SDS Seminar Series – Dr. Sivaraman Balakrishnan

Mar

2024

2:00 pm – 3:00 pm

Cost: Free

In Person (view details)

Statistical Inference for Optimal Transport

Description

The Spring 2024 SDS Seminar Series continues on March 22nd from 2:00 p.m. to 3:00 p.m. with Dr. Sivaraman Balakrishnan (Statistics and Data Science; Machine Learning, Carnegie Mellon). This event is in-person.

Title: Statistical Inference for Optimal Transport

Abstract: While the past decade has witnessed tremendous progress in the computational, methodological and applied aspects of optimal transport (OT), our understanding of various 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 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.

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