{"paper":{"title":"Sharp Variable Selection of a Sparse Submatrix in a High-Dimensional Noisy Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cristina Butucea, Irina Suslina, Yuri I. Ingster","submitted_at":"2013-03-22T15:36:21Z","abstract_excerpt":"We observe a $N\\times M$ matrix of independent, identically distributed Gaussian random variables which are centered except for elements of some submatrix of size $n\\times m$ where the mean is larger than some $a>0$. The submatrix is sparse in the sense that $n/N$ and $m/M$ tend to 0, whereas $n,\\, m, \\, N$ and $M$ tend to infinity.\n  We consider the problem of selecting the random variables with significantly large mean values. We give sufficient conditions on $a$ as a function of $n,\\, m,\\,N$ and $M$ and construct a uniformly consistent procedure in order to do sharp variable selection. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5647","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"}