Un Mokameeting a eu lieu le mercredi 8 juin 2022, à 14h, dans la salle P. Flajolet. Nous avons eu le plaisir d’écouter Alex Delalande (Orsay)
Titre : Quantitative stability of barycenters in the Wasserstein space
Résumé : Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields such as image/geometry/language processing, which calls for the study of their statistical properties. A natural question in this spirit is the question of the stability of Wasserstein barycenters: given a set of probability measures, how does a perturbation of these measures affect the corresponding barycenters?
In this talk, I will present a recent joint work with Guillaume Carlier and Quentin Mérigot where we tried to answer this question. We show that the Wasserstein barycenter depends in a Hölder-continuous way on the data, under relatively mild assumptions. Our proof relies on recent quantitative stability estimates for optimal transport maps and a new result quantifying the modulus of continuity of the push-forward operation under a (not necessarily smooth) optimal transport map.
