用经验贝叶斯方法改进高斯差分隐私输出，提升精度
Enhancing Differentially Private Mechanisms via Empirical Bayes
- 以高斯机制输出为输入，用经验贝叶斯去噪提升性能
- 在直方图、主成分分析等任务中显著降低均方误差
- 方法简单高效，适合追求实用性的隐私保护研究者
差分隐私（DP）已成为保障机器学习与统计算法隐私安全的黄金标准。尽管已有大量方法试图在保持相同隐私水平的前提下提升算法效用，但许多方法过于复杂或计算效率低。本文提出一种新方法：通过引入经验贝叶斯估计思想，对简单的加性高斯机制输出进行去噪。研究表明，仅利用高斯机制输出作为输入，经验贝叶斯方法即可有效降低均方误差。数值实验显示，该方法可广泛应用于直方图发布、主成分分析和线性回归等统计任务，常优于现有私有化算法。
原文摘要 · Abstract (English)
Differential privacy (DP) has become the gold standard for ensuring the privacy protection of machine learning and statistical algorithms in recent decades. A plethora of algorithms and methods have been developed to enhance the utility of DP algorithms while maintaining the same level of DP. However, these are often overly complex or computationally ineffective. We propose a novel approach focusing on denoising the output of the simple additive Gaussian mechanism by adopting the idea of \textit{empirical Bayes estimation}. We highlight that the empirical Bayes approach can reduce the mean-squared error solely by taking the output of the Gaussian mechanism as input. Our numerical studies show that this simple yet powerful approach can be applied to improve upon various statistical problems, including histogram release, principal component analysis, and linear regression, often outperforming existing private algorithms.
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