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

TL;DR

This paper introduces a scalable, kernel-based spatiotemporal forecasting method for sparse events, combining Gaussian process approximations with autoregressive kernels, and demonstrates superior performance in crime prediction tasks.

Contribution

The paper presents a novel, scalable kernel method that unifies KDE and SEPP approaches for high-resolution crime forecasting, outperforming existing models.

Findings

Predictions significantly outperformed baseline KDE estimates.

Model effectively captures sparse spatiotemporal event patterns.

Hyperparameters optimized via cross-validation for improved accuracy.

Abstract

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.