{"paper":{"title":"Provable Approximations for Constrained $\\ell_p$ Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dan Feldman, David Cohn, Ibrahim Jubran","submitted_at":"2019-02-27T09:24:25Z","abstract_excerpt":"The $\\ell_p$ linear regression problem is to minimize $f(x)=||Ax-b||_p$ over $x\\in\\mathbb{R}^d$, where $A\\in\\mathbb{R}^{n\\times d}$, $b\\in \\mathbb{R}^n$, and $p>0$. To avoid overfitting and bound $||x||_2$, the constrained $\\ell_p$ regression minimizes $f(x)$ over every unit vector $x\\in\\mathbb{R}^d$. This makes the problem non-convex even for the simplest case $d=p=2$. Instead, ridge regression is used to minimize the Lagrange form $f(x)+\\lambda ||x||_2$ over $x\\in\\mathbb{R}^d$, which yields a convex problem in the price of calibrating the regularization parameter $\\lambda>0$. We provide the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10407","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"}