DEVI Webinar – Elsa Cazelles (CNRS / IRIT)

Date - Heure / Date - Hour
Date(s) - 08/04/2021
10h30 - 11h30

Optimal (weak) transport and barycenters


We introduce the weak barycenter of a family of probability distributions, based on the recently developed notion of optimal weak transport of measures. We provide a theoretical analysis of the weak barycenter and its relationship to the classic Wasserstein barycenter, and discuss its meaning in the light of convex ordering between probability measures. We also provide iterative algorithms to compute a weak barycenter for either finite or infinite families of arbitrary measure (with finite moments of order 2), which are particularly well suited for the streaming setting, i.e., when measures arrive sequentially. The concept of weak barycenter and our computation approaches are illustrated on synthetic examples, validated on 2D real-world data and compared to the classical Wasserstein barycenters.

The presentation will be given in French.