Penalized Partial Least Squares with Applications to B-Splines Transformations and Functional Data
Nicole Krämer, Anne-Laure Boulesteix and Gerhard Tutz
We propose a novel framework that combines penalization with Partial Least Squares (PLS). Starting with a generalized additive model, we expand each additive component in terms of a generous amount of B-Splines basis functions. In order to prevent overfitting, we estimate the model by applying a penalized version of PLS. This new method can be computed virtually as fast as PLS. Furthermore, we prove a close connection of penalized PLS to preconditioned linear systems. The proposed approach is very general and can be applied to other problems. In particular, we show its benefit for noisy functional data.