Gradient Boosted Trees for Spatial Data and Its Application to Medical Imaging Data.

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.