{"paper":{"title":"On the limitation of spectral methods: From the Gaussian hidden clique problem to rank one perturbations of Gaussian tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Daniel Reichman, Ofer Zeitouni","submitted_at":"2014-11-22T17:42:45Z","abstract_excerpt":"We consider the following detection problem: given a realization of a symmetric matrix ${\\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and variance $1$ and the hypothesis where ${\\mathbf{X}}$ is the sum of such matrix and an independent rank-one perturbation.\n  This setup applies to the situation where under the alternative, there is a planted principal submatrix ${\\mathbf{B}}$ of size $L$ for which all upper triangular variables are i.i.d. Gaussians with mean $1$ and variance $1$, whereas all ot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6149","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"}