{"paper":{"title":"Testing Halfspaces over Rotation-Invariant Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Nathaniel Harms","submitted_at":"2018-10-31T22:25:27Z","abstract_excerpt":"We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\\tilde O(\\sqrt{n}\\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability whether $f$ is of the form $f(x) = sign(\\sum_i w_ix_i-t)$ or is $\\epsilon$-far from all such functions. This sample size is significantly smaller than the well-known requirement of $\\Omega(n)$ samples for learning halfspaces, and known lower bounds imply that our sample size is optimal (in its dependence on $n$) up to logarithmic factors. The algorithm is distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00139","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"}