Sparsification Subsampling for Partial Least Squares Regression
提出一种基于稀疏化子采样的偏最小二乘回归方法，通过构建稀疏草图矩阵和核心元素估计器，在保证估计精度的同时大幅降低计算复杂度，适用于大规模数据集。
Partial Least Squares (PLS) regression is a powerful tool for dimensionality reduction, multi-response variable regression, and multi-classification. However, its application to large-scale datasets is often hampered by significant computational burdens. Although variants of PLS algorithms have been proposed to address this challenge, an efficient algorithm that significantly reduces the time complexity remains underexplored. In this paper, we propose a novel PLS regression method based on sparsification subsampling to address this gap. We first construct a sparse sketch matrix using element-wise subsampling to obtain an unbiased approximation of the covariance matrix. Based on this, we propose a core-elements estimator that effectively incorporates the subsampled sparse matrix into the PLS regression. The resulting algorithm employs a kernel-based optimization framework to improve computational efficiency. Theoretically, we demonstrate that under specific probabilities, the approximate matrix obtained by sparsification subsampling achieves minimal variance for any given projection matrix. Finally, a series of Monte Carlo simulations and real-world data analyses validate the superior performance of our approach in terms of estimation accuracy, prediction power, and computational efficiency. Compared to row-wise sampling methods and even full-sample PLS, the proposed algorithm exhibits significant advantages.