{"paper":{"title":"Simple Heuristics Yield Provable Algorithms for Masked Low-Rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, Christopher Musco, David P. Woodruff","submitted_at":"2019-04-22T13:01:07Z","abstract_excerpt":"In $masked\\ low-rank\\ approximation$, one is given $A \\in \\mathbb{R}^{n \\times n}$ and binary mask matrix $W \\in \\{0,1\\}^{n \\times n}$. The goal is to find a rank-$k$ matrix $L$ for which: $$cost(L) = \\sum_{i=1}^{n} \\sum_{j = 1}^{n} W_{i,j} \\cdot (A_{i,j} - L_{i,j} )^2 \\leq OPT + \\epsilon \\|A\\|_F^2 ,$$ where $OPT = \\min_{rank-k\\ \\hat{L}} cost(\\hat L)$ and $\\epsilon$ is a given error parameter. Depending on the choice of $W$, this problem captures factor analysis, low-rank plus diagonal decomposition, robust PCA, low-rank matrix completion, low-rank plus block matrix approximation, and many pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09841","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.09841/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"}