Analytic properties of the sliced Wasserstein distance

Data Science Seminar

Sangmin Park
Caltech

Abstract

The sliced Wasserstein metric compares probability measures by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and machine learning, as it can be computed efficiently in high dimensions, unlike the (classical) Wasserstein distance.

In this talk, we will focus on the 'smoothing effect' of the sliced Wasserstein distance and its implications on some related gradient flows relevant to various applications, drawing analogies with corresponding flows involving the maximum mean discrepancies. This talk is based on a joint work with Dejan Slepčev (Carnegie Mellon University).