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DTEND:20230711T120000Z
UID:b216ca5e1b421fc83f0892cf757796c2-482
DTSTAMP:19700101T120016Z
DESCRIPTION:MMD-regularized Optimal Transport.
URL;VALUE=URI:https://www.csa.iisc.ac.in/newweb/event/482/mmd-regularized-optimal-transport/
SUMMARY:Optimal transport (OT) induced Wasserstein distance is a popular tool for comparing probability measures. Kantorovichs formulation for OT aims to find an optimal plan for the transport of mass between the source and the target distributions that incurs the least expected cost of transportation. While classical OT strictly enforces the marginals of the transport plan to match the source and target, Unbalanced Optimal Transport (UOT) is employed when one wants to relax this constraint. 

In this talk, we will discuss our study of the UOT problem where the marginal constraints are enforced using an Integral Probability Metric (IPM), complementing the prior works on f-divergence regularized UOT. In particular, the talk will focus on MMD-regularized UOT (MMD-UOT), a special case of our formulation. The talk will cover some of our theoretical results, including the metricity properties, sample efficiency of the proposed metrics and consistency of our convex-program-based estimators. We will also discuss how MMD-UOT can be seen as an interpolant between the MMD & the Wasserstein metrics. Finally, the talk will present how these convex programs can be solved efficiently and showcase their utility in applications, including two sample tests, domain adaptation and single-cell RNA sequencing.
DTSTART:20230711T120000Z
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