{"paper":{"title":"A closed form scale bound for the $(\\epsilon, \\delta)$-differentially private Gaussian Mechanism valid for all privacy regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.CR","authors_text":"Staal A. Vinterbo","submitted_at":"2020-12-18T21:35:26Z","abstract_excerpt":"The standard closed form lower bound on $\\sigma$ for providing $(\\epsilon, \\delta)$-differential privacy by adding zero mean Gaussian noise with variance $\\sigma^2$ is $\\sigma > \\Delta\\sqrt {2}(\\epsilon^{-1}) \\sqrt {\\log \\left( 5/4\\delta^{-1} \\right)}$ for $\\epsilon \\in (0,1)$. We present a similar closed form bound $\\sigma \\geq \\Delta (\\epsilon\\sqrt{2})^{-1} \\left(\\sqrt{az+\\epsilon} + s\\sqrt{az}\\right)$ for $z=-\\log(4\\delta(1-\\delta))$ and $(a,s)=(1,1)$ if $\\delta \\leq 1/2$ and $(a,s)=(\\pi/4,-1)$ otherwise. Our bound is valid for all $\\epsilon > 0$ and is always lower (better). We also presen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10523","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/2012.10523/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"}