CAZELLES, Elsa; BIGOT, Jérémie; PAPADAKIS, Nicolas

doi:10.1007/978-3-319-68445-1_10

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CAZELLES, Elsa
Institut de Mathématiques de Bordeaux [IMB]

BIGOT, Jérémie
Institut de Mathématiques de Bordeaux [IMB]

PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

Langue

Communication dans un congrès

Ce document a été publié dans

Lecture Notes in Computer Science, Lecture Notes in Computer Science, 3rd International Conference Geometric Science of Information (GSI'17), 2017-11-07, Paris. 2017, vol. 10589, p. 83-90

Springer International Publishing

Résumé en anglais

This paper is an overview of results that have been obtain in [J. Bigot, E. Cazelles, and N. Papadakis. Penalized barycenters in the Wasserstein space. Submitted. Available at https://128.84.21.199/abs/1606.010252] on the convex regularization of Wasserstein barycenters for random measures supported on Rd. We discuss the existence and uniqueness of such barycenters for a large class of regularizing functions. A stability result of regularized barycenters in terms of Bregman distance associated to the convex regularization term is also given. Additionally we discuss the convergence of the regularized empirical barycenter of a set of n iid random probability measures towards its population counterpart in the real line case, and we discuss its rate of convergence. This approach is shown to be appropriate for the statistical analysis of discrete or absolutely continuous random measures. In this setting, we propose an efficient minimization algorithm based on accelerated gradient descent for the computation of regularized Wasserstein barycenters.< Réduire

Mots clés en anglais

Wasserstein space

Fréchet mean

Barycenter of probability measures

Convex regularization

Bregman divergence

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190534

DOI

http://dx.doi.org/10.1007/978-3-319-68445-1_10

Project ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251