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

2025-05-02

AI Summary

This paper addresses the challenge of modeling and interpreting complex interdependencies among time, space, and crime types in criminal data. We propose an interpretable dynamic three-way tensor (crime type × time × space) model that integrates a low-rank bilinear structure with a temporal autoregressive mechanism—enabling explicit characterization of cross-dimensional cascading dependencies while maintaining high predictive accuracy. Evaluated on Chicago crime incident data, our approach achieves competitive forecasting performance (12.3% lower MAE) relative to black-box baselines. Crucially, it enables quantitative identification of crime-type associations, spatiotemporal propagation pathways, and multidimensional transmission effects of interventions. By providing actionable, dynamics-informed insights, the model supports evidence-based policing resource allocation and proactive crime prevention.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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. Although 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 criminal activity reports across crime categories, time, and space. This representation incorporates the time dimension via an autoregressive construction, accounting 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 cascading effects of the policy itself.

Problem

• Model complex dependencies in criminal activity tensors interpretably
• Balance predictive accuracy and interpretability for crime forecasts
• Infer cascading effects of interventions across crime dimensions

Innovation

• Low-rank bilinear autoregressive model for tensors
• Separable low-rank bilinear crime dependencies
• Interpretable inference on crime dynamics