets
Jan Obłój and Johannes Wiesel · 2021
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Communication-efficient agnostic federated averaging
Jae Ro, Mingqing Chen, Rajiv Mathews, Mehryar Mohri, and Ananda Theertha Suresh · 2021
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Clustering, factor discovery and optimal transport
Hongkang Yang and Esteban G. Tabak · 2021
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Multiple-source adaptation theory and algorithms
Ningshan Zhang, Mehryar Mohri, and Judy Hoffman · 2021
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Mathematical foundations of robust and distributionally robust optimization
Jianzhe Zhen, Daniel Kuhn, and Wolfram Wiesemann · 2021
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Wasserstein barycenters are NP-hard to compute
Jason M. Altschuler and Enric Boix-Adserà · 2022
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Regularization for Wasserstein distributionally robust optimization
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Bootstrap robust prescriptive analytics
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Distributionally robust optimization via ball oracle acceleration
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Statistical inference with regularized optimal transport
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Learning distributionally robust models at scale via composite optimization
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Randomized Wasserstein barycenter computation: Resampling with statistical guarantees
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On the generalization of Wasserstein robust federated learning, 2022
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Entropic regularization of Wasserstein distance between infinite-dimensional Gaussian measures and Gaussian processes
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Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator
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Fast distributionally robust learning with variance reduced min-max optimization
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What do we mean by generalization in federated learning?
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