Infinite Hidden Semi-Markov Modulated Interaction Point Process §, Ting Guo

The correlation between events is ubiquitous and important for temporal events modelling. In many cases, the correlation exists between not only events' emitted observations, but also their arrival times. State space models (e.g., hidden Markov model) and stochastic interaction point process models (e.g., Hawkes process) have been studied extensively yet separately for the two types of correlations in the past. In this paper, we propose a Bayesian nonparametric approach that considers both types of correlations via unifying and generalizing the hidden semi-Markov model and interaction point process model. The proposed approach can simultaneously model both the observations and arrival times of temporal events, and automatically determine the number of latent states from data.