{"paper":{"title":"The Overlap Gap Property in Principal Submatrix Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Aukosh Jagannath, David Gamarnik, Subhabrata Sen","submitted_at":"2019-08-26T23:46:07Z","abstract_excerpt":"We study support recovery for a $k \\times k$ principal submatrix with elevated mean $\\lambda/N$, hidden in an $N\\times N$ symmetric mean zero Gaussian matrix. Here $\\lambda>0$ is a universal constant, and we assume $k = N \\rho$ for some constant $\\rho \\in (0,1)$. We establish that {there exists a constant $C>0$ such that} the MLE recovers a constant proportion of the hidden submatrix if $\\lambda {\\geq C} \\sqrt{\\frac{1}{\\rho} \\log \\frac{1}{\\rho}}$, {while such recovery is information theoretically impossible if $\\lambda = o( \\sqrt{\\frac{1}{\\rho} \\log \\frac{1}{\\rho}} )$}. The MLE is computationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09959","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/1908.09959/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"}