{"paper":{"title":"Fast exact recovery of noisy matrix from few entries: the infinity norm approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.CO","math.PR","stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"BaoLinh Tran, Van Vu","submitted_at":"2025-01-31T15:31:01Z","abstract_excerpt":"The matrix recovery (completion) problem, a central problem in data science and theoretical computer science, is to recover a matrix $A$ from a relatively small sample of entries.\n  While such a task is impossible in general, it has been shown that one can recover $A$ exactly in polynomial time, with high probability, from a random subset of entries, under three (basic and necessary) assumptions: (1) the rank of $A$ is very small compared to its dimensions (low rank), (2) $A$ has delocalized singular vectors (incoherence), and (3) the sample size is sufficiently large.\n  There are many differe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19224","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.19224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}