{"paper":{"title":"Covariance-Aware Private Mean Estimation Without Private Covariance Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Adam Smith, Gavin Brown, Jonathan Ullman, Lydia Zakynthinou, Marco Gaboardi","submitted_at":"2021-06-24T21:40:07Z","abstract_excerpt":"We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \\gtrsim d/\\alpha^2$ samples from such a distribution with mean $\\mu$ and covariance $\\Sigma$, our estimators output $\\tilde\\mu$ such that $\\| \\tilde\\mu - \\mu \\|_{\\Sigma} \\leq \\alpha$, where $\\| \\cdot \\|_{\\Sigma}$ is the Mahalanobis distance. All previous estimators with the same guarantee either require strong a priori bounds on the covariance matrix or require $\\Omega(d^{3/2})$ samples.\n  Each of our estimators is based on a simpl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.13329","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.13329/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}