Overview of Optimal Transport Methods for Density Function Approximation

Optimal transport, broadly defined, deals with the problem of minimizing the cost of transporting one (probability) measure to another. It is of interest in a range of subjects, such as probability theory, optimization, and partial differential equations, among others. It is also used in many applications, including machine learning, Bayesian inference, and sampling. In this talk, we will give an overview of optimal transport, in relation to (probability) density function estimation, with emphasis on computational methods for constructing optimal transport maps. We will also discuss our ongoing work concerning the use of transport maps for estimating unknown density functions characterizing data, specifically when the available data is scarce ("small data" scenarios).

Bio
https://www.bnl.gov/staff/vlopezmar