Tweedie-Hawkes Processes: Interpreting the Phenomena of Outbreaks

Self-exciting event sequences, in which the occurrence of an event increases the probability of triggering subsequent ones, are common in many disciplines. In this paper, we propose a Bayesian model called Tweedie-Hawkes Processes (THP), which is able to model the outbreaks of events and find out the dominant factors behind. THP leverages on the Tweedie distribution in capturing various excitation effects. A variational EM algorithm is developed for model inference. Some theoretical properties of THP, including the sub-criticality, convergence of the learning algorithm and kernel selection method are discussed. Applications to Epidemiology and information diffusion analysis demonstrate the versatility of our model in various disciplines. Evaluations on real-world datasets show that THP outperforms the rival state-of-the-art baselines in the task of forecasting future events.