Student Probability Seminar

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Entropic estimation of optimal transport maps

Speaker: Aram Pooladian, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, April 10, 2023, 3 p.m.

Synopsis:

Abstract: The 2-Wasserstein distance is defined as the average cost of optimal transportation from a source probability measure P to a target probability measure Q. In practice, P and Q are not known, and we only have iid access to samples from these two measures. This comes with two natural questions: (1) how do we estimate the cost of transportation, and (2) how do we estimate the corresponding optimal transport map? I will focus on the second question, and talk about some recent work that uses entropic regularization, a well-known computational tool, that has also been useful in answering theoretical and statistical questions as well. We'll go through the primal and dual formulations of entropic OT, and sketch ideas for how the proofs go.