Generalized Wasserstein barycenters between probability measures living on different subspaces

Autor: Delon, Julie, Gozlan, Nathaël, Saint-Dizier, Alexandre
Rok vydání: 2021
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Databáze: arXiv