Hierarchical Skinny Gibbs Sampler in Logistic Regression Using Pólya-Gamma Latent Variables

Music City Center 

This paper introduces a highly scalable tuning-free algorithm for variable selction in logistic regression Using Pólya-Gamma data augmentation. The proposed method is both theoretically consitent and robust to potential misspecification of the tuning parameter, achived through a hierarchical approach. Exisiting works suitable for high-dimensional settings primarily rely on t-approximation of the logistic density, which is not based on the original likelihood. The proposed method not only builds upon the exact logisitc likelihood, offering superior emperical performance, but is also more computationally efficient, particularly in cases involving highly correlated covariates, as demonstrated in a comprehensive simuation study. We apply our method to a gene expression PCR data from mice and RNA-seq dataset from asthma studies in humans. By comparing its performance to existing frequentist and Bayesian methods in variable selection, we demonstrate the competitive predictive capabilities od the Pólya-Gamma-based approach. Our results indicate that this method enhances the accuracy of variable selection and improves the robutness of predictions in complex, high-dimensional datasets.

Logistic regression

Pólya-Gamma distribution

Hierarchical Skinny Gibbs

Spike-and-Slab prior 

Section on Bayesian Statistical Science