Collection 2022 - T3 - WS3 - Measure-theoretic Approaches and Optimal Transportation in Statistics

Organizer(s) Aamari, Eddie ; Aaron, Catherine ; Chazal, Frédéric ; Fisher, Aurélie ; Hoffmann, Marc ; Le Brigant, Alice ; Levrard, Clément ; Michel, Bertrand

Date(s) 21/11/2022 - 25/11/2022

linked URL https://indico.math.cnrs.fr/event/7547/

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A Wasserstein-type distance in the space of Gaussian mixture models

By Agnès Desolneux

In this talk, we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties and propose some possible extensions of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.

This is a joint work with Julie Delon (Université Paris Cité).

Information about the video

Date of recording 23/11/2022
Date of publication 26/04/2024
Institution IHP
Language English
Audience Researchers
Director(s) Alexandre Duplessis, Marco Perez
Format MP4
Venue Amphitheater Hermite, IHP

Citation data

DOI 10.57987/IHP.2022.T3.WS3.008
Cite this video Desolneux, Agnès (23/11/2022). A Wasserstein-type distance in the space of Gaussian mixture models. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T3.WS3.008
URL https://dx.doi.org/10.57987/IHP.2022.T3.WS3.008