{"paper":{"title":"Near-Optimal Statistical Query Hardness of Learning Halfspaces with Massart Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Daniel M. Kane, Ilias Diakonikolas","submitted_at":"2020-12-17T16:43:11Z","abstract_excerpt":"We study the problem of PAC learning halfspaces with Massart noise. Given labeled samples $(x, y)$ from a distribution $D$ on $\\mathbb{R}^{d} \\times \\{ \\pm 1\\}$ such that the marginal $D_x$ on the examples is arbitrary and the label $y$ of example $x$ is generated from the target halfspace corrupted by a Massart adversary with flipping probability $\\eta(x) \\leq \\eta \\leq 1/2$, the goal is to compute a hypothesis with small misclassification error. The best known $\\mathrm{poly}(d, 1/\\epsilon)$-time algorithms for this problem achieve error of $\\eta+\\epsilon$, which can be far from the optimal b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.09720","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.09720/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}