Abstract:
Wasserstein-Fisher-Rao (WFR) distance is a family of metrics to gauge the discrepancy of two Radon measures, which takes into account both transportation and weight change. Spherical WFR distance is a projected version of WFR distance for probability measures so that the space of Radon measures equipped with WFR can be viewed as metric cone over the space of probability measures with spherical WFR. Based on a Benamou-Brenier type dynamic formulation for spherical WFR, we investigate some basic properties of the particle motions for the geodesic curves and develop a machine learning framework to compute the geodesics. A Kullback-Leibler (KL) divergence term based on the inverse map is introduced into the cost function to overcome a difficulty introduced by the weight change. The geodesics can be adopted to generate weighted samples, and can be beneficial for applications with given weighted samples, especially in the Bayesian inference, compared to sample generation with previous flow models.
Speaker's bio:
Lei Li is currently a tenure-tack associate professor in the Institute of Natural Sciences and the School of Mathematical Scieces at Shanghai Jiao Tong Unviersity (SJTU). He obtained his B.S. from Tsinghua University in 2010 and Ph.D. from the University of Wisconsin-Madison in 2015. Then, he was an assistant research professor at Duke University, and joined SJTU in 2018. His main research interest is in applied mathematics, especially designing and analyzing numerical methods for stochastic models arising from physics and data sciences. Currently, he is focusing on the interacting particle systems and stochastic differential equations.