Bayesian Logistic Gaussian Process Models for Dynamic Networks
Daniele Durante, David B. Dunson · 2014
Time-varying adjacency matrices encoding the presence or absence of a relation among entities are available in many research fields. Motivated by an application to studying dy-namic networks among sports teams, we pro-pose a Bayesian nonparametric model. The proposed approach uses a logistic mapping from the probability matrix, encoding link probabilities between each team, to an em-bedded latent relational space. Within this latent space, we incorporate a dictionary of Gaussian process (GP) latent trajecto-ries characterizing changes over time in each team, while allowing learning of the number of latent dimensions through a specially tai-lored prior for the GP covariance. The model is provably flexible and borrows strength across the network and over time. We provide simulation experiments and an application to the Italian soccer Championship. 1