Robust Wasserstein barycenter
🤖 AI Summary
This work addresses the sensitivity of classical Wasserstein barycenters to outliers and their reliance on finite-moment assumptions, which limits their applicability to heavy-tailed or contaminated data. The authors introduce robust optimal transport into Wasserstein barycenter computation, proposing the Robust Wasserstein Barycenter (RWB). By integrating truncation and regularization techniques, RWB yields an estimator that is insensitive to outliers. The paper establishes theoretical guarantees for the existence and statistical consistency of RWB under mild conditions. Empirical evaluations on synthetic data, image processing tasks, and financial time series demonstrate that RWB significantly outperforms conventional methods, offering enhanced robustness and practical utility in real-world scenarios involving data corruption or heavy-tailed distributions.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Wasserstein barycenter
outliers
robustness
moment assumptions
optimal transport
Innovation
Methods, ideas, or system contributions that make the work stand out.
Robust Wasserstein barycenter
Robust optimal transport
Outlier robustness
Wasserstein barycenter
Consistency
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