A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures
Abstract
In this paper, we focus on the analysis of the regularized Wasserstein barycenter problem. We provide uniqueness and a characterization of the barycenter for two important classes of probability measures: (i) Gaussian distributions and (ii) -Gaussian distributions; each regularized by a particular entropy functional. We propose an algorithm based on gradient projection method in the space of matrices in order to compute these regularized barycenters. We also consider a general class of -exponential measures, for which only the non-regularized barycenter is studied. Finally, we numerically show the influence of parameters and stability of the algorithm under small perturbation of data.
Cite
@article{arxiv.2006.08743,
title = {A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures},
author = {S. Kum and M. H. Duong and Y. Lim and S. Yun},
journal= {arXiv preprint arXiv:2006.08743},
year = {2022}
}
Comments
39 pages, significant revised from the previous version, results were strengthened, title changed