{"id":7155,"date":"2025-09-26T07:02:27","date_gmt":"2025-09-26T07:02:27","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/09\/26\/2509-20618\/"},"modified":"2025-09-26T07:02:27","modified_gmt":"2025-09-26T07:02:27","slug":"2509-20618","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/09\/26\/2509-20618\/","title":{"rendered":"A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity"},"content":{"rendered":"<p>    A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2509.20618v1 Announce Type: new<br \/>\nAbstract: We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of cite{anthony2000function,alon1997scale}. Moreover, we show that the gapped dimensions lead to lower bounds on offset Rademacher averages, thereby strengthening existing approaches for proving lower bounds on rates of convergence in statistical and online learning.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Zeyu Jia, Yury Polyanskiy, Alexander Rakhlin<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2509.20618\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity arXiv:2509.20618v1 Announce Type: new Abstract: We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of cite{anthony2000function,alon1997scale}. Moreover, we [&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":[1331,3891,2589],"class_list":["post-7155","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-bounds","tag-gapped","tag-lower"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7155"}],"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=7155"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7155\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}