Generalized Point Process Additive Models
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: additive-model, functional regression, high-dimensional asymptotics, point processes;, random-objects
Session: IPS 781 - Advanced Topics in Functional and Object Data Analysis
Monday 6 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
In this work, we propose a generalized point process additive model for analyzing scalar responses with high-dimensional point process predictors. Our approach integrates three key components: a generalized point process regression framework, the kernel mean embedding technique with a nested reproducing kernel Hilbert space, and multiple 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 estimation and selection consistency, even as the number of predictor point processes grows. The proposed method is demonstrated through simulations and an application to electronic health record data.