Analysis of boosting algorithms using the smooth margin function

• 成果类型: Article
• 署名作者: Rudin, Cynthia; Schapire, Robert E.; Daubechies, Ingrid
• 署名单位: Columbia University; Princeton University; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000785
• 发表日期: 2007
• 页码: 2723-2768
• 关键词: logistic-regression; adaboost; CONVERGENCE

摘要

We introduce a useful tool for analyzing boosting algorithms called the smooth margin function, a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, coordinate ascent boosting and approximate coordinate ascent boosting, which are similar to Freund and Schapire's AdaBoost algorithm and Breiman's arc-gv algorithm. We give convergence rates to the maximum margin solution for both of our algorithms and for arc-gv. We then study AdaBoost's convergence properties using the smooth margin function. We precisely bound the margin attained by AdaBoost when the edges of the weak classifiers fall within a specified range. This shows that a previous bound proved by Ratsch and Warmuth is exactly tight. Furthermore, we use the smooth margin to capture explicit properties of AdaBoost in cases where cyclic behavior occurs.