In this study, we propose a novel deep spatio-temporal point process model,
Deep Kernel Mixture Point Processes (DKMPP), that incorporates multimodal
covariate information. DKMPP is an enhanced version of Deep Mixture Point
Processes (DMPP), which uses a more flexible deep kernel to model complex
relationships between events and covariate data, improving the model's
expressiveness. To address the intractable training procedure of DKMPP due to
the non-integrable deep kernel, we utilize an integration-free method based on
score matching, and further improve efficiency by adopting a scalable denoising
score matching method. Our experiments demonstrate that DKMPP and its
corresponding score-based estimators outperform baseline models, showcasing the
advantages of incorporating covariate information, utilizing a deep kernel, and
employing score-based estimators.

本研究提出了一种新颖的深空时点过程模型，它结合了多模态协变量信息，通过使用更灵活的深度核模型复杂事件与协变量数据之间的关系，提高了模型的表达能力。为了解决由于非可积深度核导致的 DKMPP 不可行的训练过程，我们采用了基于分数匹配的无积分方法，并通过采用可扩展的降噪分数匹配方法进一步提高了效率。我们的实验证明，DKMPP 及其相应的基于分数的估计器优于基准模型，展示了结合协变量信息、利用深度核以及采用基于分数的估计器的优势。