Hypothesis Testing Interpretations and Renyi Differential Privacy

Abstract

Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. A way to explain differential privacy, which is particularly appealing to statistician and social scientists is by means of its statistical hypothesis testing interpretation. Informally, one cannot effectively test whether a specific individual has contributed her data by observing the output of a private mechanism---any test cannot have both high significance and high power. In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation. These conditions are useful to analyze the distinguishability power of divergences and we use them to study the hypothesis testing interpretation of some relaxations of differential privacy based on Renyi divergence. This analysis also results in an improved conversion rule between these definitions and differential privacy.

References in corpus (1)

• Gaussian Differential Privacy

Cited by in corpus (8)

• The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation
• Deep Learning with Gaussian Differential Privacy
• Accelerating Vertical Federated Learning
• Optimal Accounting of Differential Privacy via Characteristic Function
• Federated $f$-Differential Privacy
• Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansion
• Enhancing the Antidote: Improved Pointwise Certifications against Poisoning Attacks
• Divergences on Monads for Relational Program Logics