提出SRRM方法，提升小差异下递归匹配的精度
SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime
- 基于递归排名匹配，分析其在小差异下的统计特性
- 新方法在中等计算开销下显著提升逼近精度
- 适合需要高精度距离估计的生成模型与分布比较
递归划分方法为Wasserstein距离提供计算高效的代理，但其统计行为及在小差异情形下的分辨率仍不明确。本文以锚定参考下的递归排名匹配（RRM）为例进行研究，在二次代价下建立了锚定经验RRM的一致性及显式收敛速率。进一步识别出导致小差异下分辨率下降的关键失配机制。基于此分析，提出选择性递归排名匹配（SRRM），抑制主导失配，以适度增加的计算成本实现更高保真度的Wasserstein距离实用代理。
原文摘要 · Abstract (English)
Recursive partitioning methods provide computationally efficient surrogates for the Wasserstein distance, yet their statistical behavior and their resolution in the small-discrepancy regime remain insufficiently understood. We study Recursive Rank Matching (RRM) as a representative instance of this class under a population-anchored reference. In this setting, we establish consistency and an explicit convergence rate for the anchored empirical RRM under the quadratic cost. We then identify a dominant mismatch mechanism responsible for the loss of resolution in the small-discrepancy regime. Based on this analysis, we introduce Selective Recursive Rank Matching (SRRM), which suppresses the resulting dominant mismatches and yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.
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