{"paper":{"title":"Estimating Differential Entropy under Gaussian Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Kristjan Greenewald, Yury Polyanskiy, Ziv Goldfeld","submitted_at":"2018-10-27T03:19:32Z","abstract_excerpt":"This paper studies the problem of estimating the differential entropy $h(S+Z)$, where $S$ and $Z$ are independent $d$-dimensional random variables with $Z\\sim\\mathcal{N}(0,\\sigma^2 \\mathrm{I}_d)$. The distribution of $S$ is unknown, but $n$ independently and identically distributed (i.i.d) samples from it are available. The question is whether having access to samples of $S$ as opposed to samples of $S+Z$ can improve estimation performance. We show that the answer is positive. More concretely, we first show that despite the regularizing effect of noise, the number of required samples still nee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11589","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"}