提出近最优的高斯差分隐私检验方法，适用于单调似然比场景。
Near-Optimal Private Tests for Simple and MLR Hypotheses
- 基于自适应截断的私有均值估计器，风险逼近私有最小最大率。
- 检验统计量在小样本下仍保持接近非私有最优检验的效力。
- 适合对隐私保护有要求且需高效统计推断的研究者使用。
我们在高斯差分隐私框架下，为简单及单边、双边检验（满足单调似然比条件）设计了近最优的检验方法。该机制基于一个数据驱动截断边界构造的私有均值估计器，其总体风险在对数因子内达到私有最小最大率。利用该估计器，我们构建的私有检验统计量在渐近相对效率上与非私有最优检验一致，同时保持保守的第一类错误控制。数值实验表明，该方法在中等样本量和较小隐私预算下，性能优于现有差分隐私方法，并能媲美非私有最优检验的检验力。
原文摘要 · Abstract (English)
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.
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