Transport information Bregman divergences

Wed, May 12, 2021, 12:00 pm
Speaker(s): 

Wednesday, May 12, 2021

12:00 p.m. EST

https://www.oneworldml.org/home

Speaker: Wuchen Li, University of South Carolina https://people.math.sc.edu/wuchen/

Title: Transport information Bregman divergences

Abstract:

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.