Generalized Wasserstein barycenters between probability measures living on different subspaces
Probability
2021-05-21 v1 Functional Analysis
Abstract
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R^d. We study the existence and uniqueness of this barycenter, we show how it is related to a larger multi-marginal optimal transport problem, and we propose a dual formulation. Finally, we explain how to compute numerically this generalized barycenter on discrete distributions, and we propose an explicit solution for Gaussian distributions.
Cite
@article{arxiv.2105.09755,
title = {Generalized Wasserstein barycenters between probability measures living on different subspaces},
author = {Julie Delon and Nathaël Gozlan and Alexandre Saint-Dizier},
journal= {arXiv preprint arXiv:2105.09755},
year = {2021}
}