Title: Generalizing random forests for spatially correlated data
Authors: Abhirup Datta - Johns Hopkins Bloomberg School of Public Health (United States) [presenting]
Abstract: Spatial linear mixed-models, consisting of a linear covariate effect and a Gaussian process (GP) distributed spatial random effect, are widely used for analyses of geospatial data. We consider the setting where the covariate effect is nonlinear. Random forests (RF) are popular for estimating nonlinear regression functions but applications of RF for spatial data have often ignored the spatial correlation. We show that this impacts the performance of RF adversely. We propose RF-GLS, a novel and well-principled and parsimonious extension of RF, for estimating nonlinear covariate effects in spatial mixed models where the spatial correlation is modeled using GP. RF-GLS extends RF in the same way generalized least squares (GLS) fundamentally extends ordinary least squares (OLS) to accommodate for dependence in linear models. RF becomes a special case of RF-GLS, and is substantially outperformed by RF-GLS for both estimation and prediction across extensive numerical experiments with spatially correlated data. RF-GLS can be used for functional estimation in other types of dependent data like time series. We also provide, to our knowledge, the first asymptotic consistency results for tree and forest estimators under spatial dependence.