Nested CRP with Hawkes-Gaussian Processes

There has been growing interest in learning social structure underlying interaction data, especially when such data consist of both temporal and textual information. In this paper, we propose a novel nonparametric Bayesian model that incorporates senders and receivers of messages into a hierarchical structure that governs the content and reciprocity of communications. We bring the nested Chinese restaurant process from nonparametric Bayesian statistics to Hawkes process models of point pattern data. By modeling senders and receivers in such a hierarchical framework, we are better able to make inferences about the authorship and audience of communications, as well as individual behavior such as favorite collaborators and top-pick words. Empirical results with our nonparametric Bayesian point process model show that our formulation has improved predictions about event times and clusters. In addition, the latent structure revealed by our model provides a useful qualitative understanding of the data, facilitating interesting exploratory analyses.