Thinning to improve two-sample discrepancy
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911390858477568 |
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| author | Smirnov, Gleb Vershynin, Roman |
| author_facet | Smirnov, Gleb Vershynin, Roman |
| contents | The discrepancy between two independent samples \(X_1,\dots,X_n\) and \(Y_1,\dots,Y_n\) drawn from the same distribution on $\mathbb{R}^d$ typically has order \(O(\sqrt{n})\) even in one dimension. We give a simple online algorithm that reduces the discrepancy to \(O(\log^{2d} n)\) by discarding a small fraction of the points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thinning to improve two-sample discrepancy Smirnov, Gleb Vershynin, Roman Probability Data Structures and Algorithms The discrepancy between two independent samples \(X_1,\dots,X_n\) and \(Y_1,\dots,Y_n\) drawn from the same distribution on $\mathbb{R}^d$ typically has order \(O(\sqrt{n})\) even in one dimension. We give a simple online algorithm that reduces the discrepancy to \(O(\log^{2d} n)\) by discarding a small fraction of the points. |
| title | Thinning to improve two-sample discrepancy |
| topic | Probability Data Structures and Algorithms |
| url | https://arxiv.org/abs/2506.20932 |