{"paper":{"title":"Leverage Score Sampling for Faster Accelerated Regression and ERM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Aaron Sidford, Naman Agarwal, Praneeth Netrapalli, Rahul Kidambi, Sham Kakade, Yin Tat Lee","submitted_at":"2017-11-22T18:18:22Z","abstract_excerpt":"Given a matrix $\\mathbf{A}\\in\\mathbb{R}^{n\\times d}$ and a vector $b \\in\\mathbb{R}^{d}$, we show how to compute an $\\epsilon$-approximate solution to the regression problem $ \\min_{x\\in\\mathbb{R}^{d}}\\frac{1}{2} \\|\\mathbf{A} x - b\\|_{2}^{2} $ in time $ \\tilde{O} ((n+\\sqrt{d\\cdot\\kappa_{\\text{sum}}})\\cdot s\\cdot\\log\\epsilon^{-1}) $ where $\\kappa_{\\text{sum}}=\\mathrm{tr}\\left(\\mathbf{A}^{\\top}\\mathbf{A}\\right)/\\lambda_{\\min}(\\mathbf{A}^{T}\\mathbf{A})$ and $s$ is the maximum number of non-zero entries in a row of $\\mathbf{A}$. Our algorithm improves upon the previous best running time of $ \\tilde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08426","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"}