Existence and Consistency of Wasserstein Barycenters
Statistics Theory
2016-02-15 v2 Statistics Theory
Abstract
In this paper, based on the Fr{\'e}chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the distributions or of a growing set of distributions.
Keywords
Cite
@article{arxiv.1506.04153,
title = {Existence and Consistency of Wasserstein Barycenters},
author = {Thibaut Le Gouic and Jean-Michel Loubes},
journal= {arXiv preprint arXiv:1506.04153},
year = {2016}
}