SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime

2026-03-19

AI Summary

This work addresses the limited resolution and ambiguous statistical behavior of existing recursive partitioning methods when approximating the Wasserstein distance in regions with subtle distributional discrepancies. To overcome these limitations, the authors propose Selective Recursive Rank Matching (SRRM), which introduces a population-anchored reference to uncover the dominant mismatch mechanisms in such low-signal regions and guides a selective matching strategy accordingly. Theoretical analysis establishes the consistency of the anchored empirical RRM estimator and provides explicit convergence rates. Experimental results demonstrate that SRRM substantially improves the approximation accuracy of Wasserstein distance proxies in small-difference scenarios, with only a moderate increase in computational overhead.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Recursive partitioning
• Wasserstein distance
• small-discrepancy regime
• statistical behavior
• resolution

Innovation

• Recursive Rank Matching
• Wasserstein distance
• small-discrepancy regime
• Selective Recursive Rank Matching
• transport surrogates