Math @ Duke

Publications [#287180] of Ingrid Daubechies
Papers Published
 Rudin, C; Schapire, RE; Daubechies, I, Analysis of boosting algorithms using the smooth margin function,
Annals of statistics, vol. 35 no. 6
(2007),
pp. 27232768, ISSN 00905364 [doi]
(last updated on 2017/12/16)
Abstract: 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 arcgv algorithm. We give convergence rates to the maximum margin solution for both of our algorithms and for arcgv. 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.


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