A Gaussian process regression model based on Bootstrap

Abstract

Gaussian process regression is a commonly used non-parametric regression model for the analysis of high-dimensional data. However, due to the complexity of the data fitting curve, the model may be overfitting or underfitting. Based on this, this paper proposes a Gaussian process regression model based on the Bootstrap method (BGP method) to alleviate the overfitting or underfitting phenomenon of a single Gaussian process regression model. Specifically, on the one hand, the proposed method can balance the training error and test error of the prediction model, and make the model have high robustness while reducing the fluctuation level of the estimator. On the other hand, the method uses the weighted variance of the posteriori distribution to give the response variable an uncertainty measure. A large number of simulation experiments show that the BGP method has the best accuracy and robustness compared with several commonly used regression methods, such as LASSO regression, nonlinear support vector machine regression, decision tree regression and random forest regression. Finally, the empirical analysis results on the meat dataset with ultra-high-dimensional characteristics show that the BGP method still has high applicability for high-dimensional data scenarios. In addition, the BGP model can be further extended to the development of kernel types and hyperparameter determination strategies.