## Boosting with the L_2-Loss: Regression and Classification (2001)

Citations: | 121 - 16 self |

### BibTeX

@MISC{Bühlmann01boostingwith,

author = {Peter Bühlmann and Bin Yu},

title = {Boosting with the L_2-Loss: Regression and Classification},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper investigates a variant of boosting, L 2 Boost, which is constructed from a functional gradient descent algorithm with the L 2 -loss function. Based on an explicit stagewise re tting expression of L 2 Boost, the case of (symmetric) linear weak learners is studied in detail in both regression and two-class classification. In particular, with the boosting iteration m working as the smoothing or regularization parameter, a new exponential bias-variance trade off is found with the variance (complexity) term bounded as m tends to infinity. When the weak learner is a smoothing spline, an optimal rate of convergence result holds for both regression and two-class classification. And this boosted smoothing spline adapts to higher order, unknown smoothness. Moreover, a simple expansion of the 0-1 loss function is derived to reveal the importance of the decision boundary, bias reduction, and impossibility of an additive bias-variance decomposition in classification. Finally, simulation and real data set results are obtained to demonstrate the attractiveness of L 2 Boost, particularly with a novel component-wise cubic smoothing spline as an effective and practical weak learner.