通过位移信息重塑距离度量，提升分布迁移建模的可靠性
Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport
- 用样本位移的二阶矩估计马哈拉诺比斯距离，替代欧式距离
- 在合成与真实数据上显著提升运输路径的可靠性
- 轻量高效，可适配任意OT求解器，适合实际部署
最优传输（OT）是建模分布迁移的核心框架。由于OT直接在输入空间比较分布，设计合理的样本间距离度量对保证优化器不违背真实变化几何至关重要。本文提出位移重塑最优传输（ReshapeOT），通过整合观测到的样本位移作为额外知识来重塑基础距离度量。技术上，ReshapeOT将欧氏距离替换为基于位移二阶矩估计的马哈拉诺比斯距离，有效在输入空间中“开辟快速通道”，引导传输方案更符合实际位移模式。该方法计算轻量，可无缝集成至任何基于代价矩阵的OT求解器，并支持核化以增强灵活性。在合成与真实数据上的实验表明，ReshapeOT显著提升了运输可靠性。进一步验证了其在两个实际应用场景中的有效性。
原文摘要 · Abstract (English)
Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not violate the true geometry of change. We propose Displacement-Reshaped Optimal Transport (ReshapeOT), a method that reshapes the ground metric by integrating observed sample displacements as an additional source of knowledge. Technically, ReshapeOT replaces the Euclidean metric with a Mahalanobis distance estimated from displacement second moments. This effectively carves expressways through the input space, inviting transport solutions that better align with observed displacements. Our method is computationally lightweight, integrates seamlessly into any OT solver that operates on a cost matrix, and can be kernelized for further flexibility. Experiments on synthetic and real-world data show that ReshapeOT achieves substantial gains in transport reliability. We further demonstrate our method's usefulness in two practical use cases.
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