Early stopping in L₂ Boosting

It is well known that the boosting-like algorithms, such as AdaBoost and many of its modifications, may over-fit the training data when the number of boosting iterations becomes large. Therefore, how to stop a boosting algorithm at an appropriate iteration time is a longstanding problem for the past decade (see Meir and Rtsch, 2003). Bhlmann and Yu (2005) applied model selection criteria to estimate the stopping iteration for L2Boosting, but it is still necessary to compute all boosting iterations under consideration for the training data. Thus, the main purpose of this paper is focused on studying the early stopping rule for L2Boosting during the training stage to seek a very substantial computational saving. The proposed method is based on a change point detection method on the values of model selection criteria during the training stage. This method is also extended to two-class classification problems which are very common in medical and bioinformatics applications. A simulation study and a real data example to these approaches are provided for illustrations, and comparisons are made with LogitBoost.