Nonlinear Hawkes Processes in Time-Varying System

• URL: http://arxiv.org/abs/2106.04844v1
• Date: Wed, 9 Jun 2021 07:06:05 GMT
• Title: Nonlinear Hawkes Processes in Time-Varying System
• Authors: Feng Zhou, Quyu Kong, Yixuan Zhang, Cheng Feng, Jun Zhu
• Abstract summary: Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. This work proposes a flexible, nonlinear and nonhomogeneous variant where a state process is incorporated to interact with the point processes. For inference, we utilize the latent variable augmentation technique to design two efficient Bayesian inference algorithms.
• Score: 37.80255010291703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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