Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Soft Margins for AdaBoost
 Machine learning 42 (2001), pp.287320 ISSN: 08856125 

 English 
 Journal Article 
 Fraunhofer FIRST () 
Abstract
Recently ensemble methods like ADABOOST have been applied successfully in many problems, while seemingly defying the problems of overfitting. ADABOOST rarely overfits in the low noise regime, however, we show that it clearly does so for higher noise levels. Central to the understanding of this fact is the margin distribution. ADABOOST can be viewed as a constraint gradient descent in an error function with respect to the margin. We find that ADABOOST asymptotically achieves a hard margin distribution, i.e. the algorithm concentrates its resources on a few hardtolearn patterns that are interestingly very similar to Support Vectors. A hard margin is clearly a suboptimal strategy in the noisy case, and regularization, in our case a "mistrust" in the data, must be introduced in the algorithm to alleviate the distortions that single difficult patterns (e.g. outliers) can cause to the margin distribution. We propose several regularization methods and generalizations of the original ADABOOST algorithm to achieve a soft margin. In particular we suggest (1) regularized ADABOOST(REG) where the gradient decent is done directly with respect to the soft margin and (2) regularized linear and quadratic programming (LP/QP) ADABOOST, where the soft margin is attained by introducing slack variables. Extensive simulations demonstrate that the proposed regularized ADABOOSTtype algorithms are useful and yield competitive results for noisy data.