We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.

翻译：我们提出了一种新颖的贝叶斯推理框架，用于分布式差分隐私线性回归。在分布式场景中，多方各自持有部分数据，并以隐私保护噪声形式共享其数据部分的某些汇总统计量。我们开发了一个针对隐私共享统计量的新颖生成式统计模型，该模型利用了线性回归汇总统计量之间一种有用的分布关系。回归系数的贝叶斯估计主要采用马尔可夫链蒙特卡洛算法进行，同时我们提供了一种快速版本，可在单次迭代中完成贝叶斯估计。所提方法在计算效率上优于现有方法。我们在真实数据和模拟数据上展示了数值结果，证明所提算法能提供全面的估计与预测性能。