{"paper":{"title":"Efficient Algorithms and Lower Bounds for Robust Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Alistair Stewart, Ilias Diakonikolas, Weihao Kong","submitted_at":"2018-05-31T18:23:29Z","abstract_excerpt":"We study the problem of high-dimensional linear regression in a robust model where an $\\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are drawn from a Gaussian distribution $\\mathcal{N}(0, \\Sigma)$ on $\\mathbb{R}^d$. We give nearly tight upper bounds and computational lower bounds for this problem. Specifically, our main contributions are as follows:\n  For the case that the covariance matrix is known to be the identity, we give a sample near-optimal and computationally efficient algorithm tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00040","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"}