TransCampus School on Optimal Transport

November 24th, 3.00 to 5.30 P.M.

I will introduce the problem of optimal transport with a focus on statistical estimation of the optimal transport map from i.i.d. data.
In the first part of the talk, I will provide a comprehensive analysis of the rates of convergence for general plug-in estimators of optimal transport maps defined via barycentric projections. In the second part of the talk, I will use these estimated optimal transport maps to define distribution-free statistical procedures in multi-dimensions. Prominent examples include: (a) two-sample equality of distributions testing, (b) testing for mutual independence, etc. I will summarize these recent developments and: (i) provide a general framework for distribution-free nonparametric testing in multi-dimensions, (ii) propose multivariate analogues of some classical methods (including Wilcoxon's rank sum test), and (iii) study the (asymptotic) efficiency of the proposed distribution-free methods.