Boosting Correlation Based Penalization in Generalized Linear Models

In high dimensional regression problems penalization techniques are a useful tool for estimation and variable selection. We propose a novel penalization technique that aims at the grouping effect which encourages strongly correlated predictors to be in or out of the model together. The proposed penalty uses the correlation between predictors explicitly. We consider a simple version that does not select variables and a boosted version which is able to reduce the number of variables in the model. Both methods are derived within the framework of generalized linear models. The performance is evaluated by simulations and by use of real world data sets.