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arXiv · 2105.09755

Generalized Wasserstein barycenters between probability measures living on different subspaces

Julie Delon·Nathaël Gozlan·Alexandre Saint-Dizier
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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 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.

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Julie Delon, Nathaël Gozlan, Alexandre Saint-Dizier. 2021-05-20. Generalized Wasserstein barycenters between probability measures living on different subspaces. https://arxiv.org/abs/2105.09755

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