The Prediction Error Bound in Urban Crime: Temporal Predictability

Predicting when and where crime occurs is essential and a significant task to support preventive policing. This subsequently has important outcomes for economic benefits, urban planning and human safety - predictability, which is a theoretical bound for the prediction of performance in human behavior based on limited data. Current approaches to predictability in human behavior usually measure prediction accuracy which is aimed at classification issues such as the next location of prediction and the lack of measurement for regression problems. To further research in this area, this study proposes a new method based on differential entropy to compute the prediction error as a form of mean square error to derive the minimum level of error referred to as temporal predictability. Special emphasis is placed on investigating the sensitivity of the predictability methods with regard to changing the data lengths. The method was evaluated using public crime datasets from four cities (Washington DC, Denver, New York, and Vancouver) collected between 2016 and 2022. The results from the study support the hypothesis of correlation between the minimum amount of data and the level of temporal predictability, which can guide the prediction of the regression issue.