Wednesday, May 12, 2021
12:00 p.m. EST
Speaker: Wuchen Li, University of South Carolina https://people.math.sc.edu/wuchen/
Title: Transport information Bregman divergences
In this talk, we talk about a joint intersection between optimal transport and information geometry. We study Bregman divergences in probability density space embedded with the Wasserstein-2 metric.
Several properties and dualities of transport Bregman divergences are provided. In particular, we derive the transport Kullback-Leibler (KL) divergence by a Bregman divergence of negative Boltzmann-Shannon entropy in Wasserstein-2 space. We also derive analytical formulas of transport KL divergence for one-dimensional probability densities and Gaussian families.