• Open Access

Sparse partial least squares regression for simultaneous dimension reduction and variable selection


Sündüz Keleş, Departments of Statistics and of Biostatistics and Medical Informatics, University of Wisconsin—Madison, 1300 University Avenue, 1245B Medical Sciences Center, Madison, WI 53706, USA.
E-mail: keles@stat.wisc.edu


Summary.  Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data.