{"paper":{"title":"Completing Any Low-rank Matrix, Provably","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Rachel Ward, Srinadh Bhojanapalli, Sujay Sanghavi, Yudong Chen","submitted_at":"2013-06-12T21:26:00Z","abstract_excerpt":"Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\\em incoherence}---on its row and column spaces. In these cases, the subset of elements is sampled uniformly at random.\n  In this paper, we show that {\\em any} rank-$ r $ $ n$-by-$ n $ matrix can be exactly recovered from as few as $O(nr \\log^2 n)$ randomly chosen elements, provided this random choice is made according to a {\\em specific biased distribution}: the probabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2979","kind":"arxiv","version":4},"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"}