Markov-modulated Hawkes processes for modeling sporadic and bursty event occurrences in social interactions

Abstract

Modeling event dynamics is central to many disciplines. Patterns in observed social interaction events can be commonly modeled using point processes. Such social interaction event data often exhibit self-exciting, heterogeneous and sporadic trends which is challenging for conventional models. It is reasonable to assume that there exists a hidden state process that drives different event dynamics at different states. In this paper we propose a Markov modulated Hawkes process (MMHP) model for learning such a mixture of social interaction event dynamics and develop corresponding inference algorithms. Numerical experiments using synthetic data demonstrate that MMHP with the proposed estimation algorithms consistently recover the true hidden state process in simulations, while email data from a large university and data from an animal behavior study show that the procedure captures distinct event dynamics that reveal interesting social structures in the real data.