Structure and Sensitivity in Differential Privacy: ComparingK-Norm Mechanisms

• 成果类型: Article
• 署名作者: Awan, Jordan; Slavkovic, Aleksandra
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1773831
• 发表日期: 2021
• 页码: 935-954
• 关键词: risk; disclosure; regression; notions

摘要

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 vectorT, a function of sensitive data under DP, via the class ofK-norm mechanisms with the goal of minimizing the noise added to achieve privacy. First, we introduce thesensitivity space of T, which extends the concepts of sensitivity polytope and sensitivity hull to the setting of arbitrary statisticsT. We then propose a framework consisting of three methods for comparing theK-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 optimalK-norm mechanism. In all of these criteria, the optimalK-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.