{"id":811,"date":"2024-12-25T07:02:47","date_gmt":"2024-12-25T07:02:47","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2024\/12\/25\/2412-17916\/"},"modified":"2024-12-25T07:02:47","modified_gmt":"2024-12-25T07:02:47","slug":"2412-17916","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2024\/12\/25\/2412-17916\/","title":{"rendered":"Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems"},"content":{"rendered":"<p>    Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2412.17916v1 Announce Type: new<br \/>\nAbstract: We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop general estimates for the difference between the MEM solutions with different priors $mu$ and $nu$ based upon the epigraphical distance between their respective log-moment generating functions. These estimates allow us to establish a rate of convergence in expectation for empirical means. We illustrate our results with denoising on MNIST and Fashion-MNIST data sets.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Matthew King-Roskamp, Rustum Choksi, Tim Hoheisel<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2412.17916\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems arXiv:2412.17916v1 Announce Type: new Abstract: We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,112],"tags":[84,930,929],"class_list":["post-811","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-stat-ml","tag-data","tag-driven","tag-priors"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/811"}],"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=811"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/811\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=811"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=811"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=811"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}