Feature-free regression kriging

2025-07-09

AI Summary

Traditional kriging struggles to model non-stationarity in geospatial interpolation, while regression kriging (RK) is severely constrained by its dependence on high-quality external covariates. To address these limitations, this paper proposes a novel, covariate-free regression kriging framework. Our method automatically learns local spatial dependence, heterogeneity, and geographical similarity from the target variable alone, enabling data-driven trend surface estimation; residuals are then interpolated via ordinary kriging. This represents the first RK formulation that constructs a regression trend without auxiliary variables, thereby eliminating reliance on external covariates. Evaluated on heavy metal concentration prediction across Australian mining sites, our approach outperforms 17 established interpolation methods. Results demonstrate substantial improvements in interpolation accuracy, model generalizability, and cost efficiency—particularly by reducing dependence on expensive or unavailable auxiliary data.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Spatial interpolation is a crucial task in geography. As perhaps the most widely used interpolation methods, geostatistical models -- such as Ordinary Kriging (OK) -- assume spatial stationarity, which makes it difficult to capture the nonstationary characteristics of geographic variables. A common solution is trend surface modeling (e.g., Regression Kriging, RK), which relies on external explanatory variables to model the trend and then applies geostatistical interpolation to the residuals. However, this approach requires high-quality and readily available explanatory variables, which are often lacking in many spatial interpolation scenarios -- such as estimating heavy metal concentrations underground. This study proposes a Feature-Free Regression Kriging (FFRK) method, which automatically extracts geospatial features -- including local dependence, local heterogeneity, and geosimilarity -- to construct a regression-based trend surface without requiring external explanatory variables. We conducted experiments on the spatial distribution prediction of three heavy metals in a mining area in Australia. In comparison with 17 classical interpolation methods, the results indicate that FFRK, which does not incorporate any explanatory variables and relies solely on extracted geospatial features, consistently outperforms both conventional Kriging techniques and machine learning models that depend on explanatory variables. This approach effectively addresses spatial nonstationarity while reducing the cost of acquiring explanatory variables, improving both prediction accuracy and generalization ability. This finding suggests that an accurate characterization of geospatial features based on domain knowledge can significantly enhance spatial prediction performance -- potentially yielding greater improvements than merely adopting more advanced statistical models.

Problem

• Overcomes spatial nonstationarity without external explanatory variables
• Automatically extracts geospatial features for regression-based trend modeling
• Improves prediction accuracy and generalization in spatial interpolation

Innovation

• Feature-free regression kriging for spatial interpolation
• Automatically extracts geospatial features without external variables
• Outperforms traditional kriging and machine learning methods