Wasserstein Iterative Networks for Barycenter Estimation

Alexander Korotin, Vage Egiazarian, Lingxiao Li, Evgeny Burnaev

Keywords: optimal transport, continuous barycenter, neural networks, Wasserstein-2 distance

Abstract: Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of continuous measures via a generative model. Previous approaches rely on regularization (entropic/quadratic) which introduces bias or on input convex neural networks which are not expressive enough for large-scale tasks. In contrast, our algorithm does not introduce bias and allows using arbitrary neural networks. In addition, based on the celebrity faces dataset, we construct Ave, celeba! dataset which can be used for quantitative evaluation of barycenter algorithms by using standard metrics of generative models such as FID.

TL;DR: We present an algorithm to approximate the Wasserstein-2 barycenters of continuous measures via a generative model and construct Ave, celeba! dataset which can be used for quantitative evaluation of barycenter algorithms.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2201.12245/code)