{"id":9352,"date":"2025-12-25T07:02:30","date_gmt":"2025-12-25T07:02:30","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/12\/25\/2512-20682\/"},"modified":"2025-12-25T07:02:30","modified_gmt":"2025-12-25T07:02:30","slug":"2512-20682","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/12\/25\/2512-20682\/","title":{"rendered":"Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding"},"content":{"rendered":"

Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding
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arXiv:2512.20682v1 Announce Type: new
\nAbstract: Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem, these methods are difficult to implement and, to our knowledge, lack maintained public implementations. As a result, practitioners often resort to linear programming (LP) based methods such as the simplex-based Barrodale-Roberts method and interior-point methods, or on iteratively reweighted least squares (IRLS) approximation which does not guarantee exact solutions. To close this gap, we propose the Piecewise Affine Lower-Bounding (PALB) method, an exact algorithm for LAD line fitting. PALB uses supporting lines derived from subgradients to build piecewise-affine lower bounds, and employs a subdivision scheme involving minima of these lower bounds. We prove correctness and provide bounds on the number of iterations. On synthetic datasets with varied signal types and noise including heavy-tailed outliers as well as a real dataset from the NOAA’s Integrated Surface Database, PALB exhibits empirical log-linear scaling. It is consistently faster than publicly available implementations of LP based and IRLS based solvers. We provide a reference implementation written in Rust with a Python API.<\/div>\n

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\n Stefan Volz, Martin Storath, Andreas Weinmann
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Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding arXiv:2512.20682v1 Announce Type: new Abstract: Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem, these methods are difficult to implement and, […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,112],"tags":[4501,614,2022],"class_list":["post-9352","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-stat-ml","tag-fitting","tag-least","tag-line"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9352"}],"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=9352"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9352\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9352"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}