{"paper":{"title":"The Ordered Weighted $\\ell_1$ Norm: Atomic Formulation, Projections, and Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.IT","cs.LG","math.IT"],"primary_cat":"cs.DS","authors_text":"M\\'ario A. T. Figueiredo, Xiangrong Zeng","submitted_at":"2014-09-15T14:22:34Z","abstract_excerpt":"The ordered weighted $\\ell_1$ norm (OWL) was recently proposed, with two different motivations: its good statistical properties as a sparsity promoting regularizer; the fact that it generalizes the so-called {\\it octagonal shrinkage and clustering algorithm for regression} (OSCAR), which has the ability to cluster/group regression variables that are highly correlated. This paper contains several contributions to the study and application of OWL regularization: the derivation of the atomic formulation of the OWL norm; the derivation of the dual of the OWL norm, based on its atomic formulation; "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4271","kind":"arxiv","version":5},"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"}