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Wasserstein barycenters define averages of probability measures in a geometrically meaningful way.
On the convergence of sample probability distributions
V. S. Varadarajan · 1958
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On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
Herm Jan Brascamp and Elliott H. Lieb · 1976
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Principles of risk minimization for learning theory
V. Vapnik · 1991
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Weak Convergence and Empirical Processes: With Applications to Statistics
A.W. van der Vaart and J.A. Wellner · 1996
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A convexity principle for interacting gases
Robert J. McCann · 1997
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Convex Analysis and Variational Problems
Ivar Ekeland and Roger Témam · 1999
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Probability measures on metric spaces of nonpositive curvature
Karl-Theodor Sturm · 2003
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Optimal transport: old and new
Cédric Villani · 2008
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Learnability, stability and uniform convergence
Shai Shalev-Shwartz, Ohad Shamir, Nathan Srebro, and Karthik Sridharan · 2010
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Barycenters in the Wasserstein space
Martial Agueh and Guillaume Carlier · 2011
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Wasserstein Barycenter and its Application to Texture Mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Bernot Marc · 2011
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Optimal transportation with infinitely many marginals
Brendan Pass · 2013
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Fast computation of wasserstein barycenters
Marco Cuturi and Arnaud Doucet · 2014
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Iterative bregman projections for regularized transportation problems
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré · 2015
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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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Numerical methods for matching for teams and wasserstein barycenters
Carlier, Guillaume, Oberman, Adam, and Oudet, Edouard · 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
Filippo Santambrogio · 2015
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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Justin Solomon, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas · 2015
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Convexity of the support of the displacement interpolation: Counterexamples
Convergence of a newton algorithm for semi-discrete optimal transport
Jun Kitagawa, Quentin Mérigot, and Boris Thibert · 2019
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Computational optimal transport
Gabriel Peyré and Marco Cuturi · 2019
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Jonathan Weed and Francis R. Bach · 2019
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Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics
A. Ahidar-Coutrix, T. Le Gouic, and Q. Paris · 2020
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Gradient descent algorithms for Bures-Wasserstein barycenters
Sinho Chewi, Tyler Maunu, Philippe Rigollet, and Austin J. Stromme · 2020
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Filippo Santambrogio and Xu-Jia Wang · 2016
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Multilevel clustering via Wasserstein means
Nhat Ho, XuanLong Nguyen, Mikhail Yurochkin, Hung Hai Bui, Viet Huynh, and Dinh Phung · 2017
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Wasserstein barycenters over riemannian manifolds
Young-Heon Kim and Brendan Pass · 2017
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Existence and consistency of wasserstein barycenters
Thibaut Le Gouic and Jean-Michel Loubes · 2017
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Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line
Jérémie Bigot, Raúl Gouet, Thierry Klein, and Alfredo López · 2018
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Characterization of barycenters in the wasserstein space by averaging optimal transport maps
Bigot, Jérémie and Klein, Thierry · 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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Xin Lian, Kshitij Jain, Jakub Truszkowski, Pascal Poupart, and Yaoliang Yu · 2020
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An Invitation to Statistics in Wasserstein Space
Victor M. Panaretos and Yoav Zemel · 2020
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Wasserstein barycenters can be computed in polynomial time in fixed dimension
Jason M Altschuler and Enric Boix-Adsera · 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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Automatic Text Evaluation through the Lens of Wasserstein Barycenters
Pierre Colombo, Guillaume Staerman, Pablo Piantanida, and Chloé Clavel · 2021
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Nearly tight convergence bounds for semi-discrete entropic optimal transport
Alex Delalande · 2022
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Quantitative Stability in Quadratic Optimal Transport
Alex Delalande · 2022
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Quantitative stability of optimal transport maps under variations of the target measure
Alex Delalande and Quentin Mérigot · 2022
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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 Stromme · 2022
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