Existence and Consistency of Wasserstein Barycenters
Résumé
In this paper, based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the distributions or of a growing set of distributions.
Domaines
Statistiques [math.ST]
Origine : Fichiers produits par l'(les) auteur(s)
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