Abstract. Statistics computed from data are viewed as random variables. When they are used for tasks like hypothesis testing and confidence intervals, their true sampling distributions are often replaced by approximating distributions that are easier to work with (for example, the Gaussian, which results from using approximations justified by the Central Limit Theorem). When data are perturbed by differential privacy, the approximating distributions also need to be modified. Prior work provided various competing methods for creating such approximating distributions with little formal justification beyond the fact that they worked well empirically. In this paper, we study the question of how to generate statistical approximating distributions for differentially private statistics, provide finite sample guarantees for the quality of the approximations. We also provide illustrative examples, mostly focusing on chi-squared testing.
Work by Wang et al. REF focuses on generating statistical approximating distributions for differentially private statistics, which they apply to hypothesis testing problems.
Statistical Approximating Distributions Under Differential Privacy
J. Priv. Confidentiality
J. Priv. Confidentiality
Computer Science Mathematics