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

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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.
Funding Information
  • Open Fund Project of Marine Ecological Restoration and Smart Ocean Engineering Research Center of Hebei Province (HBMESO2321, KJ2022-021, KJ2024-012, YJG2024133)
  • Technical Service Project of Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (HBMESO2321, KJ2022-021, KJ2024-012, YJG2024133)
  • Technical Service Project of Hebei Baodi Construction Engineering Co., Ltd. (HBMESO2321, KJ2022-021, KJ2024-012, YJG2024133)
  • Research Project on Graduate Education and Teaching Reform of Hebei Province of China (HBMESO2321, KJ2022-021, KJ2024-012, YJG2024133)

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