用公开数据提升差分隐私线性回归的精度与稳定性
Enhancing Differentially Private Linear Regression via Public Second-Moment
- 利用公开二阶矩矩阵变换私有数据，优化噪声注入方式
- 理论证明新方法误差更小，条件数更好，更鲁棒
- 适合注重隐私保护下模型精度的研究者使用
利用公开数据信息已成为提升差分隐私（DP）方法效用的关键。传统方法仅基于私有数据加噪，常导致性能严重下降。本文针对无界数据假设下的普通最小二乘估计（OLSE），基于充分统计量扰动（SSP）框架，提出一种新方法：通过公开二阶矩矩阵对私有数据进行变换，计算变换后的 SSP-OLSE，其二阶矩矩阵具有更优的条件数，从而提升估计准确性和鲁棒性。我们推导了该方法与标准 SSP-OLSE 到非隐私 OLSE 的理论误差界，揭示了所提方法在准确性和鲁棒性上的优势。在合成及真实数据集上的实验验证了方法的有效性与实用性。
原文摘要 · Abstract (English)
Leveraging information from public data has become increasingly crucial in enhancing the utility of differentially private (DP) methods. Traditional DP approaches often require adding noise based solely on private data, which can significantly degrade utility. In this paper, we address this limitation in the context of the ordinary least squares estimator (OLSE) of linear regression based on sufficient statistics perturbation (SSP) under the unbounded data assumption. We propose a novel method that involves transforming private data using the public second-moment matrix to compute a transformed SSP-OLSE, whose second-moment matrix yields a better condition number and improves the OLSE accuracy and robustness. We derive theoretical error bounds about our method and the standard SSP-OLSE to the non-DP OLSE, which reveal the improved robustness and accuracy achieved by our approach. Experiments on synthetic and real-world datasets demonstrate the utility and effectiveness of our method.
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