Local aggregate multiscale processes: A scalable, machine-learning-compatible spatial model

2025-10-01

AI Summary

Traditional spatial Gaussian processes (e.g., kriging) suffer from high computational complexity and poor compatibility with modern machine learning models. To address these limitations, we propose the Local Aggregation Multi-scale Process (LAMP), which replaces explicit covariance structures with multi-scale local models. LAMP captures spatial heterogeneity hierarchically—from coarse to fine scales—via iterative residual learning and employs hold-out validation for automatic early stopping. By circumventing large-scale matrix inversion, LAMP achieves superior scalability and seamlessly integrates with off-the-shelf models such as random forests and neural networks. Monte Carlo experiments demonstrate that LAMP outperforms state-of-the-art spatial models, with further accuracy gains upon integration. Empirical evaluation on residential land price prediction in the Tokyo metropolitan area confirms its high predictive accuracy, robustness to data perturbations, and practical scalability.

Technology Category

• Machine Learning: Ensemble Methods
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This study develops the Local Aggregate Multiscale Process (LAMP), a scalable and machine-learning-compatible alternative to conventional spatial Gaussian processes (GPs, or kriging). Unlike conventional covariance-based spatial models, LAMP represents spatial processes by a multiscale ensemble of local models, inspired by geographically weighted regression. To ensure stable model training, larger-scale patterns that are easier to learn are modeled first, followed by smaller-scale patterns, with training terminated once the validation score stops improving. The training procedure, which is based on holdout validation, is easily integrated with other machine learning algorithms (e.g., random forests and neural networks). LAMP training is computationally efficient as it avoids explicit matrix inversion, a major computational bottleneck in conventional GPs. Comparative Monte Carlo experiments demonstrate that LAMP, as well as its integration with random forests, achieves superior predictive performance compared to existing models. Finally, we apply the proposed methods to an analysis of residential land prices in the Tokyo metropolitan area, Japan. The R code is available from available from https://github.com/dmuraka/spLAMP_dev_version/tree/main

Problem

• Develops scalable alternative to spatial Gaussian processes
• Integrates multiscale spatial modeling with machine learning
• Addresses computational bottlenecks in spatial prediction methods

Innovation

• LAMP uses multiscale ensemble of local models
• Training prioritizes larger-scale patterns first
• Avoids matrix inversion for computational efficiency