{"paper":{"title":"Projection Theorems for the R\\'enyi Divergence on $\\alpha$-Convex Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Igal Sason, M. Ashok Kumar","submitted_at":"2015-12-08T15:49:32Z","abstract_excerpt":"This paper studies forward and reverse projections for the R\\'{e}nyi divergence of order $\\alpha \\in (0, \\infty)$ on $\\alpha$-convex sets. The forward projection on such a set is motivated by some works of Tsallis {\\em et al.} in statistical physics, and the reverse projection is motivated by robust statistics. In a recent work, van Erven and Harremo\\\"es proved a Pythagorean inequality for R\\'{e}nyi divergences on $\\alpha$-convex sets under the assumption that the forward projection exists. Continuing this study, a sufficient condition for the existence of forward projection is proved for prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02515","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"}