{"id":1717,"date":"2025-02-07T07:02:28","date_gmt":"2025-02-07T07:02:28","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/02\/07\/2502-03551\/"},"modified":"2025-02-07T07:02:28","modified_gmt":"2025-02-07T07:02:28","slug":"2502-03551","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/02\/07\/2502-03551\/","title":{"rendered":"Online Learning Algorithms in Hilbert Spaces with $beta-$ and $phi-$Mixing Sequences"},"content":{"rendered":"<p>    Online Learning Algorithms in Hilbert Spaces with $beta-$ and $phi-$Mixing Sequences<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2502.03551v1 Announce Type: new<br \/>\nAbstract: In this paper, we study an online algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes, called the mixing process. For such a process, the degree of dependence is measured by various mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain, where the dependence structure is characterized by the (beta-) and (phi-)mixing coefficients. For these dependent samples, we derive nearly optimal convergence rates. Our findings extend existing error bounds for i.i.d. observations, demonstrating that the i.i.d. case is a special instance of our framework. Moreover, we explicitly account for an additional factor introduced by the dependence structure in the Markov chain.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Priyanka Roy, Susanne Saminger-Platz<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2502.03551\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Online Learning Algorithms in Hilbert Spaces with $beta-$ and $phi-$Mixing Sequences arXiv:2502.03551v1 Announce Type: new Abstract: In this paper, we study an online algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes, called the mixing process. For such a process, the degree of dependence is measured by various mixing [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,1172,112],"tags":[1675,1199,1674],"class_list":["post-1717","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-fa","category-stat-ml","tag-hilbert","tag-mixing","tag-online"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1717"}],"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=1717"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1717\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=1717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=1717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}