Variable selection using axis-aligned random projections for partial least-squares regression

Abstract

In high-dimensional data modeling, variable selection plays a crucial role in improving predictive accuracy and enhancing model interpretability through sparse representation. Unfortunately, certain variable selection methods encounter challenges such as insufficient model sparsity, high computational overhead, and difficulties in handling large-scale data. Recently, axis-aligned random projection techniques have been applied to address these issues by selecting variables. However, these techniques have seen limited application in handling complex data within the regression framework. In this study, we propose a novel method, sparse partial least squares via axis-aligned random projection, designed for the analysis of high-dimensional data. Initially, axis-aligned random projection is utilized to obtain a sparse loading vector, significantly reducing computational complexity. Subsequently, partial least squares regression is conducted within the subspace of the top-ranked significant variables. The submatrices are iteratively updated until an optimal sparse partial least squares model is achieved. Comparative analysis with some state-of-the-art high-dimensional regression methods demonstrates that the proposed method exhibits superior predictive performance. To illustrate its effectiveness, we apply the method to four cases, including one simulated dataset and three real-world datasets. The results show the proposed method’s ability to identify important variables in all four cases.