{"paper":{"title":"Computing Approximate Statistical Discrepancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jeff M. Phillips, Michael Matheny","submitted_at":"2018-04-30T16:02:12Z","abstract_excerpt":"Consider a geometric range space $(X,\\c{A})$ where each data point $x \\in X$ has two or more values (say $r(x)$ and $b(x)$). Also consider a function $\\Phi(A)$ defined on any subset $A \\in (X,\\c{A})$ on the sum of values in that range e.g., $r_A = \\sum_{x \\in A} r(x)$ and $b_A = \\sum_{x \\in A} b(x)$. The $\\Phi$-maximum range is $A^* = \\arg \\max_{A \\in (X,\\c{A})} \\Phi(A)$. Our goal is to find some $\\hat{A}$ such that $|\\Phi(\\hat{A}) - \\Phi(A^*)| \\leq \\varepsilon.$ We develop algorithms for this problem for range spaces with bounded VC-dimension, as well as significant improvements for those def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11287","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"}