{"id":5028,"date":"2025-07-02T07:02:42","date_gmt":"2025-07-02T07:02:42","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/07\/02\/2507-00640\/"},"modified":"2025-07-02T07:02:42","modified_gmt":"2025-07-02T07:02:42","slug":"2507-00640","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/07\/02\/2507-00640\/","title":{"rendered":"Forward Reverse Kernel Regression for the Schr&#8221;{o}dinger bridge problem"},"content":{"rendered":"\n<div>Forward Reverse Kernel Regression for the Schr&#8221;{o}dinger bridge problem<\/div>\n<p> \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2507.00640v1 Announce Type: new<br \/>\nAbstract: In this paper, we study the Schr&#8221;odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin&#8211;endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure to approximate the Schr&#8221;odinger potentials in a nonparametric way. In particular, we use kernel based Monte Carlo regression in the context of Picard iteration of a corresponding fixed point problem. By preserving in the iteration positivity and contractivity in a Hilbert metric sense, we develop a provably convergent algorithm. Furthermore, we provide convergence rates for the potential estimates and prove their optimality. Finally, as an application, we propose a non-nested Monte Carlo procedure for the final dimensional distributions of the Schr&#8221;odinger Bridge process, based on the constructed potentials and the forward-reverse simulation method for conditional diffusions.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Denis Belomestny, John. Schoenmakers<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2507.00640\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Forward Reverse Kernel Regression for the Schr&#8221;{o}dinger bridge problem arXiv:2507.00640v1 Announce Type: new Abstract: In this paper, we study the Schr&#8221;odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin&#8211;endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure to approximate the Schr&#8221;odinger potentials in a nonparametric way. [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,450,451,112],"tags":[3123,3124,2781],"class_list":["post-5028","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-cs-na","category-math-na","category-stat-ml","tag-forward","tag-reverse","tag-schr"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5028"}],"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=5028"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5028\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}