INLA-RF: A Hybrid Modeling Strategy for Spatio-Temporal Environmental Data

2025-07-24

AI Summary

Environmental spatiotemporal processes often exhibit strong nonlinearity and discontinuities, leading to low predictive accuracy and unreliable uncertainty quantification in conventional geostatistical models. To address this, we propose a Bayesian–random forest (RF) hybrid modeling framework that integrates the INLA–SPDE spatiotemporal model with RF: RF predictions serve either as an offset term or as a correction to the latent Gaussian field. We design two iterative two-stage coupling algorithms to enable cross-stage propagation of uncertainty, and introduce a KL-divergence-based convergence criterion to enhance adaptivity. Experiments demonstrate that our method significantly improves prediction accuracy while preserving statistical consistency and yielding reliable, well-calibrated uncertainty estimates. Moreover, it achieves a favorable balance between interpretability—retaining the principled probabilistic structure of INLA–SPDE—and predictive performance—leveraging RF’s flexibility in capturing complex nonlinear patterns.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Environmental processes often exhibit complex, non-linear patterns and discontinuities across space and time, posing significant challenges for traditional geostatistical modeling approaches. In this paper, we propose a hybrid spatio-temporal modeling framework that combines the interpretability and uncertainty quantification of Bayesian models -- estimated using the INLA-SPDE approach -- with the predictive power and flexibility of Random Forest (RF). Specifically, we introduce two novel algorithms, collectively named INLA-RF, which integrate a statistical spatio-temporal model with RF in an iterative two-stage framework. The first algorithm (INLA-RF1) incorporates RF predictions as an offset in the INLA-SPDE model, while the second (INLA-RF2) uses RF to directly correct selected latent field nodes. Both hybrid strategies enable uncertainty propagation between modeling stages, an aspect often overlooked in existing hybrid approaches. In addition, we propose a Kullback-Leibler divergence-based stopping criterion. We evaluate the predictive performance and uncertainty quantification capabilities of the proposed algorithms through two simulation studies. Results suggest that our hybrid approach enhances spatio-temporal prediction while maintaining interpretability and coherence in uncertainty estimates.

Problem

• Modeling complex spatio-temporal environmental patterns
• Integrating Bayesian interpretability with Random Forest flexibility
• Ensuring uncertainty propagation in hybrid modeling approaches

Innovation

• Combines INLA-SPDE Bayesian models with Random Forest
• Introduces two-stage iterative INLA-RF algorithms
• Uses KL divergence for stopping criterion