XGBoostPP: Tree-based Estimation of Point Process Intensity Functions

Medium-sized point pattern data arises in many applications, however, their analyses have been overlooked in the machine learning community. In this article, we propose a novel tree-based ensemble method, named XGBoostPP, to nonparametrically estimate the intensity of a point process as a function of covariates. It extends the use of gradient-boosted regression trees of Chen and Guestrin to the point process literature via two carefully designed loss functions. The first loss is based on the Poisson likelihood and works for general point processes. The second loss derives from a weighted likelihood, where spatially dependent weights are dynamically computed and incorporated to further improve the estimation efficiency for clustered point processes. An efficient learning algorithm and an associated validation procedure are developed for model estimation, and the effectiveness of the proposed method is demonstrated through extensive simulation studies and two real data analyses. In particular, we report that XGBoostPP achieves superior performance to state-of-the-art approaches, showcasing the advantages of using tree ensembles to estimate complex intensity functions for medium-sized point patterns. Supplementary materials for this article are available online.