{"paper":{"title":"Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Alekh Agarwal, Martin J. Wainwright, Sahand N. Negahban","submitted_at":"2011-02-23T18:02:53Z","abstract_excerpt":"We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\\mathfrak{X}$ of the sum of an approximately) low rank matrix $\\Theta^\\star$ with a second matrix $\\Gamma^\\star$ endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including factor analysis, multi-task regression, and robust covariance estimation. We derive a general theorem that bounds the Frobenius norm error for an estimate of the pair "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4807","kind":"arxiv","version":3},"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"}