{"paper":{"title":"Agnostic Learning of Monomials by Halfspaces is Hard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.CC","authors_text":"Prasad Raghavendra, Venkatesan Guruswami, Vitaly Feldman, Yi Wu","submitted_at":"2010-12-03T13:11:22Z","abstract_excerpt":"We prove the following strong hardness result for learning: Given a distribution of labeled examples from the hypercube such that there exists a monomial consistent with $(1-\\eps)$ of the examples, it is NP-hard to find a halfspace that is correct on $(1/2+\\eps)$ of the examples, for arbitrary constants $\\eps > 0$. In learning theory terms, weak agnostic learning of monomials is hard, even if one is allowed to output a hypothesis from the much bigger concept class of halfspaces. This hardness result subsumes a long line of previous results, including two recent hardness results for the proper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0729","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"}