{"paper":{"title":"Sub-sampled Newton Methods with Non-uniform Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Christopher R\\'e, Farbod Roosta-Khorasani, Jiyan Yang, Michael W. Mahoney, Peng Xu","submitted_at":"2016-07-02T20:32:08Z","abstract_excerpt":"We consider the problem of finding the minimizer of a convex function $F: \\mathbb R^d \\rightarrow \\mathbb R$ of the form $F(w) := \\sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\\nabla^2 f_i(w)$ is readily available. We consider the regime where $n \\gg d$. As second-order methods prove to be effective in finding the minimizer to a high-precision, in this work, we propose randomized Newton-type algorithms that exploit \\textit{non-uniform} sub-sampling of $\\{\\nabla^2 f_i(w)\\}_{i=1}^{n}$, as well as inexact updates, as means to reduce the computational complexity. Two non-uniform s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00559","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"}