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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.18781 |
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| _version_ | 1866914409187639296 |
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| author | Zhang, Yufei Wang, Tao Zhang, Jingyi |
| author_facet | Zhang, Yufei Wang, Tao Zhang, Jingyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18781 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime Zhang, Yufei Wang, Tao Zhang, Jingyi Machine Learning Applications 49Q22, 65K10 G.1 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. |
| title | SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime |
| topic | Machine Learning Applications 49Q22, 65K10 G.1 |
| url | https://arxiv.org/abs/2603.18781 |