{"paper":{"title":"List-Decodable Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Adam R. Klivans, Pravesh K. Kothari, Sushrut Karmalkar","submitted_at":"2019-05-14T15:43:33Z","abstract_excerpt":"We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples.\n  For any $\\alpha < 1$, our algorithm takes as input a sample $\\{(x_i,y_i)\\}_{i \\leq n}$ of $n$ linear equations where $\\alpha n$ of the equations satisfy $y_i = \\langle x_i,\\ell^*\\rangle +\\zeta$ for some small noise $\\zeta$ and $(1-\\alpha)n$ of the equations are {\\em arbitrarily} chosen. It outputs a list $L$ of size $O(1/\\alpha)$ - a fixed constant - that contains an $\\ell$ that is close to $\\ell^*$.\n  Our algorithm succeeds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05679","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"}