{"paper":{"title":"The Fast Cauchy Transform and Faster Robust Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Kenneth L. Clarkson, Malik Magdon-Ismail, Michael W. Mahoney, Petros Drineas, Xiangrui Meng","submitted_at":"2012-07-19T14:26:05Z","abstract_excerpt":"We provide fast algorithms for overconstrained $\\ell_p$ regression and related problems: for an $n\\times d$ input matrix $A$ and vector $b\\in\\mathbb{R}^n$, in $O(nd\\log n)$ time we reduce the problem $\\min_{x\\in\\mathbb{R}^d} \\|Ax-b\\|_p$ to the same problem with input matrix $\\tilde A$ of dimension $s \\times d$ and corresponding $\\tilde b$ of dimension $s\\times 1$. Here, $\\tilde A$ and $\\tilde b$ are a coreset for the problem, consisting of sampled and rescaled rows of $A$ and $b$; and $s$ is independent of $n$ and polynomial in $d$. Our results improve on the best previous algorithms when $n\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4684","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}