Sparse High-Dimensional Linear Regression with PROBE

Implements an efficient and powerful Bayesian approach for sparse high-dimensional linear regression. It uses minimal prior assumptions on the parameters through plug-in empirical Bayes estimates of hyperparameters. An efficient Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm estimates maximum a posteriori (MAP) values of regression parameters and variable selection probabilities. The PX-ECM results in a robust computationally efficient coordinate-wise optimization, which adjusts for the impact of other predictor variables. The E-step is 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, implemented using one-at-a-time or all-at-once type optimization. More information can be found in McLain, Zgodic, and Bondell (2022) .