Robust Wasserstein barycenter

TL;DR

This paper introduces a robust Wasserstein barycenter that improves resilience to outliers and relaxes moment assumptions, with theoretical guarantees and demonstrated advantages in real-world applications.

Contribution

It proposes a novel robust Wasserstein barycenter based on robust optimal transport, providing theoretical guarantees and superior robustness over classical methods.

Findings

RWB shows improved robustness in image processing tasks.

RWB maintains consistency under outlier contamination.

Numerical experiments confirm RWB's effectiveness in real data.

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.