Improving social harm indices with a modulated Hawkes process

Communities are adversely affected by heterogeneous social harm events, e.g. crime, traffic crashes, medical emergencies, drug use. Police, fire, health and social service departments are tasked with mitigating social harm through various types of interventions. While social harm indices have been proposed for allocating resources to spatially fixed hotspots, the risk of social harm events is dynamic and new algorithms and software systems capable of quickly identifying risks and triggering appropriate public safety responses are needed. We propose a modulated Hawkes process for this purpose that offers a flexible approach for both i) incorporating leading indicators for variance reduction in the case of more rare event categories (e.g. homicide) and ii) capturing dynamic hotspot formation through self-excitation. We present an efficient l1-penalized EM algorithm for estimation of the model that simultaneously performs feature selection for spatial covariates of each incident type. We provide simulation results using data provided by the Indianapolis Metropolitan Police Department to illustrate the advantages of the modulated Hawkes process model of social harm over recently introduced social harm indices and property crime Hawkes processes. ∗Computer and Information Science, Indiana University Purdue University Indianapolis †School of Public and Environmental Affairs, Indiana University Purdue University Indianapolis ‡Computer and Information Science, Indiana University Purdue University Indianapolis