The Indian Buffet Hawkes Process to Model Evolving Latent Influences

Abstract

Temporal events in the real world often exhibit reinforcing dynamics, where earlier events trigger follow-up activity in the near future. A canonical example of modeling such dynamics is the Hawkes process (HP). However, previous HP models do not capture the rich dynamics of real-world activity—which can be driven by multiple latent triggering factors shared by past and future events, with the latent features themselves exhibiting temporal dependency structures. For instance, rather than view a new document just as a response to other documents in the recent past, it is important to account for the factor-structure underlying all previous documents. This structure itself is not fixed, with the influence of earlier documents decaying with time. To this end, we propose a novel Bayesian nonparametric stochastic point process model, the Indian Buffet Hawkes Processes (IBHP), to learn multiple latent triggering factors underlying streaming document/message data. The IBP facilitates the inclusion of multiple triggering factors in the HP, and the HP allows for modeling latent factor evolution in the IBP. We develop a learn- ing algorithm for the IBHP based on Sequential Monte Carlo and demonstrate the effectiveness of the model. In both synthetic and real data experiments, our model achieves equivalent or higher likelihood and provides interpretable topics and shows their dynamics.