Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data

By Nicole Krämer, Anne-Laure Boulesteix, Gerhard E. Tutz. 2006

81 citations recorded by the source corpus.

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.

Subfields: Analytical Chemistry, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d1c2826c4c8540b1d60ba98851934b3ddbb138d1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. Cristian Preda
2. Ana M. Aguilera
3. Gilbert Saporta
4. Manuel Escabias

In Statistics and Probability

1. Cristian Preda
2. Gilbert Saporta
3. Ana M. Aguilera
4. Manuel Escabias
5. Simon N. Wood

Citations in the corpus

• Using basis expansions for estimating functional PLS regression Applications with chemometric data (2010, methodology): “A combination of PLS and PCR with B-spline expansions and a roughness penalty have also been developed to estimate the functional linear regression model [19,31].”