{"paper":{"title":"Subexponential-Time Algorithms for Sparse PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Afonso S. Bandeira, Alexander S. Wein, Dmitriy Kunisky, Yunzi Ding","submitted_at":"2019-07-26T15:45:13Z","abstract_excerpt":"We study the computational cost of recovering a unit-norm sparse principal component $x \\in \\mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \\lambda xx^\\top$ with $W$ drawn from the Gaussian orthogonal ensemble, or $N$ independent samples from $\\mathcal{N}(0, I_n + \\beta xx^\\top)$, respectively). Prior work has shown that when the signal-to-noise ratio ($\\lambda$ or $\\beta\\sqrt{N/n}$, respectively) is a small constant and the fraction of nonzero entries in the planted vector is $\\|x\\|_0 / n = \\rho$, it is possible to recover $x$ in p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11635","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.11635/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"}