{"paper":{"title":"Optimal Sublinear Sampling of Spanning Trees and Determinantal Point Processes via Average-Case Entropic Independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.ML"],"primary_cat":"cs.DS","authors_text":"Nima Anari, Thuy-Duong Vuong, Yang P. Liu","submitted_at":"2022-04-06T04:11:26Z","abstract_excerpt":"We design fast algorithms for repeatedly sampling from strongly Rayleigh distributions, which include random spanning tree distributions and determinantal point processes. For a graph $G=(V, E)$, we show how to approximately sample uniformly random spanning trees from $G$ in $\\widetilde{O}(\\lvert V\\rvert)$ time per sample after an initial $\\widetilde{O}(\\lvert E\\rvert)$ time preprocessing. For a determinantal point process on subsets of size $k$ of a ground set of $n$ elements, we show how to approximately sample in $\\widetilde{O}(k^\\omega)$ time after an initial $\\widetilde{O}(nk^{\\omega-1})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.02570","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/2204.02570/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"}