{"id":7433,"date":"2025-10-08T07:03:29","date_gmt":"2025-10-08T07:03:29","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/10\/08\/2510-05447\/"},"modified":"2025-10-08T07:03:29","modified_gmt":"2025-10-08T07:03:29","slug":"2510-05447","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/10\/08\/2510-05447\/","title":{"rendered":"A Probabilistic Basis for Low-Rank Matrix Learning"},"content":{"rendered":"<p>    A Probabilistic Basis for Low-Rank Matrix Learning<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2510.05447v1 Announce Type: new<br \/>\nAbstract: Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $Vert cdot Vert_*$. However, despite the assortment of computational methods for such problems, there is a surprising lack of understanding of the underlying probability distributions being referred to. In this article, we study the distribution with density $f(X)propto e^{-lambdaVert XVert_*}$, finding many of its fundamental attributes to be analytically tractable via differential geometry. We use these facts to design an improved MCMC algorithm for low rank Bayesian inference as well as to learn the penalty parameter $lambda$, obviating the need for hyperparameter tuning when this is difficult or impossible. Finally, we deploy these to improve the accuracy and efficiency of low rank Bayesian matrix denoising and completion algorithms in numerical experiments.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Simon Segert, Nathan Wycoff<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2510.05447\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Probabilistic Basis for Low-Rank Matrix Learning arXiv:2510.05447v1 Announce Type: new Abstract: Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $Vert cdot Vert_*$. However, despite the assortment of computational methods for such problems, there is a surprising lack of understanding of [&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":[588,419,589],"class_list":["post-7433","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-low","tag-matrix","tag-rank"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7433"}],"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=7433"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7433\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}