Relevant and irrelevant predictors in PLS2

Abstract

AbstractPartial least square regression (PLS) is largely applied to solve regression problems when correlation and redundancy are present in the data. In spite of many studies about feature selection and variable importance have been published, to select the subset of relevant features useful to explain the behaviour of the system under investigation and the subset of irrelevant predictors that can be ignored is still an open issue. Here, a new strategy to measure variable importance is introduced, and a wrapper method is proposed for selecting relevant and irrelevant predictors. The variable importance measure is developed grouping the predictors in classes of equivalent features by clustering in the latent space and considering the variations of the goodness of the PLS2 model generated perturbing the block of the predictors. The wrapper method implements stability selection using bootstrap and feature selection. The behaviour of the new variable importance score and its use within the wrapper method are discussed investigating two simulated and one real data set.