Journée Statistique et Informatique pour la Science des Données à Paris Saclay

Quantitative Stability of Optimal Transport Maps and Linearization of the 2-Wasserstein Space

27 janv. 2020, 16:20

50m

Centre de Conférences Marilyn et James Simons (Le Bois-Marie)

Orateur

Prof. Quentin Merigot (Paris-Sud)

Description

This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the $2$-Wasserstein space, and enables the direct use of generic supervised and unsupervised learning algorithms on measure data. Our main result is that the embedding is (bi-)Hölder continuous, when the reference density is uniform over a convex set, and can be equivalently phrased as a dimension-independent Hölder-stability results for optimal transport maps. Joint work with A. Delalande and F. Chazal.

Documents de présentation

Merigot.pdf