用截断法实现无界数据的差分隐私统计估计，效率高且接近最优。
Private Statistical Estimation via Truncation
- 通过数据截断降低敏感度，结合最大似然与随机梯度优化
- 在高斯均值与协方差估计中实现近最优样本复杂度
- 适用于指数族分布，为隐私算法设计提供通用框架
我们提出一种基于数据截断的新型差分隐私（DP）统计估计框架，解决数据支撑集无界的难题。传统方法依赖特定问题的敏感度分析，适用性受限。利用截断统计技术，我们构建了针对指数族分布（如高斯均值与协方差）的计算高效DP估计器，达到近最优样本复杂度。此前研究仅涵盖有界或一维指数族。本方法通过截断控制敏感度，并结合最大似然估计与DP随机梯度下降校正引入偏差。过程中建立了指数族对数似然函数的改进统一收敛性保证，可能具有独立价值。结果为基于截断统计的DP算法设计提供了通用范式。
原文摘要 · Abstract (English)
We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific sensitivity analysis, limiting their applicability. By leveraging techniques from truncated statistics, we develop computationally efficient DP estimators for exponential family distributions, including Gaussian mean and covariance estimation, achieving near-optimal sample complexity. Previous works on exponential families only consider bounded or one-dimensional families. Our approach mitigates sensitivity through truncation while carefully correcting for the introduced bias using maximum likelihood estimation and DP stochastic gradient descent. Along the way, we establish improved uniform convergence guarantees for the log-likelihood function of exponential families, which may be of independent interest. Our results provide a general blueprint for DP algorithm design via truncated statistics.
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