Low-rank bilinear autoregressive models for three-way criminal activity tensors

TL;DR

This paper introduces a low-rank bilinear autoregressive model for three-way criminal activity tensors, balancing predictive accuracy with interpretability of complex dependencies across crime categories, time, and space.

Contribution

It proposes a novel low-rank bilinear autoregressive approach that provides interpretable insights into criminal activity dependencies while maintaining high predictive performance.

Findings

Model achieves comparable accuracy to black-box methods.

Reveals interpretable dependence structures in crime data.

Facilitates informed intervention policy design.

Abstract

Criminal activity data are typically available via a three-way tensor encoding the reported frequencies of different crime categories across time and space. The challenges that arise in the design of interpretable, yet realistic, model-based representations of the complex dependencies within and across these three dimensions have led to an increasing adoption of black-box predictive strategies. While this perspective has proved successful in producing accurate forecasts guiding targeted interventions, the lack of interpretable model-based characterizations of the dependence structures underlying criminal activity tensors prevents from inferring the cascading effects of these interventions across the different dimensions. We address this gap through the design of a low-rank bilinear autoregressive model which achieves comparable predictive performance to black-box strategies, while allowing interpretable inference on the dependence structures of reported criminal activities across crime categories, time and space. This representation incorporates the time dimension via an autoregressive construction that accounts for spatial effects and dependencies among crime categories through a separable low-rank bilinear formulation. When applied to Chicago police reports, the proposed model showcases remarkable predictive performance and also reveals interpretable dependence structures unveiling fundamental crime dynamics. These results facilitate the design of more refined intervention policies informed by the cascading effects of the policy itself.