{"id":238617,"date":"2026-06-09T02:42:36","date_gmt":"2026-06-09T07:42:36","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/06\/hidden-geometry-explains-why-kernel-methods-separate-complex-data-so-well"},"modified":"2026-06-09T02:42:36","modified_gmt":"2026-06-09T07:42:36","slug":"hidden-geometry-explains-why-kernel-methods-separate-complex-data-so-well","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/06\/hidden-geometry-explains-why-kernel-methods-separate-complex-data-so-well","title":{"rendered":"Hidden geometry explains why kernel methods separate complex data so well"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/hidden-geometry-explains-why-kernel-methods-separate-complex-data-so-well3.jpg\"><\/a><\/p>\n<p>Are two sets of data genuinely different, or is it because of randomness? This question, known as the two-sample testing problem, becomes notoriously difficult in modern datasets, because they are often high-dimensional, complex, and differences between them can take countless subtle forms.<\/p>\n<p>\u201cSimply put, we don\u2019t know what differences to look for, the possibilities are bewildering,\u201d says Professor Victor Panaretos at EPFL\u2019s Institute of Mathematics.<\/p>\n<p>To solve the problem, mathematicians have developed the so-called \u201ckernel methods,\u201d which have emerged as powerful solutions, widely used in fields such as genomics, finance, and artificial intelligence.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are two sets of data genuinely different, or is it because of randomness? This question, known as the two-sample testing problem, becomes notoriously difficult in modern datasets, because they are often high-dimensional, complex, and differences between them can take countless subtle forms. \u201cSimply put, we don\u2019t know what differences to look for, the possibilities are [\u2026]<\/p>\n","protected":false},"author":427,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45,2229,6],"tags":[],"class_list":["post-238617","post","type-post","status-publish","format-standard","hentry","category-finance","category-mathematics","category-robotics-ai"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/238617","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/427"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=238617"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/238617\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=238617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=238617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=238617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}