{"paper":{"title":"Consistent Parameter Estimation for LASSO and Approximate Message Passing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Ali Mousavi, Arian Maleki, Richard G. Baraniuk","submitted_at":"2015-11-03T18:05:21Z","abstract_excerpt":"We consider the problem of recovering a vector $\\beta_o \\in \\mathbb{R}^p$ from $n$ random and noisy linear observations $y= X\\beta_o + w$, where $X$ is the measurement matrix and $w$ is noise. The LASSO estimate is given by the solution to the optimization problem $\\hat{\\beta}_{\\lambda} = \\arg \\min_{\\beta} \\frac{1}{2} \\|y-X\\beta\\|_2^2 + \\lambda \\| \\beta \\|_1$. Among the iterative algorithms that have been proposed for solving this optimization problem, approximate message passing (AMP) has attracted attention for its fast convergence. Despite significant progress in the theoretical analysis of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01017","kind":"arxiv","version":2},"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"}