CAST Seminar: Marcel Nutz

Join us at the CANSSI Ontario STatistics Seminars (CAST) with

Marcel Nutz

Professor
Department of Statistics and Mathematics
Columbia University

Free Event | Registration Required

Talk Title

Sparse Regularized Optimal Transport

Abstract

Entropic optimal transport — the optimal transport problem regularized by KL divergence — is highly successful in statistical applications. Thanks to the smoothness of the entropic coupling, its sample complexity avoids the curse of dimensionality suffered by unregularized optimal transport. The flip side of smoothness is overspreading: the entropic coupling always has full support, whereas the unregularized coupling that it approximates is usually sparse, even given by a map. Regularizing optimal transport by less-smooth f-divergences such as Tsallis divergence is known to allow for sparse approximations, but is often thought to suffer from the curse of dimensionality as the couplings have limited differentiability and the dual is not strongly concave. We refute this conventional wisdom and show, for a broad family of divergences, that the key empirical quantities converge at the parametric rate, independently of the dimension. More precisely, we provide central limit theorems for the optimal cost, the optimal coupling, and the dual potentials induced by i.i.d. samples from the marginals. (Joint work with Alberto Gonzalez-Sanz and Stephan Eckstein.)

Speaker Profile

Marcel Nutz is a Professor at Columbia University‘s Department of Statistics. He is also affiliated with the Department of Mathematics and the Data Science Institute. His research focuses on quantitative finance and optimal transport. He holds a PhD in mathematics from ETH Zurich. Dr. Nutz’s work was recognized with an IMS Medallion Award and an Alfred P. Sloan Fellowship. He was also named IMS Fellow, Columbia-Ecole Polytechnique Alliance Professor and co-Chair of the IMS-FIPS. Support by five NSF grants is gratefully acknowledged. He currently serves on the editorial boards of AAP, FMF, MF, MOR, SICON, SIFIN. He previously served on the board of SPA (2018-2024).