Elastic-net regularization: error estimates and active set methods

Elastic-Net Regularization: Error estimates and Active Set Methods

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l 1 and l regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are established. Two iterative numerical ...

Elastic-net regularization in learning theory

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie [H. Zou, T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B, 67(2) (2005) 301–320] for the selection of groups of correlated variables. To investigate the statistical properties of this scheme and in partic...

Regularization and variable selection via the elastic net

We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together.The elastic net is particularly...

An active set approach to the elastic-net and its applications in mass spectrometry

This paper uses the framework of a Mass Spectrometry application to introduce a new method of peak picking as well as two active set methods for the minimization of the elastic-net-functional. The application of peak picking is essential in mass spectrometry and is often based on mean spectra. In contrast our procedure uses a set of spectra obtained from a basis learning method. Our procedure u...

Logistic Regression with Group `1 vs. Elastic Net Regularization