Random Forests for Spatially Dependent Data

Spatial linear mixed-models, consisting of a covariate effect and Gaussian process (GP) distributed spatial random effect, are widely used for analyses geospatial data. We consider the setting where is nonlinear. Random forests (RF) popular estimating nonlinear functions but applications RF data have often ignored correlation. show that this impacts performance adversely. propose RF-GLS, novel well-principled extension RF, effects in mixed models correlation modeled using GP. RF-GLS extends same way generalized least squares (GLS) fundamentally ordinary (OLS) to accommodate dependence models. becomes special case substantially outperformed by both estimation prediction across extensive numerical experiments with spatially correlated can be functional other types dependent like time series. prove consistency ?-mixing error processes include Matérn As byproduct, we also establish, our knowledge, first result under dependence. establish results independent importance, including general GLS optimizers data-driven function classes, uniform law large number weaker assumptions. These new tools potentially useful asymptotic analysis GLS-style estimators nonparametric regression