Causal inference for spatiotemporal point processes in the presence of outcome spillover and carryover

2026-04-13

AI Summary

This study addresses causal inference for continuous spatiotemporal point processes subject to spillover and lingering effects under unit-level interventions. It proposes the first causal inference framework grounded in the potential outcomes paradigm, modeling the observed post-intervention process as an unlabeled superposition of control and treated components. Identification is achieved by separately analyzing regions within and outside the support of the intervention, leveraging a structured point process model to recover causal contrasts in non-support areas. Estimation employs a likelihood-based stochastic EM algorithm, augmented with a predictable block-wise hard EM surrogate, making it applicable to history-dependent processes such as Poisson and Hawkes processes. The method provides non-asymptotic error bounds and plug-in inference guarantees. Empirical validation on wastewater injection and seismicity data from Oklahoma demonstrates its practical efficacy.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We develop a framework for causal inference with continuous spatiotemporal point-process outcomes under cell-level interventions and outcome spillover. Potential outcomes are indexed by full treatment allocations, and the observed post-treatment process is represented as an unlabelled superposition of latent control and treatment components. On the observed design support, expected post-treatment event counts in any spacetime region under a given treatment allocation are identified under consistency, exchangeability, and positivity; off-support contrasts are identified relative to a regime-stable structural point-process model. Estimation is likelihood-based and implemented with stochastic EM. To understand when this is feasible, we analyse a predictable blockwise hard-EM surrogate and show nonasymptotic contraction of estimation error to a statistical floor governed by locally ambiguous regions. This yields plug-in guarantees for cell-level and global causal functionals, and clarifies the additional array conditions needed for unnormalised growing-window contrasts. The framework covers history dependent spatiotemporal point processes including Poisson and Hawkes models, with applications to settings such as epidemiology, seismology, and finance. We provide an application assessing the causal effect of injecting wastewater into the ground on seismic activity in Oklahoma.

Problem

• causal inference
• spatiotemporal point processes
• outcome spillover
• carryover effects
• treatment allocation

Innovation

• spatiotemporal point processes
• causal inference
• outcome spillover
• stochastic EM
• Hawkes processes