{"paper":{"title":"Scalable Computation of Regularized Precision Matrices via Stochastic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Jie Chen, Rahul Mazumder, Yves F. Atchad\\'e","submitted_at":"2015-09-01T18:25:32Z","abstract_excerpt":"We consider the problem of computing a positive definite $p \\times p$ inverse covariance matrix aka precision matrix $\\theta=(\\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer $\\sum_{i,j=1}^{p} \\lambda (\\alpha|\\theta_{ij}| + \\frac{1}{2}(1- \\alpha) \\theta_{ij}^2),$ with regularization parameters $\\alpha \\in [0,1]$ and $\\lambda>0$. The associated convex semidefinite optimization problem is notoriously difficult to scale to large problems and has demanded significant attention over the past several years. We propose a new algorithmic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00426","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"}