Statistical Applications of Wasserstein Gradient Flows

Explore a distinguished seminar on statistical applications of Wasserstein gradient flows presented by Professor Philippe Rigollet from MIT. Delve into the fundamental concepts of Otto calculus in mathematical optimal transport, understanding how it imparts Riemannian structure to the Wasserstein space of probability measures. Learn about computing Riemannian gradients of functionals over this space and optimizing them using Wasserstein gradient flows. Discover the practical applications of these concepts in statistical fields such as variational inference and maximum likelihood estimation for Gaussian mixture models. Gain insights from Rigollet's expertise at the intersection of statistics, machine learning, and optimization, with a focus on high-dimensional problems and recent research in statistical optimal transport for geometric data analysis and sampling.