We propose a generic spatiotemporal event forecasting method,
which we developed for the National Institute of Justice’s (NIJ) RealTime Crime Forecasting Challenge (National Institute of Justice,
2017). 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 gradientbased 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.