Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. In this paper, we proposed a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates of hyperparameters. Efficient maximum a posteriori (MAP) estimation is completed through a Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm. The PX-ECM results in a robust computationally efficient coordinate-wise optimization, which adjusts for the impact of other predictor variables. The completion of the E-step uses an approach motivated by the popular two-groups approach to multiple testing. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression, which can be completed using one-at-a-time or all-at-once type optimization. We compare the empirical properties of PROBE to comparable approaches with numerous simulation studies and an analysis of cancer cell lines drug response study. The proposed approach is implemented in the R package probe.

翻译：贝叶斯变量选择方法是拟合和推断稀疏高维线性回归模型的强大技术。然而，许多方法计算成本高昂，或需要对模型参数施加限制性先验分布。本文提出了一种计算高效且强大的贝叶斯方法，用于稀疏高维线性回归。通过使用超参数的经验贝叶斯插件估计，对参数施加了最少的先验假设。有效的最大后验估计（MAP）通过参数扩展期望条件最大化（PX-ECM）算法完成。PX-ECM算法实现了稳健且计算高效的坐标优化，该优化调整了其他预测变量的影响。E步骤的完成采用了受流行双组多重检验方法启发的方法。由此产生的分区经验贝叶斯ECM（PROBE）算法应用于稀疏高维线性回归，可通过逐次优化或全局优化方式完成。我们通过大量模拟研究和癌症细胞系药物反应研究的分析，将PROBE的经验特性与类似方法进行了比较。所提出方法已在R包probe中实现。