{"paper":{"title":"A Fast Algorithm for Adaptive Private Mean Estimation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","cs.DS","cs.LG"],"primary_cat":"stat.ML","authors_text":"John Duchi, Rohith Kuditipudi, Saminul Haque","submitted_at":"2023-01-17T18:44:41Z","abstract_excerpt":"We design an $(\\varepsilon, \\delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\\Sigma$, that is adaptive to $\\Sigma$. To within polylogarithmic factors, the estimator achieves optimal rates of convergence with respect to the induced Mahalanobis norm $||\\cdot||_\\Sigma$, takes time $\\tilde{O}(n d^2)$ to compute, has near linear sample complexity for sub-Gaussian distributions, allows $\\Sigma$ to be degenerate or low rank, and adaptively extends beyond sub-Gaussianity. Prior to this work, other methods required exponential comput"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07078","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.07078/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"}