{"paper":{"title":"A Spectral Algorithm for List-Decodable Covariance Estimation in Relative Frobenius Norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.DS","authors_text":"Ankit Pensia, Daniel M. Kane, Ilias Diakonikolas, Jasper C. H. Lee, Thanasis Pittas","submitted_at":"2023-05-01T17:54:35Z","abstract_excerpt":"We study the problem of list-decodable Gaussian covariance estimation. Given a multiset $T$ of $n$ points in $\\mathbb R^d$ such that an unknown $\\alpha<1/2$ fraction of points in $T$ are i.i.d. samples from an unknown Gaussian $\\mathcal{N}(\\mu, \\Sigma)$, the goal is to output a list of $O(1/\\alpha)$ hypotheses at least one of which is close to $\\Sigma$ in relative Frobenius norm. Our main result is a $\\mathrm{poly}(d,1/\\alpha)$ sample and time algorithm for this task that guarantees relative Frobenius norm error of $\\mathrm{poly}(1/\\alpha)$. Importantly, our algorithm relies purely on spectral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00966","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.00966/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"}