Generalized point process additive models

• 成果类型: Article; Early Access
• 署名作者: Lee, Kuang-Yao; Sun, Jiehuan; Li, Bing; Li, Lexin
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag061
• 发表日期: 2026-04-13
• 关键词: Cox process; electronic health record; Generalized additive model; kernel embedding; point process; Reproducing Kernel Hilbert Space; CHARACTERISTIC KERNELS; selection; Consistency; Lasso

摘要

In this article, we propose a generalized point process additive model with a scalar response and high-dimensional point process predictors. Our proposal is built upon four key components: a realization of a point process as a random counting measure, a generalized point process regression framework, a new kernel function for random measure through kernel embedding, and a suite of low-dimensional structures including the additive model, reduced basis representation, and sparsity. We develop an efficient penalized likelihood procedure for model estimation, and establish both the estimation consistency and selection consistency of the estimator, while allowing the number of point process predictors to diverge. We illustrate and evaluate our method through simulations and an electronic health record data application.