Clustering then Estimation of Spatio-Temporal Self-Exciting Processes

Abstract

We propose a new estimation procedure for general spatio-temporal point processes that include a selfexciting feature. Estimating spatio-temporal self-exciting point processes with observed data is challenging, partly due to the difficulty in computing and optimizing the likelihood function. To circumvent this challenge, we employ a Poisson cluster representation for spatio-temporal self-exciting point processes to simplify the likelihood function and develop a new estimation procedure called "clustering-then-estimation" (CTE), which integrates clustering algorithms with likelihood-based estimation methods. Compared with the widelyused expectation-maximization (EM) method, our approach separates the cluster structure inference of the data from the model selection. This has the benefit of reducing the risk of model mis-specification. Our approach is computationally more efficient because it does not need to recursively solve optimization problems, which would be needed for EM. We also present asymptotic statistical results for our approach as theoretical support. Experimental results on several synthetic and real datasets illustrate the effectiveness of the proposed CTE procedure.

Keywords: spatio-temporal self-exciting point process, maximum likelihood estimation, clustering algorithm