Practical considerations for Gaussian Process modeling for causal inference quasi-experimental studies with panel data

2025-07-07

AI Summary

This paper addresses unobserved spatiotemporal confounding in panel data by proposing a Gaussian process (GP)-based causal inference framework. Methodologically, it unifies synthetic control and longitudinal regression by modeling the GP posterior mean as a spatiotemporal similarity-weighted average; heterogeneous spatiotemporal dependencies are captured via separable or nonseparable covariance kernels, and counterfactuals and uncertainties are estimated via Bayesian inference. The key contributions are threefold: (i) it is the first to formally establish the interpretability of GPs for causal estimation, (ii) it provides principled guidelines for kernel selection, and (iii) it enables nonparametric, interpretable, and uncertainty-quantified causal effect estimation. The framework is validated on both synthetic experiments and real-world mortality data following Hurricane Katrina, demonstrating robust performance. Open-source code is provided to support reproducible research and policy evaluation applications.

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
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach that can account for such complex dependencies through carefully chosen covariance kernels. In this paper, we provide a practical and interpretable framework for applying GPs to causal inference in panel data settings. We demonstrate how GPs generalize popular methods such as synthetic control and vertical regression, and we show that the GP posterior mean can be represented as a weighted average of observed outcomes, where the weights reflect spatial and temporal similarity. To support applied use, we explore how different kernel choices impact both estimation performance and interpretability, offering guidance for selecting between separable and nonseparable kernels. Through simulations and application to Hurricane Katrina mortality data, we illustrate how GP models can be used to estimate counterfactual outcomes and quantify treatment effects. All code and materials are made publicly available to support reproducibility and encourage adoption. Our results suggest that GPs are a promising and interpretable tool for addressing unmeasured spatio-temporal confounding in quasi-experimental studies.

Problem

• Estimating causal effects in spatio-temporal quasi-experiments with unmeasured confounding
• Providing interpretable Gaussian Process framework for panel data causal inference
• Selecting optimal kernels for balancing estimation performance and interpretability

Innovation

• Gaussian Processes model spatio-temporal dependencies
• GP posterior mean as weighted outcomes average
• Guidance for kernel selection in GP models