{"id":3663,"date":"2025-05-08T07:02:28","date_gmt":"2025-05-08T07:02:28","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/05\/08\/2505-04613\/"},"modified":"2025-05-08T07:02:28","modified_gmt":"2025-05-08T07:02:28","slug":"2505-04613","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/05\/08\/2505-04613\/","title":{"rendered":"From Two Sample Testing to Singular Gaussian Discrimination"},"content":{"rendered":"<p>    From Two Sample Testing to Singular Gaussian Discrimination<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2505.04613v1 Announce Type: new<br \/>\nAbstract: We establish that testing for the equality of two probability measures on a general separable and compact metric space is equivalent to testing for the singularity between two corresponding Gaussian measures on a suitable Reproducing Kernel Hilbert Space. The corresponding Gaussians are defined via the notion of kernel mean and covariance embedding of a probability measure. Discerning two singular Gaussians is fundamentally simpler from an information-theoretic perspective than non-parametric two-sample testing, particularly in high-dimensional settings. Our proof leverages the Feldman-Hajek criterion for singularity\/equivalence of Gaussians on Hilbert spaces, and shows that discrepancies between distributions are heavily magnified through their corresponding Gaussian embeddings: at a population level, distinct probability measures lead to essentially separated Gaussian embeddings. This appears to be a new instance of the blessing of dimensionality that can be harnessed for the design of efficient inference tools in great generality.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2505.04613\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>From Two Sample Testing to Singular Gaussian Discrimination arXiv:2505.04613v1 Announce Type: new Abstract: We establish that testing for the equality of two probability measures on a general separable and compact metric space is equivalent to testing for the singularity between two corresponding Gaussian measures on a suitable Reproducing Kernel Hilbert Space. The corresponding Gaussians are [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,190,112,191],"tags":[338,1184,1621],"class_list":["post-3663","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-gaussian","tag-testing","tag-two"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3663"}],"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=3663"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3663\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=3663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=3663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=3663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}