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

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/

12 14

Online learning with exponential weights in metric spaces with the measure contraction property

By Quentin Paris

This paper addresses the problem of online learning in metric spaces using exponential weights. We extend the analysis of the exponentially weighted average forecaster, traditionally studied in a Euclidean settings, to a more abstract framework. Our results rely on the notion of barycenters, a suitable version of Jensen’s inequality and a synthetic notion of lower curvature bound in metric spaces known as the measure contraction property. We also adapt the online-to-batch conversion principle to apply our results to a statistical learning framework.

Information about the video

Date of publication 05/04/2024
Institution IHP
Language English
Format MP4

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