Sparse twoblock dimension reduction for simultaneous compression and variable selection in two blocks of variables

TL;DR

This paper introduces a sparse two-block dimension reduction method that simultaneously compresses data and performs variable selection, improving multivariate regression and prediction in chemometric applications.

Contribution

It presents a novel sparse dimension reduction technique for two blocks of variables that enhances variable selection and prediction in multivariate regression.

Findings

Outperforms dense methods and multivariate PLS in simulations.

Improves joint prediction of multivariate dependent variables.

Effective in chemometric applications.

Abstract

A method is introduced to perform simultaneous sparse dimension reduction on two blocks of variables. Beyond dimension reduction, it also yields an estimator for multivariate regression with the capability to intrinsically deselect uninformative variables in both independent and dependent blocks. An algorithm is provided that leads to a straightforward implementation of the method. The benefits of simultaneous sparse dimension reduction are shown to carry through to enhanced capability to predict a set of multivariate dependent variables jointly. Both in a simulation study and in two chemometric applications, the new method outperforms its dense counterpart, as well as multivariate partial least squares.