Papers › Priv'IT: Private and Sample Efficient Identity Testing

Priv'IT: Private and Sample Efficient Identity Testing

29 Mar 2017arXiv:1703.10127archive 2025-07-28

Bryan Cai, Constantinos Daskalakis, Gautam Kamath

We develop differentially private hypothesis testing methods for the small sample regime. Given a sample D from a categorical distribution p over some domain Σ, an explicitly described distribution q over Σ, some privacy parameter ε, accuracy parameter α, and requirements β_I and β_(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) ≥α. We provide theoretical bounds for the sample size |D| so that our method both satisfies (ε,0)-differential privacy, and guarantees β_I and β_(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 χ²-test with noisy counts, or standard approaches such as repetition for endowing non-private χ²-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.

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