Empirical bayes variable selection in high-dimensional regression

Available high-throughput biotechnologies make it necessary to select important candidates out of massive biomarkers while exploiting their complicated relationship structures. Here we consider an empirical Bayes method for variable selection in regression models. In most practical situations, Markov chain Monte Carlo (MCMC) algorithms are used for implementation by many previous empirical Bayes variable selection methods. However, these MCMC based procedures are challenged by exponentially growing numbers of biomarkers and involve intensive computing. We propose an iterated conditional modes/medians (ICM/M) algorithm which will be employed to implement an empirical Bayes variable selection in regression models. First, iterative conditional modes are employed to optimize values of the hyperparameters so as to implement the empirical Bayes method; Second, iterative conditional medians are used to estimate the model coefficients and therefore implement the variable selection function. Our simulation studies suggest fast computation and superior performance of the proposed method. The developed algorithm has also been applied to real omics data.