Is Score Matching Suitable for Estimating Point Processes?

Haoqun Cao, Zizhuo Meng, Tianjun Ke, Feng Zhou

Keywords: point processes, score matching, parameter estimation

TL;DR: This study highlights the incompleteness of previously proposed score matching estimators for point processes. In addressing this issue, we introduce a novel score matching estimator for point processes.

Abstract: Score matching estimators for point processes have gained widespread attention in recent years because they do not require the calculation of intensity integrals, thereby effectively addressing the computational challenges in maximum likelihood estimation (MLE). Some existing works have proposed score matching estimators for point processes. However, this work demonstrates that the incompleteness of the estimators proposed in those works renders them applicable only to specific problems, and they fail for more general point processes. To address this issue, this work introduces the weighted score matching estimator to point processes. Theoretically, we prove the consistency of the estimator we propose. Experimental results indicate that our estimator accurately estimates model parameters on synthetic data and yields results consistent with MLE on real data. In contrast, existing score matching estimators fail to perform effectively. Codes are publicly available at \url{https://github.com/KenCao2007/WSM_TPP}.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 10007