Estimations of error bounds for neural-network function approximators

Neural networks are being increasingly used for problems involving function approximation. However, a key limitation of neural methods is the lack of a measure of how much confidence can be placed in output estimates. In the last few years many authors have addressed this shortcoming from various angles, focusing primarily on predicting output bounds as a function of the trained network's characteristics, typically as defined by the Hessian matrix. In this paper the problem of the effect of errors or noise in the presented, input, vector is examined and a method based on perturbation analysis of determining output bounds based on both the error in the input vector and the imperfections in the weight values after training is presented and demonstrated.