Analysis of boosting algorithms using the smooth margin function

Journal Article (Journal Article)

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. © Institute of Mathematical Statistics, 2007.

Full Text

Duke Authors

Cited Authors

  • Rudin, C; Schapire, RE; Daubechies, I

Published Date

  • December 1, 2007

Published In

Volume / Issue

  • 35 / 6

Start / End Page

  • 2723 - 2768

International Standard Serial Number (ISSN)

  • 0090-5364

Digital Object Identifier (DOI)

  • 10.1214/009053607000000785

Citation Source

  • Scopus