In this paper we develop the method of bounding the generalization error of a classifier in terms of its margin distribution which was introduced in the recent papers of Bartlett and Schapire, Freund, Bartlett and Lee. The theory of Gaussian and empirical processes allow us to prove the margin type inequalities for the most general functional classes, the complexity of the class being measured via the so called Gaussian complexity functions. As a simple application of our results, we obtain the bounds of Schapire, Freund, Bartlett and Lee for the generalization error of boosting. We also substantially improve the results of Bartlett on bounding the generalization error of neural networks in terms of h -norms of the weights of neurons. Furthermore, under additional assumptions on the complexity of the class of hypotheses we provide some tighter bounds, which in the case of boosting improve the results of Schapire, Freund, Bartlett and Lee.

In this paper we develop the method of bounding the generalization error of a classifier in terms of its margin distribution which was introduced in the recent papers of Bartlett and Schapire, Freund, Bartlett and Lee. The theory of Gaussian and empirical processes allow us to prove the margin type inequalities for the most general functional classes, the complexity of the class being measured via the so called Gaussian complexity functions. Asa simple application of our results, we obtain the bounds of Schapire, Freund, Bartlett and Lee for the generalization error of boosting. Wealso substantially improve the results of Bartlett on bounding the generalization error of neural networks in terms of h -norms of the weights of neurons. Furthermore, under additional assumptions on the complexity of the class of hypotheses we provide some tighter bounds, which in the case of boosting improve the results of Schapire, Freund, Bartlett and Lee.

We present a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g.

We present a computationally efficient algorithm for function approximation withpiecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished usinga new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significantadvantages over derivative-based search algorithms (e.g.