Geographical Gaussian Process Regression: A Spatial Machine-Learning Model Based on Spatial Similarity

This study proposes a new spatial machine-learning model called geographical Gaussian process regression (GGPR). GGPR is extended from Gaussian process regression (GPR) by adopting the principle of spatial similarity for calibration, and it is designed to conduct spatial prediction and exploratory spatial data analysis (ESDA). GGPR addresses several key challenges in spatial machine learning. First, as a probabilistic model, GGPR avoids the conflict between spatial autocorrelation and the assumption of independent and identically distributed (i.i.d.), thus enhancing the model's objectivity and reliability in spatial prediction. Second, GGPR is suitable for small-sample prediction, a task that most existing models struggle with. Finally, when integrated with GeoShapley, GGPR is an explainable model that can measure spatial effects and explain the outcomes. Evaluated on two distinct datasets, GGPR demonstrates superior predictive performance compared to other popular machine-learning models across various sampling ratios, with its advantage becoming especially evident with smaller sample sizes. As an ESDA model, GGPR demonstrates enhanced accuracy, better computational efficiency, and a comparable ability to measure spatial effects against both multiscale geographically weighted regression and geographical random forests. In short, GGPR offers spatial data scientists a new method for predicting and exploring complex geographical processes.