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Abstract:
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Given the network structure and ultra-high dimensional vectors of nodal attributes, to figure out the active attributes truly influencing the connection among nodes, we propose a Bayesian approach to do variable selection on nodal attributes and estimation on nodal activeness simultaneously. A class of model where the probability of a connection depends on the similarity of their nodal attributes and individual activeness is developed. Nodes have similar information or with higher activeness are more likely to be connected. Based on different sparsity assumption on nodal activeness, two kinds of models are discussed in details. The proposed models can be implemented via Gibbs sampler and the selection consistency is shown for both models, in the sense that the posterior probability of true model being selected converges to one even when the dimension grows near exponentially with the network size. Our models also allow high correlation among covariates and infinity many active variables. The performance of the proposed models are further investigated through simulation, and a real data example about Facebook friendship network demonstrates the feasibility of our model.
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