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We propose a generic spatiotemporal event forecasting method, which wedeveloped for the National Institute of Justice's (NIJ) Real-Time CrimeForecasting Challenge. Our method is a spatiotemporal forecasting modelcombining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methodsfor approximating Gaussian processes with autoregressive smoothing kernels in aregularized supervised learning framework. While the smoothing kernels capturethe 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 thepopular log-Gaussian Cox Process model. For inference, we discretize thespatiotemporal point pattern and learn a log-intensity function using thePoisson likelihood and highly efficient gradient-based optimization methods.Model hyperparameters including quality of RKHS approximation, spatial andtemporal kernel lengthscales, number of autoregressive lags, bandwidths forsmoothing kernels, as well as cell shape, size, and rotation, were learnedusing crossvalidation. Resulting predictions significantly exceeded baselineKDE estimates and SEPP models for sparse events.

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