提出隐私保护下最优e值检验方法，提升数据效率与安全性。
Optimal Rates for Differentially Private Hypothesis Testing with E-values
- 设计满足ε-差分隐私的e值检验算法，实现理论最优性能。
- 在序列检验中证明停止时间上下界匹配，确保高效决策。
- 实测显示比现有方法更省数据，适用于隐私敏感场景。
近年来，e值因其支持任意时间验证和自适应数据分析而受到广泛关注。假设检验是其核心应用之一，常涉及私密或敏感数据。本文回答了一个关键问题：给定两个分布 $\mathbb{P}$ 与 $\mathbb{Q}$，在满足 $\varepsilon$-差分隐私的e值约束下，测试 $X\sim \mathbb{P}^n$ 对 $X\sim \mathbb{Q}^n$ 的最大可实现e幂是多少？我们刻画了该问题的最优率，并给出一个能精确达到该率的算法。在序列设定中，观测逐个到达，分析者决定何时停止，我们给出了任意私密e过程停止时间的匹配上下界。数值实验表明，所提算法在多种序列检验问题与隐私级别下，所需数据量少于最近提出的DP-SPRT。
原文摘要 · Abstract (English)
E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions $\mathbb{P}$ and $\mathbb{Q}$, what is the maximum achievable e-power when testing $X\sim \mathbb{P}^n$ against $X\sim\mathbb{Q}^n$ with e-values that satisfy $\varepsilon$-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and the analyst chooses when to halt, we give matching upper and lower bounds on the stopping times of any private e-process. Numerical experiments confirm the practicality of our algorithms, which require less data than the recently proposed DP-SPRT across a range of sequential testing problems and privacy levels.
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