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.

翻译：我们提出了一种新颖的基于树集成的方法XGBoostPP，用于非参数地估计点过程强度作为协变量的函数。该方法通过两种精心设计的损失函数，将梯度提升回归树（Chen & Guestrin，2016）的应用扩展到点过程文献中。第一种损失基于泊松似然，适用于一般点过程。第二种损失基于加权泊松似然，其中引入空间依赖权重以进一步提高聚类过程的估计效率。我们开发了一种高效的贪心搜索算法用于模型估计，并通过大量模拟研究和两项实际数据分析证明了所提方法的有效性。特别地，我们报告称，在高维协变量空间中，XGBoostPP的性能优于现有方法，揭示了基于树集成方法在估计复杂强度函数方面的优势。