  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.
