{"paper":{"title":"Near-Ideal Behavior of Compressed Sensing Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mathukumalli Vidyasagar, Mehmet Eren Ahsen","submitted_at":"2014-01-26T07:38:23Z","abstract_excerpt":"In a recent paper, it is shown that the LASSO algorithm exhibits \"near-ideal behavior,\" in the following sense: Suppose $y = Az + \\eta$ where $A$ satisfies the restricted isometry property (RIP) with a sufficiently small constant, and $\\Vert \\eta \\Vert_2 \\leq \\epsilon$. Then minimizing $\\Vert z \\Vert_1$ subject to $\\Vert y - Az \\Vert_2 \\leq \\epsilon$ leads to an estimate $\\hat{x}$ whose error $\\Vert \\hat{x} - x \\Vert_2$ is bounded by a universal constant times the error achieved by an \"oracle\" that knows the location of the nonzero components of $x$. In the world of optimization, the LASSO alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6623","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"}