{"paper":{"title":"L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jun S. Liu, Matey Neykov, Tianxi Cai","submitted_at":"2015-11-25T16:00:44Z","abstract_excerpt":"It is known that for a certain class of single index models (SIMs) $Y = f(\\boldsymbol{X}_{p \\times 1}^\\intercal\\boldsymbol{\\beta}_0, \\varepsilon)$, support recovery is impossible when $\\boldsymbol{X} \\sim \\mathcal{N}(0, \\mathbb{I}_{p \\times p})$ and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design $\\boldsymbol{X}$ comes from an i.i.d. Gaussian distribution. In the present paper we analyze algorithms based on covariance s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08102","kind":"arxiv","version":3},"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"}