Relational data--like graphs, networks, and matrices--is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of underlying relations between entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components.

Statistical analysis of social networks and other relational data is becoming an increasingly important problem as the scope and availability of network data increases. Network data--such as the friendships in a social network--is often dynamic in a sense that relations between entities rise and decay over time. A fundamental problem in the analysis of such dynamic network data is to extract a summary of the common structure and the dynamics of the underlying relations between entities. Accurate models of structure and dynamics of network data have many applications. They allow us to predict missing relationships [20, 21, 23], recommend potential new relations [2], identify clusters and groups of nodes [1, 29], forecast future links [4, 9, 11, 24], and even predict group growth and longevity [15]. Here we present a new approach to modeling network dynamics by considering time-evolving interactions between groups of nodes as well as the arrival and departure dynamics of individual nodes to these groups. We develop a dynamic network model, Dynamic Multi-group Membership Graph Model, that identifies the birth and death of individual groups as well as the dynamics of node joining and leaving groups in order to explain changes in the underlying network linking structure. Our nonparametric model considers an infinite number of latent groups, where each node can belong to multiple groups simultaneously. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model.

Relational data-like graphs, networks, and matrices-is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components: We model the birth and death of individual groups with respect to the dynamics of the network structure via a distance dependent Indian Buffet Process. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model. And, we explain the dynamics of the network structure by explicitly modeling the connectivity structure of groups. We demonstrate our model's capability of identifying the dynamics of latent groups in a number of different types of network data. Experimental results show that our model provides improved predictive performance over existing dynamic network models on future network forecasting and missing link prediction.

We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as the node feature structure. The LMMG can be used to summarize the network structure, to predict links between the nodes, and to predict missing features of a node. We derive efficient inference and learning algorithms and evaluate the predictive performance of the LMMG on several social and document network datasets.