{"paper":{"title":"List-Decodable Robust Mean Estimation and Learning Mixtures of Spherical Gaussians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Alistair Stewart, Daniel M. Kane, Ilias Diakonikolas","submitted_at":"2017-11-20T09:07:08Z","abstract_excerpt":"We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved guarantees for these problems.\n  {\\bf List-Decodable Mean Estimation.} Fix any $d \\in \\mathbb{Z}_+$ and $0< \\alpha <1/2$. We design an algorithm with runtime $O (\\mathrm{poly}(n/\\alpha)^{d})$ that outputs a list of $O(1/\\alpha)$ many candidate vectors such that with high probability one of the candidates is within $\\ell_2$-distance $O(\\alpha^{-1/(2d)})$ from t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07211","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"}