An extensive study of Dynamic Bayesian Network for patrol allocation against adaptive opportunistic criminals

Police patrols are used ubiquitously to deter crimes in urban areas. A distinctive feature of urban crimes is that criminals react opportunistically to patrol officers’ assignments. Different models of adversary behavior have been proposed but their exact form remains uncertain. Recent work [Zhang et al., 2015] has explored learning the model from real-world criminal activity data. To that end, criminal behavior and the interaction with the patrol officers is represented as parameters of a Dynamic Bayesian Network (DBN), enabling application of standard algorithms such as EM to learn the parameters. More specifically, the EMC algorithm is a sequence of modifications to the DBN representation, that allows for a compact representation resulting in better learning accuracy and increased speed of learning. In this paper, we perform additional experiments showing the efficacy of the EMC algorithm. Furthermore, we explore different variations of Markov model. Unlike DBNs, the Markov models do not have hidden states, which indicate distribution of criminals, and are therefore easier to learn using standard MLE techniques. We compare all the approaches by learning from a real data set of criminal activity obtained from the police department of University of Southern California (USC) situated in Los Angeles, USA. We demonstrate a significant better accuracy of predicting the crime using the EMC algorithm compared to other approaches. This work was done in collaboration with the police department of USC.