Title: Differentially private uniformly most powerful tests for binomial data
Authors: Jordan Awan - Penn State University (United States) [presenting]
Aleksandra Slavkovic - Penn State University (United States)
Abstract: Uniformly most powerful (UMP) tests are derived for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis tests for exchangeable data can always be expressed as a function of the empirical distribution. Using this structure, we prove a `Neyman-Pearson lemma' for binomial data under DP, where the DP-UMP only depends on the sample sum. The tests can also be stated as a post-processing of a random variable, whose distribution we coin `Truncated-Uniform-Laplace' (Tulap), a generalization of the Staircase and discrete Laplace distributions. Furthermore, we obtain exact $p$-values, which are easily computed in terms of the Tulap random variable. We show that our results also apply to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that our tests have exact type I error, and are more powerful than current techniques.