New bounds for correct generalization

A theoretical approach to the determination of the number of training examples for a neural network architecture is provided by the theory of Vapnik and Chervonenkis on the minimization of the empirical risk. We report here a new bound on the joint probability that both the approximation error between the binary function learned by the input/output examples and the target binary function is larger than ε and the empirical error on the examples is smaller than a fixed non-null fraction of ε. The given bounds are independent of the probability distribution on the input space and improve some existing results on the generalization abilities of an adaptive binary function