{"id":5842,"date":"2025-08-05T07:02:36","date_gmt":"2025-08-05T07:02:36","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/08\/05\/2508-01065\/"},"modified":"2025-08-05T07:02:36","modified_gmt":"2025-08-05T07:02:36","slug":"2508-01065","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/08\/05\/2508-01065\/","title":{"rendered":"Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing"},"content":{"rendered":"

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
\n \t

\n
<\/BR>
\n
\n \t

\n
<\/BR><\/p>\n

arXiv:2508.01065v1 Announce Type: new
\nAbstract: Motivated by canonical problems in medical diagnostics, we propose and study properties of an objective function that uniformly bounds uncertainties in quantities of interest extracted from classifiers and related data analysis tools. We begin by adopting a set-theoretic perspective to show how two main tasks in diagnostics — classification and prevalence estimation — can be recast in terms of a variation on the confusion (or error) matrix ${boldsymbol {rm P}}$ typically considered in supervised learning. We then combine arguments from conditional probability with the Gershgorin circle theorem to demonstrate that the largest Gershgorin radius $boldsymbol rho_m$ of the matrix $mathbb I-boldsymbol {rm P}$ (where $mathbb I$ is the identity) yields uniform error bounds for both classification and prevalence estimation. In a two-class setting, $boldsymbol rho_m$ is minimized via a measure-theoretic “water-leveling” argument that optimizes an appropriately defined partition $U$ generating the matrix ${boldsymbol {rm P}}$. We also consider an example that illustrates the difficulty of generalizing the binary solution to a multi-class setting and deduce relevant properties of the confusion matrix.<\/div>\n

\t

\n
<\/BR>
\n Paul N. Patrone, Anthony J. Kearsley
\n \t

\n
<\/BR>
\nGo to original source<\/a>
\n \t

\n
<\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing arXiv:2508.01065v1 Announce Type: new Abstract: Motivated by canonical problems in medical diagnostics, we propose and study properties of an objective function that uniformly bounds uncertainties in quantities of interest extracted from classifiers and related data analysis tools. We begin by adopting a set-theoretic […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,420,112],"tags":[1883,1245,419],"class_list":["post-5842","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-pr","category-stat-ml","tag-boldsymbol","tag-classification","tag-matrix"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5842"}],"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=5842"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5842\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}