Neural-network prediction with noisy predictors

Very often the input variables for neural-network predictions contain measurement errors. In particular, this may happen because the original input variables are often not available at the time of prediction and have to be replaced by predicted values themselves. This issue is usually ignored and results in nonoptimal predictions. This paper shows that under some general conditions, the optimal prediction using noisy input variables can be represented by a neural network with the same structure and the same weights as the optimal prediction using exact input variables. Only the activation functions have to be adjusted. Therefore we can achieve optimal prediction without costly retraining of the neural network. We explicitly provide an exact formula for adjusting the activation functions in a logistic network with Gaussian measurement errors in input variables. This approach is illustrated by an application to short-term load forecasting.