{"paper":{"title":"MC^2: A Two-Phase Algorithm for Leveraged Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Armin Eftekhari, Michael B. Wakin, Rachel A. Ward","submitted_at":"2016-09-07T01:25:51Z","abstract_excerpt":"Leverage scores, loosely speaking, reflect the importance of the rows and columns of a matrix. Ideally, given the leverage scores of a rank-$r$ matrix $M\\in\\mathbb{R}^{n\\times n}$, that matrix can be reliably completed from just $O(rn\\log^{2}n)$ samples if the samples are chosen randomly from a nonuniform distribution induced by the leverage scores. In practice, however, the leverage scores are often unknown a priori. As such, the sample complexity in uniform matrix completion---using uniform random sampling---increases to $O(\\eta(M)\\cdot rn\\log^{2}n)$, where $\\eta(M)$ is the largest leverage "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01795","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"}