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Generalized Wasserstein barycenters between probability measures living on different subspaces

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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03231278
Contributor : Julie Delon Connect in order to contact the contributor
Submitted on : Thursday, May 20, 2021 - 3:55:14 PM
Last modification on : Thursday, April 7, 2022 - 1:58:13 PM
Long-term archiving on: : Saturday, August 21, 2021 - 6:50:48 PM

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  • HAL Id : hal-03231278, version 1

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Julie Delon, Nathael Gozlan, Alexandre Saint-Dizier. Generalized Wasserstein barycenters between probability measures living on different subspaces. 2021. ⟨hal-03231278⟩

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