Abstract: While the past decade has witnessed tremendous progress in the computational, methodological and applied aspects of optimal transport (OT), our understanding of fundamental statistical questions in this context has lagged behind.

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 context, our goal is to estimate 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. These results are based on novel stability bounds for the OT map and they show that various, easy to compute plugin estimators are minimax optimal. We will also develop some results for constructing confidence intervals/bands for the Wasserstein distance, and for the OT map, centered around our proposed plugin estimates.

This is based on joint work with Tudor Manole, Jonathan Niles-Weed and Larry Wasserman.


Sivaraman Balakirshnan is an Associate Professor with a joint appointment in the Department of Statistics and Data Science and in the Machine Learning Department at Carnegie Mellon. https://www.stat.cmu.edu/~siva/