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arXiv · 2505.21274

Sample complexity of optimal transport barycenters with discrete support

Léo Portales·Edouard Pauwels·Elsa Cazelles
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Abstract

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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Léo Portales, Edouard Pauwels, Elsa Cazelles. 2025-05-27. Sample complexity of optimal transport barycenters with discrete support. https://arxiv.org/abs/2505.21274

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