High-Dimensional Covariate-Dependent Discrete Graphical Models and Dynamic Ising Models

TL;DR

This paper introduces a covariate-dependent discrete graphical model for dynamic networks among discrete variables, utilizing pseudo-likelihood for high-dimensional parameter estimation and a MCMC algorithm for model selection.

Contribution

It develops a novel covariate-dependent framework for dynamic discrete networks, extending the dynamic Ising model, with efficient estimation and model selection methods.

Findings

Effective high-dimensional parameter estimation using pseudo-likelihood.

Successful model selection via birth-and-death MCMC algorithm.

Framework generalizes dynamic Ising models to include covariate dependence.

Abstract

We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses the dynamic Ising model as a special case. We formulate a likelihood-based approach for parameter estimation and statistical inference. We achieve efficient parameter estimation in high-dimensional settings through the use of the pseudo-likelihood method. To perform model selection, a birth-and-death Markov chain Monte Carlo algorithm is proposed to explore the model space and select the most suitable model.