提出首个满足差分隐私的分层抽样最优设计方法。
Optimal Survey Design for Private Mean Estimation
- 将分层抽样建模为子采样，结合差分隐私机制优化分组样本量。
- 在拉普拉斯、离散拉普拉斯等机制下，显著降低均值估计方差。
- 适合关注隐私保护下统计调查效率的研究者与数据科学家。
本文首次识别出在差分隐私（DP）框架下，针对拉普拉斯（Laplace）、离散拉普拉斯（DLap）和截断均匀-拉普拉斯（TuLap）机制的最优隐私感知分层抽样方案，以最小化一般私有均值估计的方差。将分层抽样视为子采样操作，可增强隐私保证；但为保持各组最终隐私预算一致，需根据子采样率分配不同的名义隐私预算。忽略差分隐私影响的传统分层策略可能导致方差显著增加。本文将最优调查设计建模为优化问题，目标是确定各组最优子采样规模以最小化估计器方差。证明了方差目标函数的强凸性，提出了高效算法求解整数最优设计，并揭示了最优设计的结构特征。
原文摘要 · Abstract (English)
This work identifies the first privacy-aware stratified sampling scheme that minimizes the variance for general private mean estimation under the Laplace, Discrete Laplace (DLap) and Truncated-Uniform-Laplace (TuLap) mechanisms within the framework of differential privacy (DP). We view stratified sampling as a subsampling operation, which amplifies the privacy guarantee; however, to have the same final privacy guarantee for each group, different nominal privacy budgets need to be used depending on the subsampling rate. Ignoring the effect of DP, traditional stratified sampling strategies risk significant variance inflation. We phrase our optimal survey design as an optimization problem, where we determine the optimal subsampling sizes for each group with the goal of minimizing the variance of the resulting estimator. We establish strong convexity of the variance objective, propose an efficient algorithm to identify the integer-optimal design, and offer insights on the structure of the optimal design.
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