Existence and consistency of Wasserstein barycenters

• 成果类型: Article
• 署名作者: Le Gouic, Thibaut; Loubes, Jean-Michel
• 署名单位: Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0727-z
• 发表日期: 2017
• 页码: 901-917
• 关键词: DISTRIBUTIONS

摘要

Based on the Fr,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 probabilities 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 probability measures or of a growing set of probability measures.