{"paper":{"title":"SLOPE - Adaptive variable selection via convex optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Chiara Sabatti, Emmanuel J. Cand\\`es, Ewout van den Berg, Ma{\\l}gorzata Bogdan, Weijie Su","submitted_at":"2014-07-14T21:29:23Z","abstract_excerpt":"We introduce a new estimator for the vector of coefficients $\\beta$ in the linear model $y=X\\beta+z$, where $X$ has dimensions $n\\times p$ with $p$ possibly larger than $n$. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to \\[\\min_{b\\in\\mathbb{R}^p}\\frac{1}{2}\\Vert y-Xb\\Vert _{\\ell_2}^2+\\lambda_1\\vert b\\vert _{(1)}+\\lambda_2\\vert b\\vert_{(2)}+\\cdots+\\lambda_p\\vert b\\vert_{(p)},\\] where $\\lambda_1\\ge\\lambda_2\\ge\\cdots\\ge\\lambda_p\\ge0$ and $\\vert b\\vert_{(1)}\\ge\\vert b\\vert_{(2)}\\ge\\cdots\\ge\\vert b\\vert_{(p)}$ are the decreasing absolute values of the entries of $b$. This is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3824","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"}