{"paper":{"title":"A Statistical Perspective on Randomized Sketching for Ordinary Least-Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Garvesh Raskutti, Michael Mahoney","submitted_at":"2014-06-23T17:12:12Z","abstract_excerpt":"We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data $(X, Y) \\in \\mathbb{R}^{n \\times p} \\times \\mathbb{R}^n$, sketching algorithms use a sketching matrix, $S\\in\\mathbb{R}^{r \\times n}$ with $r \\ll n$. Then, rather than solving the LS problem using the full data $(X,Y)$, sketching algorithms solve the LS problem using only the sketched data $(SX, SY)$. Prior work has typically adopted an algorithmic perspective, in that it has made no statistical assumptions on the input"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5986","kind":"arxiv","version":2},"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"}