Improving grade estimation using machine learning: A comparative study of ordinary kriging against machine learning algorithms

This study presents a rigorous comparison between ordinary kriging and commonly used machine learning algorithms, those being, linear regression, support vector regression, decision trees, random forests (RF), and k-nearest neighbours for spatial interpolation of platinum grade estimates in a complex ore body within the Bushveld Igneous Complex. Using only X and Y coordinates as predictors, both ordinary kriging and machine learning models were evaluated at point and block supports under traditional and spatial block cross validation frameworks. While naive validation results suggested superior performance for k-nearest neighbour and random forest (R² = 0.92 and 0.86, respectively), these were revealed to be overly optimistic under spatial dependence. Spatial block cross validation results demonstrated substantial declines in model performance, with R² often falling below zero, particularly for decision trees and k-nearest neighbour, indicating strong overfitting and limited generalisability. Ordinary kriging exhibited more stable, albeit modest, performance under spatial validation, reflecting its strength in geostatistical interpolation when contextual geological variables are unavailable. The study underscores the critical importance of spatially aware validation in resource estimation and highlights that machine learning models constrained to spatial coordinates behave as interpolators rather than true learners of geological variability. Recommendations are provided for future work incorporating geological information to enhance predictive robustness.