Course: STAT 41561=CAAM 41561
Title: Statistical Optimal Transport
Instructor: Promit Ghosal
Class Schedule: Sec 1: MW 3:00 PM–4:20 PM in TBA
Description: This course provides a comprehensive introduction to statistical optimal transport (OT), a mathematical framework that has become increasingly important in statistics, machine learning, and data science. Optimal transport theory provides tools for comparing probability distributions and has found applications in generative modeling, robust statistics, and structured data analysis. Topics covered will include classical formulations of OT, such as Monge’s problem and the Kantorovich relaxation, as well as key results on duality, cyclical monotonicity, and Brenier-McCann’s theorem. We will explore computational foundations, including the Sinkhorn algorithm, entropic OT, and its connections to Schrödinger’s bridge. The course will also examine statistical properties of OT, such as sample complexity, multidimensional ranks and quantiles, and asymptotic inference. Further topics include brief introduction to Wasserstein gradient flows, JKO schemes, and applications of gradient flows in generative models, neural networks and transformer. Weekly assignments and a final project will involve both theoretical analysis and computational implementation of OT methods.