{"id":10504,"date":"2026-02-16T07:02:30","date_gmt":"2026-02-16T07:02:30","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/16\/2602-12534\/"},"modified":"2026-02-16T07:02:30","modified_gmt":"2026-02-16T07:02:30","slug":"2602-12534","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/16\/2602-12534\/","title":{"rendered":"Linear Regression with Unknown Truncation Beyond Gaussian Features"},"content":{"rendered":"

Linear Regression with Unknown Truncation Beyond Gaussian Features
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arXiv:2602.12534v1 Announce Type: new
\nAbstract: In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^star$. This problem has a long history of study in Statistics and Machine Learning going back to the works of (Galton, 1897; Tobin, 1958) and more recently in, e.g., (Daskalakis et al., 2019; 2021; Lee et al., 2023; 2024). Despite this long history, however, most prior works are limited to the special case where $S^star$ is precisely known. The more practically relevant case, where $S^star$ is unknown and must be learned from data, remains open: indeed, here the only available algorithms require strong assumptions on the distribution of the feature vectors (e.g., Gaussianity) and, even then, have a $d^{mathrm{poly} (1\/varepsilon)}$ run time for achieving $varepsilon$ accuracy.
\n In this work, we give the first algorithm for truncated linear regression with unknown survival set that runs in $mathrm{poly} (d\/varepsilon)$ time, by only requiring that the feature vectors are sub-Gaussian. Our algorithm relies on a novel subroutine for efficiently learning unions of a bounded number of intervals using access to positive examples (without any negative examples) under a certain smoothness condition. This learning guarantee adds to the line of works on positive-only PAC learning and may be of independent interest.<\/div>\n

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\n Alexandros Kouridakis, Anay Mehrotra, Alkis Kalavasis, Constantine Caramanis
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Linear Regression with Unknown Truncation Beyond Gaussian Features arXiv:2602.12534v1 Announce Type: new Abstract: In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^star$. This problem has a long history of study in Statistics and […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,413,113,190,112,191],"tags":[496,336,4783],"class_list":["post-10504","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-ds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-linear","tag-regression","tag-unknown"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10504"}],"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=10504"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10504\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}