Max-sliced Wasserstein distances

Stochastics Seminar
Thursday, April 25, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
March Boedihardjo – Michigan State University – boedihar@msu.edu
Mayya Zhilova

I will give essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from n samples. A version of this result for Banach spaces will also be presented. From this, we will derive an upper bound for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure on a Euclidean space and its symmetrized empirical distribution.