Stochastic Wasserstein Barycenters
This work addresses a computational challenge in optimal transport for researchers and practitioners, offering a versatile method for applications like generating super samples and blue noise approximations, though it appears incremental as it builds on existing barycenter approaches.
The paper tackles the problem of computing Wasserstein barycenters for probability distributions without regularization, enabling recovery of sharp outputs with support contained within the true barycenter. It presents a stochastic algorithm that extends to continuous distributions and allows adjustable support, showing examples where it recovers more meaningful barycenters than previous work.
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.