Stochastic Wasserstein Barycenters

TL;DR

This paper introduces a stochastic algorithm for computing Wasserstein barycenters that handles continuous distributions, adapts support iteratively, and produces sharp, meaningful barycenters without regularization.

Contribution

The authors develop a versatile stochastic method that extends to continuous distributions and allows support adjustment, improving accuracy over previous approaches.

Findings

Recovers sharper barycenters without regularization

Handles continuous input distributions effectively

Generates super samples and blue noise approximations

Abstract

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.