Generalized Wasserstein barycenters between probability measures living on different subspaces

Generalized Wasserstein barycenters between probability measures living on different subspaces

In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of Rd. We study the existence and uniqueness of this barycenter, we show how it is related to a larger multimarginal optimal transport problem, and...

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Veröffentlicht in:The Annals of applied probability 2023-12, Vol.33 (6A), p.4395
Hauptverfasser: Delon, Julie, Gozlan, Nathael, Saint Dizier, Alexandre
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Center of gravity
Mathematical problems
Normal distribution
Probability
Subspaces
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Gozlan, Nathael
Saint Dizier, Alexandre
description In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of Rd. 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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subjects Center of gravity
Mathematical problems
Normal distribution
Probability
Subspaces
title Generalized Wasserstein barycenters between probability measures living on different subspaces
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