Geodetic Distance and Dynamic Outlier Exclusion in EM Optimization of Self Exciting Point Process for Homicide Prediction in Chicago

Abstract

In this paper, we propose a novel algorithm to improve the state-of-the-art results of homicide prediction in Chicago crime dataset. A marked self-exciting point process (M-SEPP) based epidemic type aftershock sequence (ETAS) model was applied to the Chicago crime dataset by Mohler [1] for improving the prediction rate of homicides over and above the traditional chronic hot spot approach. Expectation-maximization (EM)-type optimization has long been employed for the computation of the maximum likelihood estimates of parameters in the ETAS model. However, improvement in crime prediction has been slow due to the technological challenges in modeling the spatio-temporal distribution of criminal behavior, which results from a complex interaction of biological, social, psychological, and other influencing factors. We propose the GeoDOME algorithm, which incorporates geodetic distance and dynamic outlier exclusion in the EM-type algorithm of the ETAS model. It guarantees significant improvement in the prediction rate of homicides compared to the best result documented to date. A theoretical basis for the principles used in the modified algorithm is also provided. The increase in the prediction accuracy of homicides has been experimentally validated using the same Chicago crime dataset.