Date
2015
Indexation documentaire
Traitement du signal
Subject
convex optimization; Wasserstein; entropy; Optimal transport
Nom de la revue
SIAM Journal on Imaging Sciences
Volume
9
Numéro
1
Date de publication
2015
Pages article
320-343
Nom de l'éditeur
Society for Industrial and Applied Mathematics
Auteur
Cuturi, Marco
Peyré, Gabriel
Type
Article accepté pour publication ou publié
Résumé en anglais
Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. We show that the dual formulation of Wasserstein variational problems introduced recently by Carlier et al. (2014) can be regularized using an entropic smoothing, which leads to smooth, differentiable, convex optimization problems that are simpler to implement and numerically more stable. We illustrate the versatility of this approach by applying it to the computation of Wasserstein barycenters and gradient flows of spacial regularization functionals.