Boosting Trees are one of the most successful statistical learning approaches that involve sequentially growing an ensemble of simple regression trees ("weak learners"). This paper proposes a gradient Boosted Trees algorithm for Spatial Data (Boost-S) with covariate information. Boost-S integrates the spatial correlation into the classical framework of eXtreme Gradient Boosting. Each tree is constructed by solving a regularized optimization problem, where the objective function takes into account the underlying spatial correlation and involves two penalty terms on tree complexity. A computationally-efficient greedy heuristic algorithm is proposed to obtain an ensemble of trees. The proposed Boost-S is applied to the spatially-correlated FDG-PET (fluorodeoxyglucose-positron emission tomography) imaging data collected from clinical trials of cancer chemoradiotherapy. Our numerical investigations successfully demonstrate the advantages of the proposed Boost-S over existing approaches for this particular application.
Keywords: Chemoradiotherapy; FDG-PET; Gradient Boosted Trees; Spatial Statistics.