Is Score Matching Suitable for Estimating Point Processes?

TL;DR

This paper introduces a weighted score matching estimator for point processes, addressing limitations of previous methods, and demonstrates its theoretical consistency and practical effectiveness through experiments on synthetic and real data.

Contribution

It proposes a novel weighted score matching estimator for point processes, with proven consistency and improved performance over existing estimators.

Findings

Estimator is consistent and converges at a proven rate.

Accurately estimates parameters on synthetic data.

Aligns with MLE results on real data, outperforming existing score matching methods.

Abstract

Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby 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 our estimator and establish its rate of convergence. 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}.