  Hawkes processes are a class of point processes that have the ability to
model the self- and mutual-exciting phenomena. Although the classic Hawkes
processes cover a wide range of applications, their expressive ability is
limited due to three key hypotheses: parametric, linear and homogeneous. Recent
work has attempted to address these limitations separately. This work aims to
overcome all three assumptions simultaneously by proposing the flexible
state-switching Hawkes processes: a flexible, nonlinear and nonhomogeneous
variant where a state process is incorporated to interact with the point
processes. The proposed model empowers Hawkes processes to be applied to
time-varying systems. For inference, we utilize the latent variable
augmentation technique to design two efficient Bayesian inference algorithms:
Gibbs sampler and mean-field variational inference, with analytical iterative
updates to estimate the posterior. In experiments, our model achieves superior
performance compared to the state-of-the-art competitors.
