Sparse Partial Least Squares Regression for Simultaneous Dimension Reduction and Variable Selection

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…

• NS
  National Science Foundation

  Awards: 0804597, DMS 0804597
• NI
  National Institutes of Health

  Award: H6003747