Research on Partial Functional Nonparametric Regression Models Based on Gaussian Process Prior Modeling

Abstract

Aiming at data scenarios simultaneously involving vector - type and functional - type covariates, this paper proposes a partial functional regression model grounded in a Gaussian process prior. The core innovation of the method resides in: introducing a Gaussian process prior to the association structure between the functional - type covariate and the scalar response variable, while assuming the connection function between the vector - type covariate and the scalar response variable exists within the reproducing kernel Hilbert space. This dual specification empowers the model to effectively capture the nonlinear relationship between the vector - type covariate and the response variable via flexible adjustment of the kernel function, and also accounts for the characteristic depiction of the functional - type covariate. Results of actual data analysis validate the superiority of the proposed method, with its predictive performance significantly outperforming existing benchmark approaches, thereby furnishing a more effective solution for regression modeling in complex covariate scenarios.