Boosting Algorithms: Regularization, Prediction and Model Fitting

Boosting Algorithms: Regularization, Prediction and Model Fitting

2007, Vol. 22, No. 4, 477–505 | Peter Bühlmann and Torsten Hothorn
The chapter presents a statistical perspective on boosting, emphasizing its application in estimating complex parametric or non-parametric models, including generalized linear and additive models, as well as regression models for survival analysis. It discusses concepts of degrees of freedom and information criteria, particularly useful for regularization and variable selection in high-dimensional covariate spaces. The practical aspects of boosting procedures are illustrated using the open-source software package `mboost`, which implements functions for model fitting, prediction, and variable selection. The chapter covers the historical development of boosting, from ensemble methods to functional gradient descent (FGD) and its interpretation as a method for function estimation. It also explores various loss functions and boosting algorithms, such as $L_2$Boosting and BinomialBoosting, and their applications in binary classification and regression. The choice of base procedures, such as componentwise linear least squares, smoothing splines, and trees, is discussed, along with the importance of balancing variance and bias in boosting. The chapter concludes with a discussion on the low-variance principle and the need for early stopping to prevent overfitting.The chapter presents a statistical perspective on boosting, emphasizing its application in estimating complex parametric or non-parametric models, including generalized linear and additive models, as well as regression models for survival analysis. It discusses concepts of degrees of freedom and information criteria, particularly useful for regularization and variable selection in high-dimensional covariate spaces. The practical aspects of boosting procedures are illustrated using the open-source software package `mboost`, which implements functions for model fitting, prediction, and variable selection. The chapter covers the historical development of boosting, from ensemble methods to functional gradient descent (FGD) and its interpretation as a method for function estimation. It also explores various loss functions and boosting algorithms, such as $L_2$Boosting and BinomialBoosting, and their applications in binary classification and regression. The choice of base procedures, such as componentwise linear least squares, smoothing splines, and trees, is discussed, along with the importance of balancing variance and bias in boosting. The chapter concludes with a discussion on the low-variance principle and the need for early stopping to prevent overfitting.
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