论文标题
稀疏的高维线性回归，具有分区的经验贝叶斯ECM算法
Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm
论文作者
论文摘要
贝叶斯变量选择方法是适合和推断稀疏高维线性回归模型的强大技术。但是，许多在计算密集型上或需要对模型参数的限制性先验分布。在本文中，我们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。通过使用插件的经验贝叶斯估算超参数的估计，需要对参数的最小假设。有效的最大后验（MAP）估计是通过参数扩展的期望 - 条件最大化（PX-ECM）算法完成的。 PX-ECM会产生强大的计算有效坐标优化的优化，在更新特定预测变量的系数时，可以调整其他预测变量的影响。 E-Step的完成使用了一种通过流行的两组方法进行多次测试的方法。结果是应用于稀疏高维线性回归的划分经验贝叶斯ECM（探针）算法，该算法可以使用一次性或全面的一致类型优化来完成。我们将探针的经验特性与可比较方法进行了比较，并对癌细胞药物反应进行了许多模拟研究和分析。提出的方法在R软件包探针中实现。
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 required 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 -- when updating the coefficient for a particular predictor -- adjusts for the impact of other predictor variables. The completion of the E-step uses an approach motivated by the popular two-group 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 analyses of cancer cell drug responses. The proposed approach is implemented in the R package probe.
