Consistency of two stage method in classification: Dimension reduction boosting

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method-dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application.