提出新方法，让多个数据分布的平均更抗噪声和异常值。
Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport
- 用半不平衡最优传输的对偶形式设计鲁棒估计框架。
- 在真实数据中表现稳定，有效抵抗异常值和类别不平衡。
- 适合需要融合多源数据且质量参差的场景，如医疗图像分析。
多源数据聚合可形式化为最优传输（OT）巴氏中心问题，旨在以OT距离为度量计算概率分布的均值。然而，现实中数据测量中的异常值和噪声会严重削弱传统巴氏中心估计方法的性能。为此，本文提出一种新颖的可扩展连续巴氏中心鲁棒估计方法，基于（半）不平衡OT问题的对偶形式构建。据我们所知，这是首个在连续分布设定下实现鲁棒巴氏中心估计的算法。该方法被建模为一个极小-极大优化问题，适用于一般代价函数。我们严格建立了理论基础，并通过多个示例实验验证了其对异常值和类别不平衡的鲁棒性。源代码已公开于 https://github.com/milenagazdieva/U-NOTBarycenters。
原文摘要 · Abstract (English)
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.
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