Hypothesis Testing Interpretations and Renyi Differential Privacy
This work provides a theoretical analysis for statisticians and social scientists to better understand privacy guarantees, though it is incremental in nature.
The paper tackles the problem of interpreting privacy definitions through statistical hypothesis testing, specifically for relaxations of differential privacy based on Rényi divergence, and results in an improved conversion rule between these definitions and standard differential privacy.
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.