Variational Bayesian Network Centrality

We present an eigenvector-based Bayesian centrality model for determining node importance in a graph or network. In contrast to existing methods, our model explicitly considers noisy weighted links and thus, allows for the assimilation of multiple observations, the inclusion of priors and the extraction of uncertainties. To enable tractable inference, we develop a variational lower bound that is demonstrated to be effective on a variety of networks (two synthetic and six real-world graphs). We further extend our approach incorporate node attributes, yielding the sparse variational Bayesian centrality Gaussian process (VBC-GP). This model learns a mapping between node attributes/features to latent centrality and hence, is able to represent a large number of nodes using only a limited number of inducing inputs. Experiments show that the VBC-GP learns high-quality mappings and compares favorably to a full-GP trained directly on the node attributes and true network centralities.