Globally Sparse PLS Regression

Abstract Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. It provides better predictive ability than principle component analysis by taking into account both the independent and re-sponse variables in the dimension reduction procedure. However, PLS suffers from over-fitting problems for few samples but many variables. We formulate a new crite-rion for sparse PLS by adding a structured sparsity constraint to the global SIMPLS optimization. The constraint is a sparsity-inducing norm, which is useful for select-ing the important variables shared among all the components. The optimization is solved by an augmented Lagrangian method to obtain the PLS components and to perform variable selection simultaneously. We propose a novel greedy algorithm to overcome the computation difficulties. Experiments demonstrate that our approach to PLS regression attains better performance with fewer selected predictors