{"paper":{"title":"Universality of Computational Lower Bounds for Submatrix Detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Guy Bresler, Matthew Brennan, Wasim Huleihel","submitted_at":"2019-02-19T06:37:02Z","abstract_excerpt":"In the general submatrix detection problem, the task is to detect the presence of a small $k \\times k$ submatrix with entries sampled from a distribution $\\mathcal{P}$ in an $n \\times n$ matrix of samples from $\\mathcal{Q}$. This formulation includes a number of well-studied problems, such as biclustering when $\\mathcal{P}$ and $\\mathcal{Q}$ are Gaussians and the planted dense subgraph formulation of community detection when the submatrix is a principal minor and $\\mathcal{P}$ and $\\mathcal{Q}$ are Bernoulli random variables. These problems all seem to exhibit a universal phenomenon: there is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06916","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"}