Abstract:
Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. One way of explaining 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 distinguishing power of divergences and we use them to study the hypothesis testing interpretation of some relaxations of differential privacy based on Renyi divergence. Our analysis also results in an improved conversion rule between these definitions and differential privacy.
