Functional Multicore Gaussian Process Regression Modeling Based on Kalman Filtering

Abstract

Aiming at the regression problem in which the response variable is scalar and the predictor variable is functional-type variable, this paper innovatively proposes a functional-type multicore Gaussian process regression model based on Kalman filtering. Firstly, a functional principal component base expansion method is applied to extract features of functional predictor variables to realize the approximate characterization of functional data; then, the potential function between each principal component score and the response variable is assigned to the Gaussian process a priori and multiple Gaussian process regression submodels are constructed using different kernel functions for fitting; finally, the Kalman filtering algorithm is utilized to dynamically integrate the results of the submodels to obtain the final Prediction results. Compared with the traditional integration learning algorithm, this model integrates the uncertainty estimation into the integration framework, fully considers the adaptability of different regenerative kernel Hilbert space from the probability level, and significantly improves the robustness and generalization ability of the model. Empirical studies on meat and maize near-infrared spectral analysis datasets show that the model in this paper exhibits superior prediction performance in both MSE and MAE metrics compared to benchmark methods such as traditional machine learning models: XGBoost, single-kernel Gaussian process regression (GPR): using RBF kernel function. In addition, the construction of differentiated sub-models by adjusting the number of principal component truncations in functional principal component analysis provides a new path for model performance optimization.