XGBoostPP: Tree-based Estimation of Point Process Intensity Functions
提出一种基于梯度提升树的集成方法XGBoostPP，通过两种损失函数非参数估计点过程强度，适用于中等规模点模式数据，在模拟和真实数据中优于现有方法。
Medium-sized point pattern data arises in many applications, however, their analyses have been overlooked in the machine learning community. In this paper, 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 and Guestrin, 2016) 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.