Sampler for the Wasserstein barycenter

Abstract: Wasserstein barycenters have become a central object in applied optimal transport as a tool to summarize complex objects that can be represented as distributions. Such objects include posterior distributions in Bayesian statistics, functions in functional data analysis and images in graphics. In a nutshell a Wasserstein barycenter is a probability distribution that provides a compelling summary of a finite set of input distributions. While the question of computing Wasserstein barycenters has received significant attention, this talk focuses on a new and important question: sampling from a barycenter given a natural query access to the input distribution. We describe a new methodology built on the theory of Gradient flows over Wasserstein space together with convergence guarantees.

This is joint work with Chiheb Daaloul, Magali Tournus and Jacques Liandrat.

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Bio: Thibaut Le Gouic is an associate professor at the Ecole Centrale de Marseille and the Institut de Mathématiques de Marseille in France. Since 2019, he is a visiting professor at the Department of Mathematics at MIT. He received his PhD at the Université Paul Sabatier at Toulouse, France. His work lies at the interaction between geometry, statistics and probability theory, in particular via optimal transport.