{"paper":{"title":"Near-Optimal Density Estimation in Near-Linear Time Using Variable-Width Histograms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Ilias Diakonikolas, Rocco A. Servedio, Siu-on Chan, Xiaorui Sun","submitted_at":"2014-11-01T21:03:59Z","abstract_excerpt":"Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a hypothesis distribution that is close to $p$. The main contribution of this paper is a highly efficient density estimation algorithm for learning using a variable-width histogram, i.e., a hypothesis distribution with a piecewise constant probability density function.\n  In more detail, for any $k$ and $\\epsilon$, we give an algorithm that makes $\\tilde{O}(k/\\epsilon^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0169","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":""},"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"}