Variable Selection for High-Dimensional Nodal Attributes in Social Networks with Degree Heterogeneity

We consider a class of network models, in which the connection probability depends on ultrahigh-dimensional nodal covariates (homophily) and node-specific popularity (degree heterogeneity). A Bayesian method is proposed to select nodal features in both dense and sparse networks under a mild assumption on popularity parameters. The proposed approach is implemented via Gibbs sampling. To alleviate the computational burden for large sparse networks, we further develop a working model in which parameters are updated based on a dense sub-graph at each step. Model selection consistency is established for both models, in the sense that the probability of the true model being selected converges to one asymptotically, even when the dimension grows with the network size at an exponential rate. The performance of the proposed models and estimation procedures are illustrated through Monte Carlo studies and three real world examples. for this article are available online.

Automated summary

This article introduces a class of network models where the likelihood of connection is influenced by high-dimensional nodal covariates and node-specific popularity. A Bayesian method is proposed for feature selection, with implementation via Gibbs sampling. To address computational challenges in large sparse networks, a working model is developed for parameter updates based on dense sub-graphs. Model selection consistency is proven for both models, even when dimension grows exponentially. Monte Carlo studies and real world examples illustrate the performance of the proposed models and estimation procedures. Supplementary materials are available online.