{"paper":{"title":"Robust subgaussian estimation of a mean vector in nearly linear time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Guillaume Lecu\\'e, Jules Depersin","submitted_at":"2019-06-07T13:09:43Z","abstract_excerpt":"We construct an algorithm, running in time $\\tilde{\\mathcal O}(N d + uK d)$, which is robust to outliers and heavy-tailed data and which achieves the subgaussian rate from [Lugosi, Mendelson] \\begin{equation}\\label{eq:intro_subgaus_rate} \\sqrt{\\frac{{\\rm Tr}(\\Sigma)}{N}}+\\sqrt{\\frac{||\\Sigma||_{op}K}{N}} \\end{equation}with probability at least $1-\\exp(-c_0K)-\\exp(-c_1 u)$ where $\\Sigma$ is the covariance matrix of the informative data, $K\\in\\{1, \\ldots, K\\}$ is some parameter (number of block means) and $u>0$ is another parameter of the algorithm. This rate is achieved when $K\\geq c_1 |\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03058","kind":"arxiv","version":4},"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"}