A Partial Functional Gaussian Process Regression Model Based on Additive Structure

Abstract

A partially functional linear model is a widely studied and used method whose response variables are related to both vector-valued and functional predictors. However, due to the constraints of linear structure, the model lacks some flexibility. Based on this, this paper proposes a partial functional Gaussian process regression model. On the one hand, the proposed method uses truncation rule to approximate the functional predictors. Then, the different predictors are mapped into a unified regenerated kernel Hilbert space (RKHS) for modeling using kernel techniques. By assigning a priori of additive structure to the Gaussian process and orthogonalizing the kernel function, this paper uses Sobol index to measure the importance of each prediction component's influence on the prediction of response variables. In addition to quantifying the uncertainty of predictions, the proposed method enables joint modeling of non-Euclidean predictors and response variables by selecting appropriate kernels for non-Euclidean spaces. Both simulation studies and empirical data analyses demonstrate that the proposed approach exhibits strong competitiveness compared to several classical predictive methods.