  We propose a generic spatiotemporal event forecasting method, which we
developed for the National Institute of Justice's (NIJ) Real-Time Crime
Forecasting Challenge. Our method is a spatiotemporal forecasting model
combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods
for approximating Gaussian processes with autoregressive smoothing kernels in a
regularized supervised learning framework. While the smoothing kernels capture
the two main approaches in current use in the field of crime forecasting,
kernel density estimation (KDE) and self-exciting point process (SEPP) models,
the RKHS component of the model can be understood as an approximation to the
popular log-Gaussian Cox Process model. For inference, we discretize the
spatiotemporal point pattern and learn a log-intensity function using the
Poisson likelihood and highly efficient gradient-based optimization methods.
Model hyperparameters including quality of RKHS approximation, spatial and
temporal kernel lengthscales, number of autoregressive lags, bandwidths for
smoothing kernels, as well as cell shape, size, and rotation, were learned
using crossvalidation. Resulting predictions significantly exceeded baseline
KDE estimates and SEPP models for sparse events.
