Differentially Private Uniformly Most Powerful Tests for Binomial Data

By Jordan Awan, Aleksandra B. Slavkovic. 2018

58 citations recorded by the source corpus.

We derive uniformly most powerful (UMP) tests 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. Our 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.

Subfields: Artificial Intelligence, Management Science and Operations Research

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Citations in the corpus

The structure of optimal private tests for simple hypotheses (2018, background): “A recent work by Awan and Slavkovic [5] gives a universally optimal test when the domain size is two, however Brenner and Nissim [13] shows that such universally optimal tests cannot exist when the domain has more than two elements.”
Differentially Private Nonparametric Hypothesis Testing (2019, background): “Awan and Slavkovic recently presented a test for simple binomial data [1].”