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Uncertainty-Aware Crime Prediction With Spatial Temporal Multivariate Graph Neural Networks

Zepu Wang, Xiaobo Ma, Huajie Yang, Weimin Lvu, Peng Sun, Sharath Chandra Guntuku

TL;DR

This work tackles sparse, non-Gaussian urban crime data by introducing STMGNN-ZINB, a framework that jointly forecasts crime counts and their uncertainty. It integrates Diffusion Graph Convolutional Networks for spatial learning and Multivariate-Temporal Convolutional Networks for cross-crime-type temporal dynamics, parameterizing a Zero-Inflated Negative Binomial distribution to handle zero-inflation and dispersion. The method optimizes a direct negative log-likelihood loss and fuses spatial and multivariate-temporal information via Hadamard product to produce distribution parameters $(\pi, p, r)$. Empirical results on NYC and Chicago crime datasets show superior point predictions and reliable uncertainty intervals, with the sparsity parameter $\pi$ offering interpretable insights for resource planning.

Abstract

Crime forecasting is a critical component of urban analysis and essential for stabilizing society today. Unlike other time series forecasting problems, crime incidents are sparse, particularly in small regions and within specific time periods. Traditional spatial-temporal deep learning models often struggle with this sparsity, as they typically cannot effectively handle the non-Gaussian nature of crime data, which is characterized by numerous zeros and over-dispersed patterns. To address these challenges, we introduce a novel approach termed Spatial Temporal Multivariate Zero-Inflated Negative Binomial Graph Neural Networks (STMGNN-ZINB). This framework leverages diffusion and convolution networks to analyze spatial, temporal, and multivariate correlations, enabling the parameterization of probabilistic distributions of crime incidents. By incorporating a Zero-Inflated Negative Binomial model, STMGNN-ZINB effectively manages the sparse nature of crime data, enhancing prediction accuracy and the precision of confidence intervals. Our evaluation on real-world datasets confirms that STMGNN-ZINB outperforms existing models, providing a more reliable tool for predicting and understanding crime dynamics.

Uncertainty-Aware Crime Prediction With Spatial Temporal Multivariate Graph Neural Networks

TL;DR

This work tackles sparse, non-Gaussian urban crime data by introducing STMGNN-ZINB, a framework that jointly forecasts crime counts and their uncertainty. It integrates Diffusion Graph Convolutional Networks for spatial learning and Multivariate-Temporal Convolutional Networks for cross-crime-type temporal dynamics, parameterizing a Zero-Inflated Negative Binomial distribution to handle zero-inflation and dispersion. The method optimizes a direct negative log-likelihood loss and fuses spatial and multivariate-temporal information via Hadamard product to produce distribution parameters . Empirical results on NYC and Chicago crime datasets show superior point predictions and reliable uncertainty intervals, with the sparsity parameter offering interpretable insights for resource planning.

Abstract

Crime forecasting is a critical component of urban analysis and essential for stabilizing society today. Unlike other time series forecasting problems, crime incidents are sparse, particularly in small regions and within specific time periods. Traditional spatial-temporal deep learning models often struggle with this sparsity, as they typically cannot effectively handle the non-Gaussian nature of crime data, which is characterized by numerous zeros and over-dispersed patterns. To address these challenges, we introduce a novel approach termed Spatial Temporal Multivariate Zero-Inflated Negative Binomial Graph Neural Networks (STMGNN-ZINB). This framework leverages diffusion and convolution networks to analyze spatial, temporal, and multivariate correlations, enabling the parameterization of probabilistic distributions of crime incidents. By incorporating a Zero-Inflated Negative Binomial model, STMGNN-ZINB effectively manages the sparse nature of crime data, enhancing prediction accuracy and the precision of confidence intervals. Our evaluation on real-world datasets confirms that STMGNN-ZINB outperforms existing models, providing a more reliable tool for predicting and understanding crime dynamics.
Paper Structure (15 sections, 4 equations, 4 figures, 2 tables)

This paper contains 15 sections, 4 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Definition
  4. Zero-Inflated Negative Binomial Distribution
  5. Diffusion Graph Convolution Networks (DGCNs)
  6. Multivariate-Temporal Convolutional Networks (MTCNs)
  7. General Structure
  8. Experiments
  9. Experiment Setup
  10. Data
  11. Evaluation Metrics
  12. Baseline Methods
  13. Experimental Results and Analysis
  14. Interpretation of Parameter $\pi$
  15. Conclusion

Figures (4)

  • Figure 1: Framework of our STMGNN-ZINB method
  • Figure 2: Comparison of KL-Divergence in NYC Dataset
  • Figure 3: Comparison of KL-Divergence in Chicago Dataset
  • Figure 4: Heatmap of $\pi$ in the entire urban space of NYC (left) and Chicago (right). Results are averaged over the multivariate dimension and temporal dimension.