{"paper":{"title":"Overcoming The Limitations of Phase Transition by Higher Order Analysis of Regularization Techniques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Arian Maleki, Haolei Weng, Le Zheng","submitted_at":"2016-03-23T21:52:36Z","abstract_excerpt":"We study the problem of estimating $\\beta \\in \\mathbb{R}^p$ from its noisy linear observations $y= X\\beta+ w$, where $w \\sim N(0, \\sigma_w^2 I_{n\\times n})$, under the following high-dimensional asymptotic regime: given a fixed number $\\delta$, $p \\rightarrow \\infty$, while $n/p \\rightarrow \\delta$. We consider the popular class of $\\ell_q$-regularized least squares (LQLS) estimators, a.k.a. bridge, given by the optimization problem: \\begin{equation*} \\hat{\\beta} (\\lambda, q ) \\in \\arg\\min_\\beta \\frac{1}{2} \\|y-X\\beta\\|_2^2+ \\lambda \\|\\beta\\|_q^q, \\end{equation*} and characterize the almost su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07377","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"}