Interpretable Hawkes Process Spatial Crime Forecasting with TV-Regularization

Interpretable models for criminal justice forecasting are desirable due to the high-stakes nature of the application. While interpretable models have been developed for individual level forecasts of recidivism, interpretable models are lacking for the application of space-time crime hotspot forecasting. Here we introduce an interpretable Hawkes process model of crime that allows forecasts to capture near-repeat effects and spatial heterogeneity while being consumable in the form of easy-to-read score cards. For this purpose we employ penalized likelihood estimation of the point process with a total-variation regularization that enforces the triggering kernel to be piece-wise constant. We derive an efficient expectation-maximization algorithm coupled with forward backward splitting for the TV constraint to estimate the model. We apply our methodology to synthetic data and space-time crime data from Indianapolis. The TV-Hawkes process achieves similar accuracy to standard Hawkes process models of crime while increasing interpretability and transparency.