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.

翻译：本文提出了一种新颖的深度时空点过程模型——深度核混合点过程（Deep Kernel Mixture Point Processes, DKMPP），该模型整合了多模态协变量信息。DKMPP是深度混合点过程（DMPP）的增强版本，通过引入更灵活的深度核来建模事件与协变量数据之间的复杂关系，从而提升了模型的表达能力。针对深度核不可积分导致的DKMPP难以训练的问题，我们采用基于分数匹配的无积分方法，并通过可扩展的降噪分数匹配方法进一步提高效率。实验结果表明，DKMPP及其相应基于分数的估计器优于基线模型，充分展示了整合协变量信息、利用深度核以及采用基于分数估计器的优势。