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断框架，用于分布式差分隐私线性回归。考虑一个分布式设置，其中多方持有部分数据，并以保护隐私的噪声形式共享其部分数据的特定汇总统计量。我们为隐私保护的共享统计量开发了一种新颖的生成式统计模型，该模型利用了线性回归汇总统计量之间的有用分布关系。回归系数的贝叶斯估计主要通过马尔可夫链蒙特卡洛算法进行，同时我们也提供了一种快速版本，可在一次迭代中完成贝叶斯估计。所提出的方法在计算上优于现有方法。我们在真实和模拟数据上提供了数值结果，表明所提出的算法能够提供全面的估计和预测。