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 self-exciting feature. Estimating spatio-temporal self-exciting point processes with observed data is challenging, partly because of 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 widely used 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 misspecification. 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 data sets illustrate the effectiveness of the proposed CTE procedure. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: J. Anderson is supported by NSF [Grant ECCS-2144634]. R. Righter is supported by the Ron Wolff Chaired Professorship. Z. Zheng is supported by NSF [Grant DMS-2220537]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0351 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0351 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .