A refined MISD algorithm based on Gaussian process regression

Abstract

Time series data is a common data type in real life, and modelling of time series data along with its underlying temporal dynamics is always a challenging job. Temporal point process is an outstanding method to model time series data in domains that require temporal continuity, and includes homogeneous Poisson process, inhomogeneous Poisson process and Hawkes process. We focus on Hawkes process which can explain self-exciting phenomena in many real applications. In classical Hawkes process, the triggering kernel is always assumed to be an exponential decay function, which is inappropriate for some scenarios, so nonparametric methods have been used to deal with this problem, such as model independent stochastic de-clustering (MISD) algorithm. However, MISD algorithm has a strong dependence on the number of bins, which leads to underfitting for some bins and overfitting for others, so the choice of bin number is a critical step. In this paper, we innovatively embed a Gaussian process regression into the iterations of MISD to make this algorithm less sensitive to the choice of bin number.