Entropic optimal transport: limit theorems and algorithms

Abstract: In this talk, I will discuss my recent work on entropic optimal transport (EOT). In the first part, I will discuss limit theorems for EOT maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to the marginals, from which the limit theorems, bootstrap consistency, and asymptotic efficiency of the empirical estimators follow. The second part concerns the entropic Gromov-Wasserstein (EGW) distance, which serves as a computationally efficient proxy for the Gromov-Wasserstein distance. By leveraging a variational representation that ties the EGW problem with a series of EOT problems, we derive stability results of EGW with respect to the auxiliary matrix, which enables us to develop efficient algorithms for solving the EGW problem. This talk is based on joint work with Ziv Goldfeld, Gabriel Rioux, and Ritwik Sadhu.

Bio: Kengo Kato is a professor in the Department of Statistics and Data Science at Cornell University. He obtained his PhD in the Graduate School of Economics at the University of Tokyo. Prior to moving to Cornell in 2018, he was on the faculty of the Department of Mathematics at Hiroshima University and the Graduate School of Economics at the University of Tokyo, and spent a year in 2011-2012 as a visiting scholar at MIT. His research concerns quantile regression, high-dimensional limit theorems, and statistical optimal transport. He received the Japan Academy Medal from the Japan Academy (Japanese equivalent of the National Academy of Sciences) and the Analysis Award from the Mathematical Society of Japan.