Cross-validation for geospatial data: Estimating generalization performance in geostatistical problems

Geostatistical learning problems are frequently characterized by spatial autocorrelation in the input features and/or the potential for covariate shift at test time. These realities violate the classical assumption of independent, identically distributed data, upon which most cross-validation algorithms rely in order to estimate the generalization performance of a model. In this paper, we present a theoretical criterion for unbiased cross-validation estimators in the geospatial setting. We also introduce a new cross-validation algorithm to
evaluate models, inspired by the challenges of geospatial problems. We apply a framework for categorizing problems into different types of geospatial scenarios to help practitioners select an appropriate cross-validation strategy. Our empirical analyses compare cross-validation algorithms on both simulated and several real datasets to develop recommendations for a variety of geospatial settings. This paper aims to draw attention to some challenges that arise in model evaluation for geospatial problems and to provide guidance for users.