Pré-Publication, Document De Travail Année : 2025

Sample complexity of optimal transport barycenters with discrete support

Résumé

Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures.We provide an $O(\sqrt{N/n})$ statistical generalization bounds for the empirical sparse optimal transport barycenters problem, where $N$ is the maximum cardinality of the barycenter (sparse support) and $n$ is the sample size of the target measures empirical approximation. Our analysis includes various optimal transport divergences including Wasserstein, Sinkhorn and Sliced-Wasserstein. We discuss the application of our result to specific settings including K-means, constrained K-means, free and fixed support Wasserstein barycenters.

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Dates et versions

hal-05087164 , version 1 (27-05-2025)
hal-05087164 , version 2 (18-11-2025)

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  • HAL Id : hal-05087164 , version 2

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Léo Portales, Edouard Pauwels, Elsa Cazelles. Sample complexity of optimal transport barycenters with discrete support. 2025. ⟨hal-05087164v2⟩
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