{"paper":{"title":"Optimal Robust Linear Regression in Nearly Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"stat.ML","authors_text":"Efe Aras, Michael I. Jordan, Nicolas Flammarion, Nilesh Tripuraneni, Peter L. Bartlett, Yeshwanth Cherapanamjeri","submitted_at":"2020-07-16T06:44:44Z","abstract_excerpt":"We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \\langle X,w^* \\rangle + \\epsilon$ (with $X \\in \\mathbb{R}^d$ and $\\epsilon$ independent), in which an $\\eta$ fraction of the samples have been adversarially corrupted. We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $\\mathbb{E} [XX^\\top]$ has bounded condition number and $\\epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $\\epsilon$ is sub-Gaussian. In both settings,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.08137","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/2007.08137/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"}