Probabilistic Network Metrics: Variational Bayesian Network Centrality
Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we connect network metrics to modern probabilistic machine learning. We focus on the centrality metric, which is used a wide variety of applications from web search to gene-analysis. First, we formulate an eigenvector-based Bayesian centrality model for determining node importance. Compared to existing methods, our probabilistic model allows for the assimilation of multiple edge weight observations, the inclusion of priors and the extraction of uncertainties. To enable tractable inference, we develop a variational lower bound (VBC) that is demonstrated to be effective on a variety of networks (two synthetic and five real-world graphs). We then bridge this model to sparse Gaussian processes. The sparse variational Bayesian centrality Gaussian process (VBC-GP) learns a mapping between node attributes to latent centrality and hence, is capable of predicting centralities from node features and can potentially 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 two-step baseline, i.e., a full GP trained on the node attributes and pre-computed centralities. Finally, we present two case-studies using the VBC-GP: first, to ascertain relevant features in a taxi transport network and second, to distribute a limited number of vaccines to mitigate the severity of a viral outbreak.