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

Abstract

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. Supplementary materials for this article are available online.

Keywords:

• Bayesian variable selection
• Degree heterogeneity
• Network analysis
• Selection consistency

Supplementary Materials

The supplement of this article consists of several technical lemmas and technical proofs of Lemma 2.2 and Theorem 2.3, estimation procedure for BSM-net.sp and additional numerical results.

Disclosure Statement

There are no relevant competing interests to declare.

Additional information

Funding

The authors made equal contribution to this work and are listed in the order of seniority. The authors would like to thank the AE and reviewers for their constructive comments, which leads to a significant improvement of this work. Wang and Li’s research was supported by National Science Foundation DMS-1820702 and NIAID/NIH grants R01AI170249 and R01-AI136664. Niu’s research was partially supported by NIAID/NIH R01-AI136664. The content is solely the responsibility of the authors and does not necessarily represent the official views of NSF or NIH.