TY - JOUR

T1 - Soft margins for AdaBoost

AU - Rätsch, G.

AU - Onoda, T.

AU - Müller, K. R.

N1 - Funding Information:
We thank for valuable discussions with B. Schölkopf, A. Smola, T. Frieß, D. Schuurmans and B. Williamson. Partial funding from EC STORM project number 25387 is gratefully acknowledged. Furthermore, we acknowledge the referees for valuable comments.

PY - 2001/3

Y1 - 2001/3

N2 - 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 hard-to-learn patterns that are interestingly very similar to Support Vectors. A hard margin is clearly a sub-optimal 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 ADABOOSTREG 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 ADABOOST-type algorithms are useful and yield competitive results for noisy data.

AB - 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 hard-to-learn patterns that are interestingly very similar to Support Vectors. A hard margin is clearly a sub-optimal 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 ADABOOSTREG 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 ADABOOST-type algorithms are useful and yield competitive results for noisy data.

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U2 - 10.1023/A:1007618119488

DO - 10.1023/A:1007618119488

M3 - Article

AN - SCOPUS:0342502195

VL - 42

SP - 287

EP - 320

JO - Machine Learning

JF - Machine Learning

SN - 0885-6125

IS - 3

ER -