BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Philippe Rigollet (MIT) DTSTART:20200408T140000Z DTEND:20200408T150000Z DTSTAMP:20260423T035536Z UID:MADPlus/1 DESCRIPTION:Title: Statistical and Computational aspects of Wasserstein Barycenters\nby P hilippe Rigollet (MIT) as part of MAD+\n\n\nAbstract\nThe notion of averag e is central to most statistical methods. In this talk we study a generali zation of this notion over the non-​Euclidean space of probability measu res equipped with a certain Wasserstein distance. This generalization is o ften called Wasserstein Barycenters and empirical evidence suggests that t hese barycenters allow to capture interesting notions of averages in graph ics\, data assimilation and morphometrics. However the statistical (rates of convergence) and computational (efficient algorithms) for these Wassers tein barycenters are largely unexplored. The goal of this talk is to revie w two recent results: 1. Fast rates of convergence for empirical barycente rs in general geodesic spaces\, and\, 2. Provable guarantees for gradient descent and stochastic gradient descent to compute Wasserstein barycenters . Both results leverage geometric aspects of optimal transport. Based on j oint works (arXiv:1908.00828\, arXiv:2001.01700) with Chewi\, Le Gouic\, M aunu\, Paris\, and Stromme.\n LOCATION:https://researchseminars.org/talk/MADPlus/1/ END:VEVENT END:VCALENDAR