{"paper":{"title":"Sharpened Error Bounds for Random Sampling Based $\\ell_2$ Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Shusen Wang","submitted_at":"2014-03-30T11:21:39Z","abstract_excerpt":"Given a data matrix $X \\in R^{n\\times d}$ and a response vector $y \\in R^{n}$, suppose $n>d$, it costs $O(n d^2)$ time and $O(n d)$ space to solve the least squares regression (LSR) problem. When $n$ and $d$ are both large, exactly solving the LSR problem is very expensive. When $n \\gg d$, one feasible approach to speeding up LSR is to randomly embed $y$ and all columns of $X$ into a smaller subspace $R^c$; the induced LSR problem has the same number of columns but much fewer number of rows, and it can be solved in $O(c d^2)$ time and $O(c d)$ space.\n  We discuss in this paper two random sampl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7737","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"}