{"paper":{"title":"Support union recovery in high-dimensional multivariate regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Guillaume Obozinski, Martin J. Wainwright, Michael I. Jordan","submitted_at":"2008-08-05T20:17:40Z","abstract_excerpt":"In multivariate regression, a $K$-dimensional response vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\\in\\mathbb{R}^{p\\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the $\\ell_1/\\ell_2$ norm is used for support union recovery, or recovery of the set of $s$ rows for which $B^*$ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0711","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"}