Minimax-Optimal Two-Sample Test with Sliced Wasserstein
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| Format: | Preprint |
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2025
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| _version_ | 1866908622752055296 |
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| author | Tran, Binh Thuan Schreuder, Nicolas |
| author_facet | Tran, Binh Thuan Schreuder, Nicolas |
| contents | We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees and computational efficiency, its theoretical foundations for hypothesis testing remain limited. We address this gap by proposing a permutation-based SW test and analyzing its performance. The test inherits finite-sample Type I error control from the permutation principle. Moreover, we establish non-asymptotic power bounds and show that the procedure achieves the minimax separation rate $n^{-1/2}$ over multinomial and bounded-support alternatives, matching the optimal guarantees of kernel-based tests while building on the geometric foundations of Wasserstein distances. Our analysis further quantifies the trade-off between the number of projections and statistical power. Finally, numerical experiments demonstrate that the test combines finite-sample validity with competitive power and scalability, and -- unlike kernel-based tests, which require careful kernel tuning -- it performs consistently well across all scenarios we consider. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_27498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimax-Optimal Two-Sample Test with Sliced Wasserstein Tran, Binh Thuan Schreuder, Nicolas Machine Learning Statistics Theory Methodology We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees and computational efficiency, its theoretical foundations for hypothesis testing remain limited. We address this gap by proposing a permutation-based SW test and analyzing its performance. The test inherits finite-sample Type I error control from the permutation principle. Moreover, we establish non-asymptotic power bounds and show that the procedure achieves the minimax separation rate $n^{-1/2}$ over multinomial and bounded-support alternatives, matching the optimal guarantees of kernel-based tests while building on the geometric foundations of Wasserstein distances. Our analysis further quantifies the trade-off between the number of projections and statistical power. Finally, numerical experiments demonstrate that the test combines finite-sample validity with competitive power and scalability, and -- unlike kernel-based tests, which require careful kernel tuning -- it performs consistently well across all scenarios we consider. |
| title | Minimax-Optimal Two-Sample Test with Sliced Wasserstein |
| topic | Machine Learning Statistics Theory Methodology |
| url | https://arxiv.org/abs/2510.27498 |