Likelihood-Free Estimation for Spatiotemporal Hawkes processes with missing data and application to predictive policing

TL;DR

This paper presents a likelihood-free estimation method using Wasserstein GANs to handle missing data in spatiotemporal Hawkes processes, improving crime hotspot prediction accuracy for better policing strategies.

Contribution

It introduces a novel WGAN-based likelihood-free approach to address missing crime data in Hawkes models, enhancing parameter estimation and predictive reliability.

Findings

Improved accuracy in estimating Hawkes process parameters with missing data.

Enhanced crime hotspot prediction reliability.

Potential for more equitable policing strategies.

Abstract

With the growing use of AI technology, many police departments use forecasting software to predict probable crime hotspots and allocate patrolling resources effectively for crime prevention. The clustered nature of crime data makes self-exciting Hawkes processes a popular modeling choice. However, one significant challenge in fitting such models is the inherent missingness in crime data due to non-reporting, which can bias the estimated parameters of the predictive model, leading to inaccurate downstream hotspot forecasts, often resulting in over or under-policing in various communities, especially the vulnerable ones. Our work introduces a Wasserstein Generative Adversarial Networks (WGAN) driven likelihood-free approach to account for unreported crimes in Spatiotemporal Hawkes models. We demonstrate through empirical analysis how this methodology improves the accuracy of parametric estimation in the presence of data missingness, leading to more reliable and efficient policing strategies.