Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data
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| Authors | Nicole Krämer, Anne-Laure Boulesteix, Gerhard Tutz |
| Journal/Conference Name | Chemometrics and Intelligent Laboratory Systems |
| Paper Category | Other |
| Paper Abstract | We propose a novel framework that combines penalization techniques with Partial Least Squares (PLS). We focus on two important applications. (1) We combine PLS with a roughness penalty to estimate high-dimensional regression problems with functional predictors and scalar response. (2) Starting with an additive model, we expand each variable in terms of a generous number of B-spline basis functions. To prevent overfitting, we estimate the model by applying a penalized version of PLS. We gain additional model flexibility by incorporating a sparsity penalty. Both applications can be formulated in terms of a unified algorithm called Penalized Partial Least Squares, which can be computed virtually as fast as PLS using the kernel trick. Furthermore, we prove a close connection of penalized PLS to preconditioned linear systems. In experiments, we show the benefits of our method to noisy functional data and to sparse nonlinear regression models. |
| Date of publication | 2008 |
| Code Programming Language | R |
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