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Generalized Wasserstein barycenters between probability measures living on different subspaces

Authors
  • Delon, Julie
  • Gozlan, Nathael
  • Saint-Dizier, Alexandre
Publication Date
Jan 01, 2021
Source
HAL-INRIA
Keywords
Language
English
License
Unknown
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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 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 explicit solution for Gaussian distributions.

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