Title: The Stein Geometry in Machine Learning: Gradient Flows, Optimal Transport and Large Deviations
Abstract: Sampling or approximating high-dimensional probability distributions is a key challenge in computational statistics and machine learning. This talk will present connections to gradient flow PDEs, optimal transport and interacting particle systems, focusing on the recently introduced Stein variational gradient descent methodology and some variations. The construction induces a novel geometrical structure on the set of probability distributions related to a positive definite kernel function. We discuss the corresponding geodesic equations, infinitesimal optimal transport maps, as well as large deviation functionals. This is joint work with A. Duncan (Imperial College London), L. Szpruch (University of Edinburgh) and M. Renger (Weierstrass Institute Berlin).