A new regularization method for regression models is proposed. The criterion to be minimized contains a penalty term which explicitly links strength of penalization to the correlation between predictors. As the elastic net, the method encourages a grouping effect where strongly correlated...

We review variable selection and variable screening in high-dimensional linear models. Thereby, a major focus is an empirical comparison of various estimation methods with respect to true and false positive selection rates based on 128 different sparse scenarios from semi-real data (real data...

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...

Grouping effect of the elastic net asserts that coefficients corresponding to highly correlated predictors in a linear regression setting have small differences. A quantitative estimate for such small differences was given in Zou and Hastie (2005) when the coefficients have the same sign. We...

Many present day applications of statistical learning involve large numbers of predictor variables. Often, that number is much larger than the number of cases or observations available for training the learning algorithm. In such situations, traditional methods fail. Recently, new techniques...

Varying-coefficient models are useful tools for analyzing longitudinal data. They can effectively describe a relationship between predictors and responses which are repeatedly measured. We consider the problem of selecting variables in the varying-coefficient models via adaptive elastic net...