Bayesian Analysis of High-dimensional Discrete Graphical Models

TL;DR

This paper develops a scalable Bayesian approach with spike-and-slab priors and Langevin MCMC for high-dimensional discrete graphical models, enabling efficient variable selection and accurate estimation.

Contribution

It introduces a novel quasi-likelihood method with parallel computation and a Langevin MCMC algorithm for scalable Bayesian analysis of large discrete graphical models.

Findings

Method demonstrates high scalability and accuracy in simulations.

Successfully applied to 16 Personality Factors dataset.

Enables simultaneous variable selection and estimation.

Abstract

This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced computational complexity. We introduce a scalable Langevin MCMC algorithm for sampling from the quasi-posterior distribution which enables variable selection and estimation simultaneously. We present extensive simulation results to demonstrate scalability and accuracy of the method. We also analyze the 16 Personality Factors (PF) dataset to illustrate performance of the method.