2025/05/27 by Portales, Léo, Pauwels, Edouard, Cazelles, Elsa
#FOS: Mathematics #Optimization and Control (math.OC) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2505.21274
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(√(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.