{"paper":{"title":"Testing Matrix Rank, Optimally","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Hongyang Zhang, Maria-Florina Balcan, Yi Li","submitted_at":"2018-10-18T17:24:52Z","abstract_excerpt":"We show that for the problem of testing if a matrix $A \\in F^{n \\times n}$ has rank at most $d$, or requires changing an $\\epsilon$-fraction of entries to have rank at most $d$, there is a non-adaptive query algorithm making $\\widetilde{O}(d^2/\\epsilon)$ queries. Our algorithm works for any field $F$. This improves upon the previous $O(d^2/\\epsilon^2)$ bound (SODA'03), and bypasses an $\\Omega(d^2/\\epsilon^2)$ lower bound of (KDD'14) which holds if the algorithm is required to read a submatrix. Our algorithm is the first such algorithm which does not read a submatrix, and instead reads a carefu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08171","kind":"arxiv","version":1},"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"}