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.

翻译：我们提出了一种通过数据截断实现差分隐私（DP）统计估计的新框架，以解决数据支撑集无界时DP估计的关键挑战。传统方法依赖于问题特定的敏感性分析，限制了其适用性。通过利用截断统计技术，我们为指数族分布（包括高斯均值和协方差估计）开发了计算高效的DP估计器，实现了接近最优的样本复杂度。先前关于指数族的工作仅考虑有界或一维分布族。我们的方法通过截断降低敏感性，同时利用最大似然估计和DP随机梯度下降仔细校正引入的偏差。在此过程中，我们为指数族对数似然函数建立了改进的均匀收敛保证，这可能具有独立的研究价值。我们的结果为通过截断统计设计DP算法提供了通用蓝图。