Wasserstein Iterative Networks for Barycenter Estimation
This work addresses the challenge of computing geometrically meaningful averages of probability distributions for applications in machine learning and data analysis, representing an incremental improvement over existing methods.
The paper tackles the problem of approximating Wasserstein-2 barycenters for continuous measures by introducing an algorithm that uses a generative model without introducing bias, unlike previous methods that rely on regularization or less expressive networks. It results in the creation of the Ave, celeba! dataset for quantitative evaluation, using metrics like FID.
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.