{"paper":{"title":"A General Characterization of the Statistical Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Vitaly Feldman","submitted_at":"2016-08-07T09:35:44Z","abstract_excerpt":"Statistical query (SQ) algorithms are algorithms that have access to an {\\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\\phi:X \\rightarrow [-1,1]$, the oracle returns an estimate of ${\\bf E}_{ x\\sim D}[\\phi(x)]$ within some tolerance $\\tau_\\phi$ that roughly corresponds to the number of samples.\n  In this work we demonstrate that the complexity of solving general problems over distributions using SQ algorithms can be captured by a relatively simple notion of statistical dimension that we introduce. SQ algorithms capture a broad spectr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02198","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"}