Sampling and Optimal Transport

Graduate / Professional

MCMC sampling and variational inference have long been utilized in Bayesian statistics and machine learning; what can we say about the convergence of these methods? Recently, a modern theory has emerged which blends principles from convex optimization with a geometric perspective on the space of probability distributions based on optimal transport. This course provides an introduction to this theory, as well as to related tools used for modern algorithmic analysis: Markov semigroup theory and stochastic calculus, coupling, and functional inequalities. Much of the course focuses on the complexity of log-concave sampling, but we also discuss applications to diffusion models and variational inference. Prerequisite: Advanced Probability (S&DS 400 / S&DS 600 MATH 330). The following are helpful but not required: Optimization (S&DS 431 / S&DS 631, S&DS 432 / S&DS 632) and Stochastic Processes (S&DS 351 / S&DS 551). Enrollment is limited; requires permission of the instructor. TTh 1:05pm-2:20pm