Optimal Transport Maps for Conditional Simulation

Data Science Seminar

Bamdad Hosseini (University of Washington)

Abstract

Optimal transport (OT) considers the problem of finding a mapping that warps a reference probability measure to a target of interest. Such a map can naturally be viewed as a generative model in the context of machine learning applications making the framework of OT a natural candidate for the analysis of generative modeling. In this talk I will discuss the foundational theory of a particular class of OT problems where the resulting map does not only transport the reference measure to the target but is also capable of providing samples from certain conditionals of the target. This problem is very interesting in the context of Bayesian inference and in particular in the setting of amortized and simulation based inference.