{"paper":{"title":"Phase Transitions for High Dimensional Clustering and Related Problems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jiashun Jin, Wanjie Wang, Zheng Tracy Ke","submitted_at":"2015-02-24T20:58:44Z","abstract_excerpt":"Consider a two-class clustering problem where we observe $X_i = \\ell_i \\mu + Z_i$, $Z_i \\stackrel{iid}{\\sim} N(0, I_p)$, $1 \\leq i \\leq n$. The feature vector $\\mu\\in R^p$ is unknown but is presumably sparse. The class labels $\\ell_i\\in\\{-1, 1\\}$ are also unknown and the main interest is to estimate them.\n  We are interested in the statistical limits. In the two-dimensional phase space calibrating the rarity and strengths of useful features, we find the precise demarcation for the Region of Impossibility and Region of Possibility. In the former, useful features are too rare/weak for successful"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06952","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"}