Variable Selection for High-Dimensional Nodal Attributes in Social Networks with Degree Heterogeneity
提出一种贝叶斯方法，用于在稠密和稀疏网络中从超高维节点特征中选择重要变量，同时考虑节点流行度差异，并通过吉布斯采样实现。
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.