{"paper":{"title":"Tight Sample Bounds for Renyi and Min-Entropy Estimation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Arman Adibi, Piotr Krysta","submitted_at":"2026-07-18T21:01:38Z","abstract_excerpt":"Estimating entropy from samples is fundamental in information theory and property testing. Shannon entropy measures average uncertainty and can be estimated to constant additive accuracy over a $k$-symbol alphabet using $\\Theta(k/\\log k)$ samples. Min-entropy depends only on the most likely symbol. Both are special cases of order-$\\alpha$ R'{e}nyi entropy, $H_\\alpha$.\n  We characterize the sample complexity of estimating min-entropy and R'{e}nyi entropy for $k$ and integer $\\alpha>1$; our lower bounds also hold for noninteger $\\alpha\\ge1.001$. We prove that min-entropy estimation to constant a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16966","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/2607.16966/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"}