Research On Regression of High-Dimensional Redundant Data Based on Elastic Net and Gaussian Process

Abstract

In modern scientific research and engineering practice, managing high-dimensional and redundant datasets has become a prevalent challenge. Such datasets often contain a substantial amount of noise and irrelevant information, which significantly complicates traditional regression modeling approaches. Consequently, the development of a regression model that can effectively tackle high-dimensional redundant data, thereby extracting valuable information from complex datasets and making precise predictions, is of paramount importance. To tackle this challenge, this paper introduces an innovative regression model. The method integrates L1 and L2 regularization techniques to diminish redundant information within high-dimensional data, thereby enhancing the model's generalization capabilities. Simultaneously, the elastic net approach balances the model's complexity with noise sensitivity when handling high-dimensional data, preventing overfitting and underfitting, and thus improving prediction accuracy. The model parameters are determined using the maximum likelihood estimation algorithm. Simulation experiments and actual data analysis demonstrate that the proposed method surpasses benchmark methods in performance, showcasing its robust competitiveness.