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Activity Number: 57 - Nonparametric Modeling I
Type: Contributed
Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #318931
Title: Entropy-Regularized Schroedinger Bridge and Two-Sample Homogeneity Testing
Author(s): Zaid Harchaoui and Lang Liu* and Soumik Pal
Companies: University of Washington and University of Washington and University of Washington
Keywords: optimal transport; Schroedinger bridge; entropy regularization; two-sample testing; chaos decomposition

We introduce an entropy-regularized statistic that defines a divergence between probability distributions. The statistic admits an expression as a weighted average of Monge couplings with respect to a Gibbs measure. This coupling is related to the static Schr\"odinger bridge given a finite number of particles. We establish the asymptotic consistency of the statistic as the sample size goes to infinity and show that the population limit is the solution of F\"ollmer's entropy-regularized optimal transport. The proof technique relies on a chaos decomposition for paired samples. We illustrate the interest of the approach on the two-sample homogeneity testing problem.

Authors who are presenting talks have a * after their name.

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