{"paper":{"title":"Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.PR","authors_text":"Nawaf Bou-Rabee, Stefan Oberd\\\"orster","submitted_at":"2024-10-09T15:17:01Z","abstract_excerpt":"We prove that the mixing time of the No-U-Turn Sampler (NUTS), when initialized in the concentration region of the canonical Gaussian measure, scales as $d^{1/4}$, up to logarithmic factors, where $d$ is the dimension. This scaling is expected to be sharp. This result is based on a coupling argument that leverages the geometric structure of the target distribution. Specifically, concentration of measure results in a striking uniformity in NUTS' locally adapted transitions, which holds with high probability. This uniformity is formalized by interpreting NUTS as an accept/reject Markov chain, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06978","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/2410.06978/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"}