Robust Wasserstein barycenter
Methodology
2026-03-10 v1
Abstract
In this paper, we address a fundamental limitation of the classical Wasserstein barycenter -- its sensitivity to outliers and its reliance on finite first/second moment assumptions. To overcome these issues, we propose the robust Wasserstein barycenter (RWB) based on a recent concept of the robust optimal transport. Theoretical guarantees, including existence and consistency, are established for the proposed RWB. Through extensive numerical experiments on both simulated and real-world data -- including image processing and financial time series analysis -- we demonstrate that the RWB exhibits superior robustness compared to the classical Wasserstein barycenter.
Keywords
Cite
@article{arxiv.2603.07563,
title = {Robust Wasserstein barycenter},
author = {Zixiong Cheng and Hang Liu},
journal= {arXiv preprint arXiv:2603.07563},
year = {2026}
}