{"paper":{"title":"Optimal Covariance Estimation for Condition Number Loss in the Spiked Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Behrooz Ghorbani, David L. Donoho","submitted_at":"2018-10-17T07:11:02Z","abstract_excerpt":"We study estimation of the covariance matrix under relative condition number loss $\\kappa(\\Sigma^{-1/2} \\hat{\\Sigma} \\Sigma^{-1/2})$, where $\\kappa(\\Delta)$ is the condition number of matrix $\\Delta$, and $\\hat{\\Sigma}$ and $\\Sigma$ are the estimated and theoretical covariance matrices. Optimality in $\\kappa$-loss provides optimal guarantees in two stylized applications: Multi-User Covariance Estimation and Multi-Task Linear Discriminant Analysis. We assume the so-called spiked covariance model for $\\Sigma$, and exploit recent advances in understanding that model, to derive a nonlinear shrinke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07403","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"}