Data‐driven sparse partial least squares

Abstract

In the supervised high dimensional settings with a large number of variables and a low number of individuals, variable selection allows a simpler interpretation and more reliable predictions. That subspace selection is often managed with supervised tools when the real question is motivated by variable prediction. We propose a partial least square (PLS) based method, called data‐driven sparse PLS (ddsPLS), allowing variable selection both in the covariate and the response parts using a single hyperparameter per component. The subspace estimation is also performed by tuning a number of underlying parameters. The ddsPLS method is compared with existing methods such as classical PLS and two well established sparse PLS methods through numerical simulations. The observed results are promising both in terms of variable selection and prediction performance. This methodology is based on new prediction quality descriptors associated with the classical R2 and Q2 , and uses bootstrap sampling to tune parameters and select an optimal regression model.