BIGOT, Jérémie; CAZELLES, Elsa; PAPADAKIS, Nicolas

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BIGOT, Jérémie
Institut de Mathématiques de Bordeaux [IMB]

CAZELLES, Elsa
Institut de Mathématiques de Bordeaux [IMB]

PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

SIAM Journal on Mathematical Analysis. 2019, vol. 51, n° 3, p. 2261–2285

Society for Industrial and Applied Mathematics

Résumé en anglais

A regularization of Wasserstein barycenters for random measures supported on $R^$d is introduced via convex penalization. The existence and uniqueness of such barycenters is proved for a large class of penalization functions. A stability result of regularized barycenters in terms of Bregman distance associated to the penalization term is also given. This allows to compare the case of data made of n probability measures with the more realistic setting where we have only access to a dataset of random variables sampled from unknown distributions. We also analyze the convergence of the regularized empirical barycenter of a set of n iid random probability measures towards its population counterpart, 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 efficient algorithms for the computation of penalized Wasserstein barycenters. This approach is finally illustrated with simulated and real data sets.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193631

Project ANR

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

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251