Differential privacy is typically ensured by perturbation with additive noise that is sampled from a known distribution. Conventionally, independent and identically distributed (i.i.d.) noise samples are added to each coordinate. In this work, propose to add noise which is independent, but not identically distributed (i.n.i.d.) across the coordinates. In particular, we study the i.n.i.d. Gaussian and Laplace mechanisms and obtain the conditions under which these mechanisms guarantee privacy. The optimal choice of parameters that ensure these conditions are derived theoretically. Theoretical analyses and numerical simulations show that the i.n.i.d. mechanisms achieve higher utility for the given privacy requirements compared to their i.i.d. counterparts.

翻译：差分隐私通常通过添加来自已知分布的加性噪声来实现扰动。传统上，对每个坐标添加独立同分布（i.i.d.）的噪声样本。本文提出一种各坐标间独立但非同分布（i.n.i.d.）的加噪方法。具体而言，我们研究了i.n.i.d.高斯机制和拉普拉斯机制，推导了这些机制保障隐私所需的条件，并从理论上给出了满足条件的最优参数选择。理论分析与数值模拟表明，与对应的i.i.d.机制相比，i.n.i.d.机制在给定隐私需求下能够实现更高的效用。