Near-Optimal Private Tests for Simple and MLR Hypotheses

TL;DR

This paper introduces a near-optimal Gaussian differential privacy testing framework for simple and monotone likelihood ratio hypotheses, achieving high efficiency and strong error control with practical performance benefits.

Contribution

It presents a novel private testing mechanism based on a data-driven private mean estimator that matches the non-private test efficiency up to logarithmic factors.

Findings

Private tests outperform existing DP methods in experiments.

Achieves asymptotic efficiency similar to non-private tests.

Maintains conservative type I error control.

Abstract

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.