{"paper":{"title":"Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.IT","math.IT","stat.ML"],"primary_cat":"cs.DS","authors_text":"Gautam Kamath, Mahbod Majid, Samuel B. Hopkins","submitted_at":"2021-11-25T09:31:15Z","abstract_excerpt":"We give the first polynomial-time algorithm to estimate the mean of a $d$-variate probability distribution with bounded covariance from $\\tilde{O}(d)$ independent samples subject to pure differential privacy. Prior algorithms for this problem either incur exponential running time, require $\\Omega(d^{1.5})$ samples, or satisfy only the weaker concentrated or approximate differential privacy conditions. In particular, all prior polynomial-time algorithms require $d^{1+\\Omega(1)}$ samples to guarantee small privacy loss with \"cryptographically\" high probability, $1-2^{-d^{\\Omega(1)}}$, while our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.12981","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.12981/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"}