  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 (Chen &
Guestrin, 2016) to the point process literature via two carefully designed loss
functions. The first loss is based on the Poisson likelihood, working for
general point processes. The second loss is based on the weighted Poisson
likelihood, where spatially dependent weights are introduced to further improve
the estimation efficiency for clustered processes. An efficient greedy search
algorithm is 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 existing approaches when the dimension of the covariate space is
high, revealing the advantages of tree-based ensemble methods in estimating
complex intensity functions.
