Partially Functional Linear Regression Based on Gaussian Process Prior and Ensemble Learning

Weice Sun, Jiaqi Xu and Tao Liu ()
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Weice Sun: Sydney Smart Technology College, Northeastern University, Shenyang 110004, China
Jiaqi Xu: Sydney Smart Technology College, Northeastern University, Shenyang 110004, China
Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Mathematics, 2025, vol. 13, issue 5, 1-25

Abstract: A novel partially functional linear regression model with random effects is proposed to address the case of Euclidean covariates and functional covariates. Specifically, the model assumes that the random effects follow a Gaussian process prior to establish the linkage structure between Euclidean covariates and scalar responses. For functional covariates, a linear relationship with scalar responses is assumed, and the functional covariates are approximated using the Karhunen–Loève expansion. To enhance the robustness of the predictive model, a cross-validation-based ensemble strategy is employed to optimize the proposed method. Results from both simulation studies and real-world data analyses demonstrate the superior performance and competitiveness of the proposed approach in terms of prediction accuracy and model stability.

Keywords: partially functional linear regression; random effects; ensemble learning; Gaussian process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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