{"id":10230,"date":"2026-02-04T07:02:34","date_gmt":"2026-02-04T07:02:34","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/04\/2602-02577\/"},"modified":"2026-02-04T07:02:34","modified_gmt":"2026-02-04T07:02:34","slug":"2602-02577","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/04\/2602-02577\/","title":{"rendered":"Relaxed Triangle Inequality for Kullback-Leibler Divergence Between Multivariate Gaussian Distributions"},"content":{"rendered":"<p>    Relaxed Triangle Inequality for Kullback-Leibler Divergence Between Multivariate Gaussian Distributions<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2602.02577v1 Announce Type: new<br \/>\nAbstract: The Kullback-Leibler (KL) divergence is not a proper distance metric and does not satisfy the triangle inequality, posing theoretical challenges in certain practical applications. Existing work has demonstrated that KL divergence between multivariate Gaussian distributions follows a relaxed triangle inequality. Given any three multivariate Gaussian distributions $mathcal{N}_1, mathcal{N}_2$, and $mathcal{N}_3$, if $KL(mathcal{N}_1, mathcal{N}_2)leq epsilon_1$ and $KL(mathcal{N}_2, mathcal{N}_3)leq epsilon_2$, then $KL(mathcal{N}_1, mathcal{N}_3)<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Shiji Xiao, Yufeng Zhang, Chubo Liu, Yan Ding, Keqin Li, Kenli Li<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2602.02577\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Relaxed Triangle Inequality for Kullback-Leibler Divergence Between Multivariate Gaussian Distributions arXiv:2602.02577v1 Announce Type: new Abstract: The Kullback-Leibler (KL) divergence is not a proper distance metric and does not satisfy the triangle inequality, posing theoretical challenges in certain practical applications. Existing work has demonstrated that KL divergence between multivariate Gaussian distributions follows a relaxed triangle inequality. [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,414,113,415,112],"tags":[3581,2110,2248],"class_list":["post-10230","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-it","category-cs-lg","category-math-it","category-stat-ml","tag-kl","tag-mathcal","tag-triangle"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10230"}],"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=10230"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10230\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}