Penalization of barycenters for $\varphi$-exponential distributions

S. Kum, M. H. Duong, Y. Lim, S. Yun

Published 2020-06-15Version 1

In this paper we study the penalization of barycenters in the Wasserstein space for $\varphi$-exponential distributions. We obtain an explicit characterization of the barycenter in terms of the variances of the measures generalizing existing results for Gaussian measures. We then develop a gradient projection method for the computation of the barycenter establishing a Lipstchitz continuity for the gradient function. We also numerically show the influence of parameters and stability of the algorithm under small perturbation of data.