{"paper":{"title":"Sparse Support Recovery with Non-smooth Loss Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gabriel Peyr\\'e, Jalal M. Fadili, K\\'evin Degraux, Laurent Jacques","submitted_at":"2016-11-03T14:10:46Z","abstract_excerpt":"In this paper, we study the support recovery guarantees of underdetermined sparse regression using the $\\ell_1$-norm as a regularizer and a non-smooth loss function for data fidelity. More precisely, we focus in detail on the cases of $\\ell_1$ and $\\ell_\\infty$ losses, and contrast them with the usual $\\ell_2$ loss. While these losses are routinely used to account for either sparse ($\\ell_1$ loss) or uniform ($\\ell_\\infty$ loss) noise models, a theoretical analysis of their performance is still lacking. In this article, we extend the existing theory from the smooth $\\ell_2$ case to these non-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01030","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"}