New Developments in Sparse PLS Regression - Magnanensi, Jérémy; Maumy-Bertrand, Myriam; Meyer, Nicolas; Bertrand, Frédéric (Frontiers in Applied Mathematics and Statistics, 2021)
Methods based on partial least squares (PLS) regression, which has recently gained much attention in the analysis of high-dimensional genomic datasets, have been developed since the early 2000s for performing variable selection. Most of these techniques rely on tuning parameters that are often determined by cross-validation (CV) based methods, which raises important stability issues. To overcome this, we have developed a new dynamic bootstrap-based method for significant predictor selection, suitable for both PLS regression and its incorporation into generalized linear models (GPLS). It relies on the establishment of bootstrap confidence intervals, which allows testing of the significance of predictors at preset type I risk $α$, and avoids the use of CV. We have also developed adapted versions of sparse PLS (SPLS) and sparse GPLS regression (SGPLS), using a recently introduced non-parametric bootstrap-based technique for the determination of the numbers of components. We compare their variable selection reliability and stability concerning tuning parameters determination, as well as their predictive ability, using simulated data for PLS and real microarray gene expression data for PLS-logistic classification. We observe that our new dynamic bootstrap-based method has the property of best separating random noise in $y$ from the relevant information with respect to other methods, leading to better accuracy and predictive abilities, especially for non-negligible noise levels.