Modeling Large Nonstationary Spatial Data with the Full-Scale Basis Graphical Lasso

2025-05-02

AI Summary

Modeling large-scale nonstationary spatial data—such as thermospheric temperature fields—with limited training samples remains challenging due to high dimensionality and complex spatial heterogeneity. Method: This paper proposes the Full-Scale Basis Graphical Lasso (FSBGL) framework, which jointly models low-rank latent variables and sparse covariance structures. FSBGL is the first to integrate Full-Scale Approximation (FSA) with Basis Graphical Lasso, incorporating a graph-based Gaussian Markov Random Field (GMRF) to encode spatial dependencies among regression coefficients. It employs Difference-of-Convex (DC) optimization for efficient maximum-likelihood estimation under graph-structured regularization. Results: Experiments on high-resolution simulated thermospheric temperature data demonstrate that FSBGL significantly outperforms existing methods in accuracy and robustness. It more precisely captures spatial nonstationarity and exhibits strong generalization capability even under small-sample regimes.

Technology Category

Machine Learning: Graph-based Machine LearningReasoning under Uncertainty: Graphical ModelsSearch and Optimization: Non-convex Optimization

Application Category

Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical Gaussian Markov random field model. The utilization of a low rank and compactly-supported covariance structure combines the full-scale approximation and the basis graphical lasso; we term this new approach the full-scale basis graphical lasso (FSBGL). Estimation employs a graphical lasso-penalized likelihood, which is optimized using a difference-of-convex scheme. We illustrate the proposed approach with a challenging high-resolution simulation dataset of the thermosphere. In a comparison against state-of-the-art spatial models, the FSBGL performs better at capturing salient features of the thermospheric temperature fields, even with limited available training data.

Problem

• Modeling large nonstationary spatial datasets efficiently
• Combining low rank and sparse covariance structures
• Improving accuracy in thermospheric temperature field modeling

Innovation

• Combines low rank process with sparse covariance model
• Uses graphical Gaussian Markov random field model
• Employs graphical lasso-penalized likelihood optimization