{"paper":{"title":"Active Linear Regression for $\\ell_p$ Norms and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Cameron Musco, Christopher Musco, David P. Woodruff, Taisuke Yasuda","submitted_at":"2021-11-09T00:20:01Z","abstract_excerpt":"We study active sampling algorithms for linear regression, which aim to query only a few entries of a target vector $b\\in\\mathbb R^n$ and output a near minimizer to $\\min_{x\\in\\mathbb R^d} \\|Ax-b\\|$, for a design matrix $A\\in\\mathbb R^{n \\times d}$ and loss $\\|\\cdot\\|$.\n  For $p$ norm regression for any $0<p<\\infty$, we give an algorithm based on Lewis weight sampling outputting a $(1+\\epsilon)$-approximate solution using just $\\tilde O(d/\\epsilon^2)$ queries to $b$ for $p\\in(0,1)$, $\\tilde{O}(d/\\epsilon)$ queries for $1<p<2$, and $\\tilde{O}(d^{p/2}/\\epsilon^p)$ queries for $2<p<\\infty$. For $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.04888","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.04888/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}