Integration-free Training for Spatio-temporal Multimodal Covariate Deep
  Kernel Point Processes
Yixuan Zhang Quyu Kong Feng Zhou
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.