密度重加权熵最优传输：将几何与采样密度解耦
Density-Reweighted Entropic Optimal Transport: Decoupling Geometry from Sampling Density
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对熵最优传输（EOT）在采样密度差异大时易产生误导性对应关系的问题，提出密度重加权EOT框架，可解耦几何与采样密度，实验验证其能恢复几何忠实对应关系且性能更优。
AI中文摘要：
数据集对齐是科学与工程领域数据分析的核心步骤，目标是匹配不同数据集间的观测值。熵最优传输（EOT）为此任务提供了计算可处理的框架，通过传输计划编码跨数据集的亲和性。但当两个数据集从几何相似的低维结构采样，且采样密度差异显著时，EOT计划可能会基于相对采样密度而非几何邻近性匹配点，产生几何上误导性的对应关系。为解决该问题，我们提出密度重加权EOT框架，可按期望程度降低采样密度对传输计划的影响，范围从标准EOT到纯由底层几何驱动的对齐。在合适的正则性条件下，我们证明重加权EOT计划收敛于一类总体水平计划，其对采样密度的依赖被明确体现。通过模拟实验，我们表明所提方法能恢复几何上忠实的对应关系，当数据集存在显著采样密度差异时，其性能优于相关的基于EOT的框架。
英文摘要：
Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets. Entropic Optimal Transport (EOT) offers a computationally tractable framework for this task by encoding cross-dataset affinities in a transport plan. However, when two datasets are sampled from geometrically similar low-dimensional structures with substantially different sampling densities, the EOT plan may match points by relative sampling density rather than geometric proximity, yielding geometrically misleading correspondences. To address this issue, we propose a density-reweighted EOT framework in which the influence of sampling density on the transport plan can be discounted to a desired degree, ranging from standard EOT to alignment driven purely by underlying geometry. Under suitable regularity conditions, we establish convergence of the reweighted EOT plan to a family of population-level plans whose dependence on sampling density is made explicit. Through simulations, we show that our approach recovers geometrically faithful correspondences, improving over related EOT-based frameworks when datasets exhibit substantial sampling density disparity.
