Metric extrapolation in the Wasserstein space - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Metric extrapolation in the Wasserstein space

Résumé

In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients in the classical variational characterization of Wasserstein barycenters. We show that this problem admits two equivalent convex formulations: the first can be seen as particular instance of Toland duality and the second is a barycentric optimal transport problem. We propose an efficient numerical scheme to solve this latter formulation based on entropic regularization and a variant of Sinkhorn algorithm.
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Dates et versions

hal-04647125 , version 1 (13-07-2024)
hal-04647125 , version 2 (19-07-2024)

Identifiants

  • HAL Id : hal-04647125 , version 1

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Thomas O. Gallouët, Andrea Natale, Gabriele Todeschi. Metric extrapolation in the Wasserstein space. 2024. ⟨hal-04647125v1⟩
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