AM Seminar: Wasserstein Information Geometric Learning

Speaker Name: 
Wuchen Li
Speaker Title: 
Computational and Applied Mathematics Assistant Professor
Speaker Organization: 
University of California, Los Angeles
Start Time: 
Monday, March 4, 2019 - 4:00pm
End Time: 
Monday, March 4, 2019 - 5:00pm
Location: 
BE 372
Organizer: 
Abhishek Halder

Abstract

Optimal transport and Wasserstein metric nowadays play important roles in data science. In this talk, we will briefly review its development and applications in machine learning. In particular, we will focus its induced differential structure. We will introduce the Wasserstein natural gradient in parametric models. The L2-Wasserstein metric tensor in probability density space is pulled back to the one on parameter space, under which the parameter space forms a Riemannian manifold. We derive the Wasserstein gradient flows and proximal operator in parameter space. We demonstrate that the Wasserstein natural gradient works efficiently in several statistical machine learning problems, including Boltzmann machine, generative adversary models (GANs) and variational Bayesian statistics.

 

Bio

Wuchen Li was born in Linyi, Shandong, China. He received his BSc in Mathematics  from Shandong university in 2009. He obtained M.S. degree in Statistics, and Ph.D. degree in Mathematics from Georgia institute of Technology in 2016. He is currently Computational and Applied Mathematics Assistant Professor in the Department of Mathematics at University of California, Los Angeles.