论文标题
log-concove和多元规范噪声分布，用于差异隐私
Log-Concave and Multivariate Canonical Noise Distributions for Differential Privacy
论文作者
论文摘要
规范噪声分布（CND）是一种添加机制，旨在满足$ f $ -Difference的隐私（$ f $ -DP），而没有任何浪费的隐私预算。 $ f $ -DP是一种基于假设检验的基于折衷函数的隐私措辞的表述，它捕捉了假设检验的难度。在本文中，我们考虑了对数 - 孔孔CND和多元CND的存在和构建。对数符号分布对于确保机制的较高输出对应于较高的输入值很重要，而多变量噪声分布对于确保多个输出的联合释放具有紧密的隐私表征很重要。我们表明，两种类型问题的CND的存在和构建与功能组成（与组隐私）或机制组成有关的权衡函数是否可以分解。特别是，我们表明，纯$ε$ -DP不能以两种方式分解，并且既没有log-concove cnd，也不有任何以$ε$ -DP为单位的CND。另一方面，我们表明高斯-DP，$（0，δ）$ -DP和Laplace-DP每个都具有对数concove和多元CND的含量。
A canonical noise distribution (CND) is an additive mechanism designed to satisfy $f$-differential privacy ($f$-DP), without any wasted privacy budget. $f$-DP is a hypothesis testing-based formulation of privacy phrased in terms of tradeoff functions, which captures the difficulty of a hypothesis test. In this paper, we consider the existence and construction of both log-concave CNDs and multivariate CNDs. Log-concave distributions are important to ensure that higher outputs of the mechanism correspond to higher input values, whereas multivariate noise distributions are important to ensure that a joint release of multiple outputs has a tight privacy characterization. We show that the existence and construction of CNDs for both types of problems is related to whether the tradeoff function can be decomposed by functional composition (related to group privacy) or mechanism composition. In particular, we show that pure $ε$-DP cannot be decomposed in either way and that there is neither a log-concave CND nor any multivariate CND for $ε$-DP. On the other hand, we show that Gaussian-DP, $(0,δ)$-DP, and Laplace-DP each have both log-concave and multivariate CNDs.
