Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: a winning solution to the NIJ "Real-Time Crime Forecasting Challenge"

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 solution to the challenge 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, heatmap-based (kernel density estimation) 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 temporal crossvalidation. Resulting predictions significantly exceeded baseline KDE estimates; we had winning submissions to the competition in each of the different crime types and across different timescales, suggesting that our method is generically applicable.