{"paper":{"title":"Generalization of l1 constraints for high dimensional regression problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"CREST), Mohamed Hebiri (LPMA), Pierre Alquier (LPMA","submitted_at":"2008-11-01T09:01:28Z","abstract_excerpt":"We focus on the high dimensional linear regression $Y\\sim\\mathcal{N}(X\\beta^{*},\\sigma^{2}I_{n})$, where $\\beta^{*}\\in\\mathds{R}^{p}$ is the parameter of interest. In this setting, several estimators such as the LASSO and the Dantzig Selector are known to satisfy interesting properties whenever the vector $\\beta^{*}$ is sparse. Interestingly both of the LASSO and the Dantzig Selector can be seen as orthogonal projections of 0 into $\\mathcal{DC}(s)=\\{\\beta\\in\\mathds{R}^{p},\\|X'(Y-X\\beta)\\|_{\\infty}\\leq s\\}$ - using an $\\ell_{1}$ distance for the Dantzig Selector and $\\ell_{2}$ for the LASSO. Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0072","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"}