🤖 AI Summary
This paper addresses the problem of modeling discrete dynamic graphs under high-dimensional covariate-dependent dependencies. We propose a class of covariate-driven dynamic discrete graph models that capture smoothly evolving network structures among discrete random variables as functions of covariates, subsuming the dynamic Ising model as a special case. Methodologically, we introduce a pseudo-likelihood-based high-dimensional parameter estimation framework to circumvent the intractability of exact likelihood computation, and integrate a birth-death MCMC algorithm for adaptive sparse graph structure selection. Theoretically and empirically, our approach achieves both statistical consistency and computational efficiency in high-dimensional settings, substantially improving identification accuracy and inferential robustness for covariate-dependent dynamic networks. This work provides a novel paradigm for modeling conditional dependence structures in complex systems—such as neural activity and social contagion—where interactions evolve with contextual covariates.
📝 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.