Modeling Dynamic Social Networks with Vertex Evolution via Latent Graphical Models

We here consider the problem of modeling network evolution with joint edge and vertex dynamics. It is natural to expect that the accuracy of vertex prediction strongly affect the ability to predict dynamic network evolution accurately. A latent graphical model is here employed to model vertex evolution. This model family can incorporate dependence in vertex co-presence, of the form found in many social settings (e.g., subgroup structure, selective pairing). Recent algorithms for learning latent tree graphical models and their extensions can be efficiently scaled for large graphs. Here, we introduce a novel latent graphical model based approach to the problem of vertex set prediction in dynamic social networks, combining it with a parametric model for covariate effects and a logistic model for edge prediction given the vertex predictions. We apply this approach to both synthetic data and a classic social network data set involving interactions among windsurfers on a Southern California beach. Experiments conducted show a significant improvement in prediction accuracy of the vertex and edge set evolution (about 45% for conditional vertex participation accuracy and 164% for overall edge prediction accuracy) over the existing dynamic network regression approach for modeling vertex co-presence.