{"id":7595,"date":"2025-10-15T07:03:07","date_gmt":"2025-10-15T07:03:07","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/10\/15\/2510-11910\/"},"modified":"2025-10-15T07:03:07","modified_gmt":"2025-10-15T07:03:07","slug":"2510-11910","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/10\/15\/2510-11910\/","title":{"rendered":"Simplifying Optimal Transport through Schatten-$p$ Regularization"},"content":{"rendered":"<p>    Simplifying Optimal Transport through Schatten-$p$ Regularization<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2510.11910v1 Announce Type: new<br \/>\nAbstract: We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional structure. The convexity of our formulation enables direct theoretical analysis: we derive optimality conditions and prove recovery guarantees for low-rank couplings and barycentric maps in simplified settings. To efficiently solve the proposed program, we develop a mirror descent algorithm with convergence guarantees for $p geq 1$. Experiments on synthetic and real data demonstrate the method&#8217;s efficiency, scalability, and ability to recover low-rank transport structures.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Tyler Maunu<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2510.11910\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Simplifying Optimal Transport through Schatten-$p$ Regularization arXiv:2510.11910v1 Announce Type: new Abstract: We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional [&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":[588,1486,2428],"class_list":["post-7595","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-low","tag-optimal","tag-transport"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7595"}],"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=7595"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7595\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}