{"paper":{"title":"Fast Regression with an $\\ell_\\infty$ Guarantee","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Eric Price, Zhao Song","submitted_at":"2017-05-30T16:20:34Z","abstract_excerpt":"Sketching has emerged as a powerful technique for speeding up problems in numerical linear algebra, such as regression. In the overconstrained regression problem, one is given an $n \\times d$ matrix $A$, with $n \\gg d$, as well as an $n \\times 1$ vector $b$, and one wants to find a vector $\\hat{x}$ so as to minimize the residual error $\\|Ax-b\\|_2$. Using the sketch and solve paradigm, one first computes $S \\cdot A$ and $S \\cdot b$ for a randomly chosen matrix $S$, then outputs $x' = (SA)^{\\dagger} Sb$ so as to minimize $\\|SAx' - Sb\\|_2$.\n  The sketch-and-solve paradigm gives a bound on $\\|x'-x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10723","kind":"arxiv","version":1},"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"}