Convergence rate of empirical measures in the subspace robust Wasserstein distance

TL;DR

This paper provides an estimate for how quickly the empirical measure converges to the true measure in the subspace robust Wasserstein distance within a Hilbert space setting.

Contribution

It introduces a convergence rate estimate for empirical measures under the subspace robust Wasserstein distance in infinite-dimensional spaces.

Findings

Derived explicit convergence rate bounds.

Applicable to probability measures on Hilbert spaces.

Enhances understanding of empirical measure behavior in robust Wasserstein metrics.

Abstract

We obtain an estimate for the expected subspace robust Wasserstein distance between any probability measure on the unit ball of a separable Hilbert space, and its empirical distribution from $n$ i.i.d. samples.