{"paper":{"title":"Better and Simpler Lower Bounds for Differentially Private Statistical Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DS","cs.IT","cs.LG","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Shyam Narayanan","submitted_at":"2023-10-10T04:02:43Z","abstract_excerpt":"We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\\alpha \\le O(1)$, estimating the covariance of a Gaussian up to spectral error $\\alpha$ requires $\\tilde{\\Omega}\\left(\\frac{d^{3/2}}{\\alpha \\varepsilon} + \\frac{d}{\\alpha^2}\\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\\alpha \\le O\\left(\\frac{1}{\\sqrt{d}}\\right)$, and is also simpler than previous work. Next, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.06289","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/2310.06289/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"}