{"paper":{"title":"A Sharp Lower Bound for Mixed-membership Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jiashun Jin, Zheng Tracy Ke","submitted_at":"2017-09-17T03:23:43Z","abstract_excerpt":"Consider an undirected network with $n$ nodes and $K$ perceivable communities, where some nodes may have mixed memberships. We assume that for each node $1 \\leq i \\leq n$, there is a probability mass function $\\pi_i$ defined over $\\{1, 2, \\ldots, K\\}$ such that \\[ \\pi_i(k) = \\mbox{the weight of node $i$ on community $k$}, \\qquad 1 \\leq k \\leq K. \\] The goal is to estimate $\\{\\pi_i, 1 \\leq i \\leq n\\}$ (i.e., membership estimation).\n  We model the network with the {\\it degree-corrected mixed membership (DCMM)} model \\cite{Mixed-SCORE}. Since for many natural networks, the degrees have an approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05603","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":""},"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"}