Abstract: Otto calculus is a fundamental toolbox in mathematical optimal transport, imparting the Wasserstein space of probability measures with a Riemmanian structure. In particular, one can compute the Riemannian gradient of a functional over this space and, in turn, optimize it using Wasserstein gradient flows. The necessary background to define and compute Wasserstein gradient flows will be presented in the first part of the talk before moving to several statistical applications ranging from variational inference to maximum likelihood estimation in Gaussian mixture models. Emphasis will be placed on conceptual ideas in order for the talk to be accessible to a broad audience.

Bio: Philippe Rigollet works at the intersection of statistics, machine learning, and optimization, focusing primarily on the design and analysis of statistical methods for high-dimensional problems. His recent research focuses on statistical optimal transport and its applications to geometric data analysis and sampling. Website: www-math.mit.edu/~rigollet