We study the spatio-temporal prediction problem, which has attracted the
attention of many researchers due to its critical real-life applications. In
particular, we introduce a novel approach to this problem. Our approach is
based on the Hawkes process, which is a non-stationary and self-exciting point
process. We extend the formulations of a standard point process model that can
represent time-series data to represent a spatio-temporal data. We model the
data as nonstationary in time and space. Furthermore, we partition the spatial
region we are working on into subregions via an adaptive decision tree and
model the source statistics in each subregion with individual but mutually
interacting point processes. We also provide a gradient based joint
optimization algorithm for the point process and decision tree parameters.
Thus, we introduce a model that can jointly infer the source statistics and an
adaptive partitioning of the spatial region. Finally, we provide experimental
results on real-life data, which provides significant improvement due to space
adaptation and joint optimization compared to standard well-known methods in
the literature.

本文提出了一种新方法，利用 Hawkes 过程和自适应决策树来对时空数据进行建模，通过非平稳的时空表达，对每个子区域进行点处理来对其进行统计，且提供了一种基于梯度的联合优化算法， 实验结果表明，与文献中常用的标准方法相比，该方法在空间适应性和联合优化方面显著提高了预测结果。