PAC learning algorithms for functions approximated by feedforward networks

The authors present a class of efficient algorithms for PAC learning continuous functions and regressions that are approximated by feedforward networks. The algorithms are applicable to networks with unknown weights located only in the output layer and are obtained by utilizing the potential function methods of Aizerman et al. Conditions relating the sample sizes to the error bounds are derived using martingale-type inequalities. For concreteness, the discussion is presented in terms of neural networks, but the results are applicable to general feedforward networks, in particular to wavelet networks. The algorithms can be directly adapted to concept learning problems