2018/01/28 by Jordan Awan, Awan, Jordan, Aleksandra Slavković +1 · 2 citations
Computer Science · Mathematics · #62J05 #62J07 #62J12 #68W20 #Advanced Causal Inference Techniques #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Methodology (stat.ME) #Privacy-Preserving Technologies in Data #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1801.09236
openalex publication_date 2018/01/28 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Differential privacy (DP), provides a framework for provable privacy\nprotection against arbitrary adversaries, while allowing the release of summary\nstatistics and synthetic data. We address the problem of releasing a noisy\nreal-valued statistic vector T, a function of sensitive data under DP, via\nthe class of K-norm mechanisms with the goal of minimizing the noise added to\nachieve privacy. First, we introduce the sensitivity space of T, which\nextends the concepts of sensitivity polytope and sensitivity hull to the\nsetting of arbitrary statistics T. We then propose a framework consisting of\nthree methods for comparing the K-norm mechanisms: 1) a multivariate\nextension of stochastic dominance, 2) the entropy of the mechanism, and 3) the\nconditional variance given a direction, to identify the optimal K-norm\nmechanism. In all of these criteria, the optimal K-norm mechanism is\ngenerated by the convex hull of the sensitivity space. Using our methodology,\nwe extend the objective perturbation and functional mechanisms and apply these\ntools to logistic and linear regression, allowing for private releases of\nstatistical results. Via simulations and an application to a housing price\ndataset, we demonstrate that our proposed methodology offers a substantial\nimprovement in utility for the same level of risk.\n