GENERALIZED WASSERSTEIN BARYCENTERS BETWEEN PROBABILITY MEASURES LIVING ON DIFFERENT SUBSPACES

• 成果类型: Article
• 署名作者: Delon, Julie; Gozlan, Nathael; SAINT Dizier, Alexandre
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1922
• 发表日期: 2023
• 页码: 4395-4423
• 关键词: optimal transport; distance

摘要

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 multimarginal 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 ex-plicit solution for Gaussian distributions.