Analysis of boosting algorithms using the smooth margin function

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dc.creatorRudin, Cynthia
dc.creatorSchapire, Robert E.
dc.creatorDaubechies, Ingrid
dc.date2008-03-28
dc.date.accessioned2026-07-07T12:17:56Z
dc.date.available2026-07-07T12:17:56Z
dc.descriptionWe 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 Rätsch and Warmuth is exactly tight. Furthermore, we use the smooth margin to capture explicit properties of AdaBoost in cases where cyclic behavior occurs.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000785 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0803.4092
dc.identifierhttp://arxiv.org/abs/0803.4092
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 6, 2723-2768
dc.identifierdoi:10.1214/009053607000000785
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212243
dc.subjectMachine Learning
dc.subjectStatistics Theory
dc.subject68W40, 68Q25 (Primary) 68Q32 (Secondary)
dc.titleAnalysis of boosting algorithms using the smooth margin function
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