{"id":2667,"date":"2025-03-27T07:02:28","date_gmt":"2025-03-27T07:02:28","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/27\/2503-20272\/"},"modified":"2025-03-27T07:02:28","modified_gmt":"2025-03-27T07:02:28","slug":"2503-20272","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/27\/2503-20272\/","title":{"rendered":"An $(epsilon,delta)$-accurate level set estimation with a stopping criterion"},"content":{"rendered":"

An $(epsilon,delta)$-accurate level set estimation with a stopping criterion
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arXiv:2503.20272v1 Announce Type: new
\nAbstract: The level set estimation problem seeks to identify regions within a set of candidate points where an unknown and costly to evaluate function’s value exceeds a specified threshold, providing an efficient alternative to exhaustive evaluations of function values. Traditional methods often use sequential optimization strategies to find $epsilon$-accurate solutions, which permit a margin around the threshold contour but frequently lack effective stopping criteria, leading to excessive exploration and inefficiencies. This paper introduces an acquisition strategy for level set estimation that incorporates a stopping criterion, ensuring the algorithm halts when further exploration is unlikely to yield improvements, thereby reducing unnecessary function evaluations. We theoretically prove that our method satisfies $epsilon$-accuracy with a confidence level of $1 – delta$, addressing a key gap in existing approaches. Furthermore, we show that this also leads to guarantees on the lower bounds of performance metrics such as F-score. Numerical experiments demonstrate that the proposed acquisition function achieves comparable precision to existing methods while confirming that the stopping criterion effectively terminates the algorithm once adequate exploration is completed.<\/div>\n

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\n Hideaki Ishibashi, Kota Matsui, Kentaro Kutsukake, Hideitsu Hino
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An $(epsilon,delta)$-accurate level set estimation with a stopping criterion arXiv:2503.20272v1 Announce Type: new Abstract: The level set estimation problem seeks to identify regions within a set of candidate points where an unknown and costly to evaluate function’s value exceeds a specified threshold, providing an efficient alternative to exhaustive evaluations of function values. Traditional methods often […]<\/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":[161,883,2139],"class_list":["post-2667","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-level","tag-set","tag-stopping"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2667"}],"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=2667"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2667\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2667"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2667"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2667"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}