Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport

TL;DR

This paper introduces a scalable, robust method for estimating barycenters of probability distributions using semi-unbalanced neural optimal transport, effectively handling outliers and noise in real-world data.

Contribution

It presents the first algorithm for robust barycenter estimation under continuous distributions using semi-unbalanced optimal transport with a min-max formulation.

Findings

Demonstrates robustness to outliers and class imbalance

Provides theoretical guarantees for the proposed method

Shows effectiveness through illustrative experiments

Abstract

Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios, the presence of outliers and noise in the data measures can significantly hinder the performance of traditional statistical methods for estimating OT barycenters. To address this issue, we propose a novel scalable approach for estimating the robust continuous barycenter, leveraging the dual formulation of the (semi-)unbalanced OT problem. To the best of our knowledge, this paper is the first attempt to develop an algorithm for robust barycenters under the continuous distribution setup. Our method is framed as a min-max optimization problem and is adaptable to general cost functions. We rigorously establish the theoretical underpinnings of the proposed method and demonstrate its robustness to outliers and class imbalance through a number of illustrative experiments. Our source code is publicly available at https://github.com/milenagazdieva/U-NOTBarycenters.