Low Rank Correction Quantile Variational Bayesian Algorithm for Multi-Source Heterogeneous Models

A Low Rank Correction Variational Bayesian algorithm for high-dimensional multi-source heterogeneous quantile linear models. More details have been written up in a paper submitted to the journal Statistics in Medicine, and the details of variational Bayesian methods can be found in Ray and Szabo (2021) . It simultaneously performs parameter estimation and variable selection. The algorithm supports two model settings: (1) local models, where variable selection is only applied to homogeneous coefficients, and (2) global models, where variable selection is also performed on heterogeneous coefficients. Two forms of parameter estimation are output: one is the standard variational Bayesian estimation, and the other is the variational Bayesian estimation corrected with low-rank adjustment.