Recently ensemble methods like AdaBoost were successfully applied to character recognition tasks, seemingly defying the problems of overfitting. This paper shows that although AdaBoost rarely overfits in the low noise regime it clearly does so for higher noise levels. Central for understanding this fact is the margin distribution and we find that AdaBoost achieves -- doing gradient descent in an error function with respect to the margin -- asymptotically a hard margin distribution, i.e. the algorithm concentrates its resources on a few hard-to-learn patterns (here an interesting overlap emerge to Support Vectors). This is clearly a sub-optimal strategy in the noisy case, and regularization, i.e. a mistrust in the data, must be introduced in the algorithm to alleviate the distortions that a difficult pattern (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 -- a ...

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Boosting methods maximize a hard classification margin and are known as powerful techniques that do not exhibit overfitting for low noise cases. Also for noisy data boosting will try to enforce a hard margin and thereby give too much weight to outliers, which then leads to the dilemma of non-smooth fits and overfitting. Therefore we propose three algorithms to allow for soft margin classification by introducing regularization with slack variables into the boosting concept: (1) AdaBoost reg and regularized versions of (2) linear and (3) quadratic programming AdaBoost. Experiments show the usefulness of the proposed algorithms in comparison to another soft margin classifier: the support vector machine.

Recent work has shown that combining multiple versions of weak classifiers such as decision trees or neural networks results in reduced test set error. To study this in greater detail, we analyze the asymptotic behavior of AdaBoost. The theoretical analysis establishes the relation between the distribution of margins of the training examples and the generated voting classification rule. The paper shows asymptotic experimental results with RBF networks for the binary classification case underlining the theoretical findings. Our experiments show that AdaBoost does overfit, indeed. In order to avoid this and to get better generalization performance, we propose a regularized improved version of AdaBoost, which is called AdaBoostreg . We show the usefulness of this improvement in numerical simulations. KEYWORDS: ensemble learning, AdaBoost, margin distribution, generalization, support vectors, RBF networks 1. Introduction An ensemble is a collection of neural networks or other types of c...