Near-Optimal Private Tests for Simple and MLR Hypotheses
This provides improved privacy-preserving statistical testing for data analysts working with sensitive data, representing a strong incremental advance in differential privacy methodology.
The paper tackles the problem of developing differentially private hypothesis tests that maintain statistical power while controlling type I error, achieving asymptotic relative efficiency matching non-private most powerful tests and outperforming competing DP methods in numerical experiments.
We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator with data-driven clamping bounds, whose population risk matches the private minimax rate up to logarithmic factors. Using this estimator, we construct private test statistics that achieve the same asymptotic relative efficiency as the non-private, most powerful tests while maintaining conservative type I error control. In addition to our theoretical results, our numerical experiments show that our private tests outperform competing DP methods and offer comparable power to the non-private most powerful tests, even at moderately small sample sizes and privacy loss budgets.