{"paper":{"title":"Relaxed Leverage Sampling for Low-rank Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Abhisek Kundu","submitted_at":"2015-03-22T03:27:15Z","abstract_excerpt":"We consider the problem of exact recovery of any $m\\times n$ matrix of rank $\\varrho$ from a small number of observed entries via the standard nuclear norm minimization framework. Such low-rank matrices have degrees of freedom $(m+n)\\varrho - \\varrho^2$. We show that any arbitrary low-rank matrices can be recovered exactly from a $\\Theta\\left(((m+n)\\varrho - \\varrho^2)\\log^2(m+n)\\right)$ randomly sampled entries, thus matching the lower bound on the required number of entries (in terms of degrees of freedom), with an additional factor of $O(\\log^2(m+n))$. To achieve this bound on sample size w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06379","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"}