Online Program Home
My Program

Abstract Details

Activity Number: 5 - New Developments in Modern Statistical Theory
Type: Invited
Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #300110 Presentation
Title: Empirical Optimal Transport: Inference, Algorithms, Applications
Author(s): Axel Munk*
Companies: Inst. for Mathematical Stochastics, Göttingen University
Keywords: optimal transport; bootstrap; Wasserstein distance; limit law; subsampling; cell biology

We discuss recent developments in statistical data analysis based on empirical optimal transport (EOT). Fundamental are limit laws for EOT plans and distances on finite and discrete spaces. These are characterized by dual optimal transport problems over a gaussian process. Our proofs are based on a combination of sensitivity analysis from convex optimization and discrete empirical process theory. We examine an upper bound for such limiting distributions based on a spanning tree approximation which can be computed explicitly. This can be used for statistical inference, fast simulation, and for fast randomized computation of optimal transport in large scale data applications at pre-specified computational cost as it provides error bounds to balance computational and statistical error. Our methodology is illustrated in computer experiments and on biological data from super-resolution cell microscopy. Finally, this is contrasted and compared with recent results on regularized empirical optimal transport. This is based on joint work with M. Klatt, M. Sommerfeld, C. Tameling and Y. Zemel.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2019 program