Prediction Intervals for Neural Network Models

Neural networks are a consistent example of non-parametric estimation, with powerful universal approximation properties. However, the effective development and deployment of neural network applications, has to be based on established procedures for estimating confidence and especially prediction intervals. This holds particularly true in cases where there is a strong culture for testing the predictive power of a model, e.g., in financial applications. In this paper we review the major state-of-the-art approaches for constructing confidence and prediction intervals for neural networks, discuss their assumptions, strengths and weaknesses and we compare them in the context of a controlled simulation. Our preliminary results, which are being presented in this paper, indicate a clear superiority of the combination of the bootstrap and maximum likelihood approaches in constructing prediction intervals, relative to the analytical approaches. Key-Words: neural networks, confidence intervals, prediction intervals, bootstrap, maximum likelihood.