Simultaneous Variable and Covariance Selection With the Multivariate Spike-and-Slab LASSO
提出一种贝叶斯方法，在多元线性回归中同时选择重要变量和协方差，通过ECM算法估计系数和精度矩阵，在模拟和高中橄榄球对晚年影响的实证研究中表现优于正则化方法。
We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Ročková and George targeting modal estimates of the matrix of regression coefficients and residual precision matrix. Varying the scale of the continuous spike densities facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial covariances gradually. Our method is seen to substantially outperform regularization competitors on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several later-life cognition, psychological, and socio-economic outcomes. An R package, scripts for replicating examples in this article, and results from further simulation studies are provided in the supplementary materials available online.