提出加权得分匹配方法，解决点过程估计中现有方法不完整的问题。
Is Score Matching Suitable for Estimating Point Processes?
- 引入加权得分匹配，克服传统方法对一般点过程的适用性缺陷。
- 理论证明估计器一致且收敛速率可分析，实验验证在真实数据上媲美MLE。
- 适合需要精确参数估计的点过程建模任务，尤其在无归一化常数积分时有用。
近年来，得分匹配估计器因无需计算归一化常数积分而受到广泛关注，从而缓解了最大似然估计（MLE）中的计算挑战。已有研究提出了针对点过程的得分匹配估计器，但本文指出这些方法因估计量不完备，仅适用于特定问题，无法推广至更一般的点过程。为此，本文提出了面向点过程的加权得分匹配估计器。理论上，我们证明了该估计器的一致性并建立了其收敛速率。实验结果表明，该方法在合成数据上能准确估计模型参数，在真实数据上的表现与MLE一致；而现有得分匹配方法则表现不佳。代码已公开于 https://github.com/KenCao2007/WSM_TPP。
原文摘要 · Abstract (English)
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}.
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