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Boosting Trees are one of the most successful statistical learning approachesthat involve sequentially growing an ensemble of simple regression trees (i.e.,"weak learners"). However, gradient boosted trees are not yet available forspatially correlated data. This paper proposes a new gradient Boosted Treesalgorithm for Spatial Data (Boost-S) with covariate information. Boost-Sintegrates the spatial correlation structure into the classical framework ofgradient boosted trees. Each tree is grown by solving a regularizedoptimization problem, where the objective function involves two penalty termson tree complexity and takes into account the underlying spatial correlation. Acomputationally-efficient algorithm is proposed to obtain the ensemble trees.The proposed Boost-S is applied to the spatially-correlated FDG-PET(fluorodeoxyglucose-positron emission tomography) imaging data collected duringcancer chemoradiotherapy. Our numerical investigations successfully demonstratethe advantages of the proposed Boost-S over existing approaches for thisparticular application.

Boost-S: Gradient Boosted Trees for Spatial Data and Its Application to FDG-PET Imaging Data