Structure and Sensitivity in Differential Privacy: Comparing K-Norm Mechanisms
Structure and Sensitivity in Differential Privacy: Comparing K-Norm Mechanisms
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DOI：
10.1080/01621459.2020.1773831
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发表时间：
2018-01
影响因子：
3.7
通讯作者：
Jordan Awan;A. Slavkovic
中科院分区：
文献类型：
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作者：
Jordan Awan;A. Slavkovic
摘要差分隐私（DP）提供了一个框架，可证明的隐私保护对任意的对手，同时允许发布摘要统计和合成数据。我们解决的问题，释放一个嘈杂的实值统计向量T，DP下的敏感数据的函数，通过类的K-范数机制的目标是最大限度地减少噪音，以实现隐私。首先引入T的灵敏度空间，将灵敏度多面体和灵敏度船体的概念推广到任意统计量T的设置。然后，我们提出了一个框架，包括三种方法来比较K-范数机制：（1）随机优势的多元扩展，（2）机制的熵，（3）给定方向的条件方差，以确定最佳的K-范数机制。在所有这些准则中，最优K-范数机构由灵敏度空间的凸船体生成。使用我们的方法，我们扩展了客观扰动和功能机制，并将这些工具应用于逻辑和线性回归，允许私人发布的统计结果。通过模拟和住房价格数据集的应用，我们证明了我们提出的方法提供了一个实质性的改进，在相同的风险水平的效用。
Abstract Differential privacy (DP) provides a framework for provable privacy protection against arbitrary adversaries, while allowing the release of summary statistics and synthetic data. We address the problem of releasing a noisy real-valued statistic vector T, a function of sensitive data under DP, via the class of K-norm mechanisms with the goal of minimizing the noise added to achieve privacy. First, we introduce the sensitivity space of T, which extends the concepts of sensitivity polytope and sensitivity hull to the setting of arbitrary statistics T. We then propose a framework consisting of three methods for comparing the K-norm mechanisms: (1) a multivariate extension of stochastic dominance, (2) the entropy of the mechanism, and (3) the conditional variance given a direction, to identify the optimal K-norm mechanism. In all of these criteria, the optimal K-norm mechanism is generated by the convex hull of the sensitivity space. Using our methodology, we extend the objective perturbation and functional mechanisms and apply these tools to logistic and linear regression, allowing for private releases of statistical results. Via simulations and an application to a housing price dataset, we demonstrate that our proposed methodology offers a substantial improvement in utility for the same level of risk.