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

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.