{"paper":{"title":"Fast and Sample Near-Optimal Algorithms for Learning Multidimensional 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, Jerry Li, Ludwig Schmidt","submitted_at":"2018-02-23T13:07:32Z","abstract_excerpt":"We study the problem of robustly learning multi-dimensional histograms. A $d$-dimensional function $h: D \\rightarrow \\mathbb{R}$ is called a $k$-histogram if there exists a partition of the domain $D \\subseteq \\mathbb{R}^d$ into $k$ axis-aligned rectangles such that $h$ is constant within each such rectangle. Let $f: D \\rightarrow \\mathbb{R}$ be a $d$-dimensional probability density function and suppose that $f$ is $\\mathrm{OPT}$-close, in $L_1$-distance, to an unknown $k$-histogram (with unknown partition). Our goal is to output a hypothesis that is $O(\\mathrm{OPT}) + \\epsilon$ close to $f$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08513","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"}