Generalized point process additive models
Kuang-Yao Lee, Jiehuan Sun, Bing Li, Lexin Li
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · Mon
Abstract
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.
Keywords
Cox process, electronic health record, generalized additive model, kernel embedding, point process, reproducing kernel Hilbert space
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