{"paper":{"title":"Sparse regression with highly correlated predictors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behrooz Ghorbani, Ozgur Yilmaz","submitted_at":"2015-04-04T06:08:31Z","abstract_excerpt":"We consider a linear regression $y=X\\beta+u$ where $X\\in\\mathbb{\\mathbb{{R}}}^{n\\times p}$, $p\\gg n,$ and $\\beta$ is $s$-sparse. Motivated by examples in financial and economic data, we consider the situation where $X$ has highly correlated and clustered columns. To perform sparse recovery in this setting, we introduce the \\emph{clustering removal algorithm} (CRA), that seeks to decrease the correlation in $X$ by removing the cluster structure without changing the parameter vector $\\beta$. We show that as long as certain assumptions hold about $X$, the decorrelated matrix will satisfy the rest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00984","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"}