SDS Seminar Series – Dr. Sivaraman Balakrishnan

One of the central objects in the OT framework is the OT map -- the map which optimally transports samples from a source to a target distribution. In the statistical setting, our goal is to estimate or construct confidence bands for this map from samples from the source and target distributions. We will discuss some of our recent results on estimating the optimal transport map between smooth distributions, and also present a central limit theorem for the estimated transport map. These results are based on novel stability bounds for and linearizations of the OT map and they show that various, easy to compute plugin estimators are minimax optimal and allow for uncertainty quantification.