{"paper":{"title":"Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Daniel M. Kane, Ilias Diakonikolas, Jasper C. H. Lee, Thanasis Pittas","submitted_at":"2023-12-19T01:01:53Z","abstract_excerpt":"We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \\sum_{i =1}^k w_i P_i$, where each $w_i \\ge \\alpha$ for some known parameter $\\alpha$, and each $P_i$ has unknown covariance $\\Sigma_i \\preceq \\sigma^2_i \\cdot I_d$ for some unknown $\\sigma_i$, the goal is to cluster the samples assuming a pairwise mean separation in the order of $(\\sigma_i+\\sigma_j)/\\sqrt{\\alpha}$ between every pair of components $P_i$ and $P_j$. Our contributions are as follows"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11769","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/2312.11769/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"}