A modified backpropagation algorithm for training neural networks on data with error bars Original Research Article

A method is proposed for training multilayer feedforward neural networks on data contaminated with noise. Specifically, we consider the case that the artificial neural system is required to learn a physical mapping when the available target values for the output variable are subject to experimental uncertainties, but are characterized by error bars. The proposed method, based on a maximum-likelihood criterion for parameter estimation that allows for nonzero model error, introduces two simple modifications of the on-line backpropagation learning algorithm: