How can we explain Random Forests in a spatial framework?

Random Forest (RF) is a Machine Learning algorithm, very popular in environmental applications thanks to its flexibility and predictive performances. Even if its working mechanism is simple and intelligible, RF is considered a black box model since it prevents grasping how predictors are combined to generate the response variable predictions. This lack of interpretability represents a limitation of RF, especially when some knowledge is required on the response-predictors relationship from the decision-making perspective. In this work, we aim to explain RF using a Post-Hoc approach, i.e. by extracting a compact and simple list of rules from an estimated RF focusing on a spatial regression context. By means of a spatial dataset, we compare the final sets of rules and discuss the predictive accuracies of the standard RF and its gold standard for the case of spatially correlated data.