Multi-marginal optimal partial transport and partial barycenter problems

Jeudi 18 mai 14:15-15:15 Jun Kitagawa - Michigan State University

Résumé : The classical two-marginal optimal transport problem can be interpreted as the coupling of two probability distributions subject to an optimality criterion, determined by a “cost function” defined on the domains. Recently, there has been much activity on two generalizations of this problem. The first is the partial transport problem, where the total masses of the two distributions to be coupled may not match, and one is forced to choose submeasures of the constraints for coupling. The other generalization is the multi-marginal transport problem, where there are 3 or more probability distributions to be coupled together in an optimal manner. By combining the above two generalizations we obtain a natural extension : the multi-marginal optimal partial transport problem. In joint work with Brendan Pass (University of Alberta), we have obtained uniqueness of solutions (under hypotheses analogous to the two-marginal partial transport problem given by Figalli) by relating the problem to what we call the “partial barycenter problem” for finite measures. A notable difference is that in some cases, solutions can exhibit significantly different qualitative behavior compared to those of the two marginal case.

Lieu : Bât 425, salle 113-115

Multi-marginal optimal partial transport and partial barycenter problems  Version PDF