{"paper":{"title":"Learning Noisy Halfspaces with a Margin: Massart is No Harder than Random","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.LG","authors_text":"Gautam Chandrasekaran, Kevin Tian, Konstantinos Stavropoulos, Vasilis Kontonis","submitted_at":"2025-01-16T21:46:53Z","abstract_excerpt":"We study the problem of PAC learning $\\gamma$-margin halfspaces with Massart noise. We propose a simple proper learning algorithm, the Perspectron, that has sample complexity $\\widetilde{O}((\\epsilon\\gamma)^{-2})$ and achieves classification error at most $\\eta+\\epsilon$ where $\\eta$ is the Massart noise rate. Prior works [DGT19,CKMY20] came with worse sample complexity guarantees (in both $\\epsilon$ and $\\gamma$) or could only handle random classification noise [DDK+23,KIT+23] -- a much milder noise assumption. We also show that our results extend to the more challenging setting of learning g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09851","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.09851/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"}