{"paper":{"title":"Optimal Noise-Adding Mechanism in Additive Differential Privacy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CR","authors_text":"Quan Geng, Ruiqi Guo, Sanjiv Kumar, Wei Ding","submitted_at":"2018-09-26T20:41:01Z","abstract_excerpt":"We derive the optimal $(0, \\delta)$-differentially private query-output independent noise-adding mechanism for single real-valued query function under a general cost-minimization framework. Under a mild technical condition, we show that the optimal noise probability distribution is a uniform distribution with a probability mass at the origin. We explicitly derive the optimal noise distribution for general $\\ell^p$ cost functions, including $\\ell^1$ (for noise magnitude) and $\\ell^2$ (for noise power) cost functions, and show that the probability concentration on the origin occurs when $\\delta "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10224","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":""},"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"}