Generalized Wasserstein barycenters between probability measures living on different subspaces

par Julie Delon (MAP5, Université de Paris)

lundi 14 mars 2022, 10:00 → 11:00 Europe/Paris

1013 (Université Paris-Cité - Bâtiment Sophie Germain)

In recent years, Wasserstein barycenters have become an essential tool to interpolate between probability distributions. In this talk, we introduce a generalization of the notion of Wasserstein barycenter to a case where the initial probability measures live on different subspaces of R^d. A possible application of this generalized barycenter is the reconstruction of a multidimensional distribution from a finite set of projections, which is a classical problem in medical or geophysical imaging. We study the existence and uniqueness of this Wasserstein barycenter, we show how it is related to a larger multi-marginal optimal transport problem, and we propose a dual formulation. Finally, we explain how to compute numerically this generalized barycenter on discrete distributions, and we propose an explicit solution for Gaussian distributions.