# Sample complexity of optimal transport barycenters with discrete support

arXiv: https://arxiv.org/abs/2505.21274 · HTML: https://mlsanity.com/paper/2505.21274/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2025.

## Built on by (most cited first, 1 of 1)

- [Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation](https://mlsanity.com/paper/2510.04602/) (2025)

## Abstract (arXiv)

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.