{"paper":{"title":"R\\'enyi Divergence and Kullback-Leibler Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.IT","authors_text":"Peter Harremo\\\"es, Tim van Erven","submitted_at":"2012-06-12T08:34:47Z","abstract_excerpt":"R\\'enyi divergence is related to R\\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by R\\'enyi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the R\\'enyi divergence of order 1 equals the Kullback-Leibler divergence.\n  We review and extend the most important properties of R\\'enyi divergence and Kullback-Leibler divergence, including convexity, continuity, limits of $\\sigma$-algebras and the rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2459","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":""},"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"}