Priv’IT: Private and Sample Efficient Identity Testing

Abstract

We develop differentially private hypothesis testing methods for the small sample regime. Given a sample D from a categorical distribution p over some domain , an explicitly described distribution q over , some privacy parameter , accuracy parameter , and requirements _I and _II for the type I and type II errors of our test, the goal is to distinguish between p=q and d_tv(p,q) . We provide theoretical bounds for the sample size |D| so that our method both satisfies (,0)-differential privacy, and guarantees _I and _II type I and type II errors. We show that differential privacy may come for free in some regimes of parameters, and we always beat the sample complexity resulting from running the ^2-test with noisy counts, or standard approaches such as repetition for endowing non-private ^2-style statistics with differential privacy guarantees. We experimentally compare the sample complexity of our method to that of recently proposed methods for private hypothesis testing.

Tasks

Reproductions