{"id":3457,"date":"2025-04-30T07:02:29","date_gmt":"2025-04-30T07:02:29","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/04\/30\/2504-20617\/"},"modified":"2025-04-30T07:02:29","modified_gmt":"2025-04-30T07:02:29","slug":"2504-20617","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/04\/30\/2504-20617\/","title":{"rendered":"Sobolev norm inconsistency of kernel interpolation"},"content":{"rendered":"<p>    Sobolev norm inconsistency of kernel interpolation<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2504.20617v1 Announce Type: new<br \/>\nAbstract: We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis space. These lower bounds imply that kernel interpolation is always inconsistent, when the smoothness index of the norm is larger than a constant that depends only on the embedding index of the hypothesis space and the decay rate of the eigenvalues.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Yunfei Yang<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2504.20617\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sobolev norm inconsistency of kernel interpolation arXiv:2504.20617v1 Announce Type: new Abstract: We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[2518,1135,1973],"class_list":["post-3457","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-interpolation","tag-kernel","tag-norm"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3457"}],"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=3457"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3457\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=3457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=3457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=3457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}