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

• 成果类型: Article
• 署名作者: Wang, Jia; Cai, Xizhen; Niu, Xiaoyue; Li, Runze
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Williams College; Williams College
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2187815
• 发表日期: 2024
• 页码: 1322-1335
• 关键词: model; binary; gibbs

摘要

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.