Optimal Intervention for Self-triggering Spatial Networks with Application to Urban Crime Analytics

TL;DR

The paper tackles cascading activity in self-exciting spatiotemporal networks by formulating an optimal intervention framework that accounts for post-intervention persistence and background-rate dampening. It derives analytical expressions for post-intervention intensities and expected event counts, and casts the intervention problem as LP/MILP programs to select budget-constrained target nodes. Through simulations and a Los Angeles crime case study, the authors show that LP-based strategies outperform heuristics, with greater gains when interventions also reduce background activity (lower $\gamma$) and when the cascade is moderately budgeted. The work advances predictive policing and similar applications by enabling network-aware, data-driven patrol and mitigation strategies that exploit spillover effects and realistic intervention dynamics.

Abstract

In many network systems, events at one node trigger further activity at other nodes, e.g., social media users reacting to each other's posts or the clustering of criminal activity in urban environments. These systems are typically referred to as self-exciting networks. In such systems, targeted intervention at critical nodes can be an effective strategy for mitigating undesirable consequences such as further propagation of criminal activity or the spreading of misinformation on social media. In our work, we develop an optimal network intervention model to explore how targeted interventions at critical nodes can mitigate cascading effects throughout a Spatiotemporal Hawkes network. Similar models have been studied previously in the literature in purely temporal Hawkes networks, but in our work, we extend them to a spatiotemporal setup and demonstrate the efficacy of our methods by comparing the post-intervention reduction in intensity to other heuristic strategies in simulated networks. Subsequently, we use our method on crime data from the LA police department database to find neighborhoods for strategic intervention to demonstrate an application in predictive policing.

Figures (3)

• Figure 1: Effect of varying $p$ and $\gamma$ on expected total rate reduction across different budget levels.
• Figure 2: Effect of varying $p$ and $\gamma$ on expected number of events reduction across different budget levels.
• Figure 3: Crime Event Locations for Each Precinct in Los Angeles in the first week of September.