Discussion of “ Boosting Algorithms : Regularization , Prediction and Model Fitting ” by Peter Bühlmann and Torsten Hothorn

We congratulate the authors (hereafter BH) for an interesting take on the boosting technology, and for developing a modular computational environment in R for exploring their models. Their use of low-degree-of-freedom smoothing splines as a base learner provides an interesting approach to adaptive additive modeling. The notion of “Twin Boosting” is interesting as well; besides the adaptive lasso, we have seen the idea applied more directly for the lasso and Dantzig selector (James, Radchenko & Lv 2007). In this discussion we elaborate on the connections between L2-boosting of a linear model and infinitesimal forward stagewise linear regression (Section 5.2.1 in BH). We then take the authors to task on their definition of degrees of freedom (Section 5.3 of BH).