{"paper":{"title":"Estimating Renyi Entropy of Discrete Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Alon Orlitsky, Ananda Theertha Suresh, Himanshu Tyagi, Jayadev Acharya","submitted_at":"2014-08-02T18:52:52Z","abstract_excerpt":"It was recently shown that estimating the Shannon entropy $H({\\rm p})$ of a discrete $k$-symbol distribution ${\\rm p}$ requires $\\Theta(k/\\log k)$ samples, a number that grows near-linearly in the support size. In many applications $H({\\rm p})$ can be replaced by the more general R\\'enyi entropy of order $\\alpha$, $H_\\alpha({\\rm p})$. We determine the number of samples needed to estimate $H_\\alpha({\\rm p})$ for all $\\alpha$, showing that $\\alpha < 1$ requires a super-linear, roughly $k^{1/\\alpha}$ samples, noninteger $\\alpha>1$ requires a near-linear $k$ samples, but, perhaps surprisingly, int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1000","kind":"arxiv","version":3},"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"}