36-738 Statistical Optimal Transport I

This course will explore some of the contact points between statistics and optimal transport (OT). The OT framework gives rise to a useful set of ideas and methods which have found numerous applications across machine learning and statistics. Our primary focus will be on understanding how well we can estimate various objects in the OT framework (Wasserstein distances, OT maps, entropic OT) in a statistical minimax setup. Our secondary goal will be to study ideas at the intersection of high-dimensional probability and OT (concentration inequalities, gradient flows, sampling). Along the way we will introduce many ideas from convex analysis, non-parametric statistics and minimax theory.

Instructor

• Sivaraman Balakrishnan