BRUNCH: Branching Structure Inference of Hybrid Multivariate Hawkes Processes with Application to Social Media

Multivariate Hawkes processes (MHPs) are a class of point processes where an arrival in one dimension can affect the future arrivals in all dimensions. Existing MHPs are associated with homogeneous link functions. However, in reality, different dimensions may exhibit different temporal characteristics. In this paper, we augment MHPs by incorporating heterogeneous link functions, referred to as hybrid MHPs, to capture the temporal characteristics in different dimensions. Since the branching structure can be utilized to equivalently represent MHPs, we propose a novel model called BRUNCH via intensity-driven Chinese Restaurant Processes (intCRP) to identify the optimal branching structure of hybrid MHPs. Furthermore, we relax the constraint on the shapes of triggering kernels in MHPs. We develop a Monte Carlo-based inference algorithm called MEDIA to infer the branching structure. Experiments on real-world datasets demonstrate the superior performance of BRUNCH and its usefulness in social media applications.