{"paper":{"title":"Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Daniel Kongsgaard, Daniel M. Kane, Ilias Diakonikolas, Jerry Li, Kevin Tian","submitted_at":"2021-06-16T03:34:14Z","abstract_excerpt":"We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\\mathbb{R}^d$ and a parameter $0< \\alpha <\\frac 1 2$ such that an $\\alpha$-fraction of the points in $T$ are i.i.d. samples from a well-behaved distribution $\\mathcal{D}$ and the remaining $(1-\\alpha)$-fraction are arbitrary. The goal is to output a small list of vectors, at least one of which is close to the mean of $\\mathcal{D}$. We develop new algorithms for list-decodable mean estimation, achieving nearly-optimal statistica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.08537","kind":"arxiv","version":2},"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/2106.08537/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"}