Comment: Boosting Algorithms: Regularization, Prediction and Model Fitting

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-offreedom 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 and Lv, 2007). In this discussion we elaborate on the connections between L2-boosting of a linear model and infinitesimal forward stagewise linear regression. We then take the authors to task on their definition of degrees of freedom.