{"paper":{"title":"Compressed Sensing with Adversarial Sparse Noise via L1 Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Eric Price, Sushrut Karmalkar","submitted_at":"2018-09-21T12:15:49Z","abstract_excerpt":"We present a simple and effective algorithm for the problem of \\emph{sparse robust linear regression}. In this problem, one would like to estimate a sparse vector $w^* \\in \\mathbb{R}^n$ from linear measurements corrupted by sparse noise that can arbitrarily change an adversarially chosen $\\eta$ fraction of measured responses $y$, as well as introduce bounded norm noise to the responses. For Gaussian measurements, we show that a simple algorithm based on L1 regression can successfully estimate $w^*$ for any $\\eta < \\eta_0 \\approx 0.239$, and that this threshold is tight for the algorithm. The n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08055","kind":"arxiv","version":4},"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"}