{"id":8064,"date":"2025-11-03T07:02:37","date_gmt":"2025-11-03T07:02:37","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/11\/03\/2510-27498\/"},"modified":"2025-11-03T07:02:37","modified_gmt":"2025-11-03T07:02:37","slug":"2510-27498","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/11\/03\/2510-27498\/","title":{"rendered":"Minimax-Optimal Two-Sample Test with Sliced Wasserstein"},"content":{"rendered":"

Minimax-Optimal Two-Sample Test with Sliced Wasserstein
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arXiv:2510.27498v1 Announce Type: new
\nAbstract: 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.<\/div>\n

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\n Binh Thuan Tran, Nicolas Schreuder
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Minimax-Optimal Two-Sample Test with Sliced Wasserstein arXiv:2510.27498v1 Announce Type: new Abstract: 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. […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,190,183,112,191],"tags":[31,1106,1485],"class_list":["post-8064","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-me","category-stat-ml","category-stat-th","tag-sample","tag-test","tag-wasserstein"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8064"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=8064"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8064\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=8064"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=8064"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=8064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}