Models for calculating confidence intervals for neural networks

This research focused on coding and analyzing existing models to calculate confidence intervals on the results of neural networks. The three techniques for determining confidence intervals determination were the non-linear regression, the bootstrapping estimation, and the maximum likelihood estimation. Confidence intervals for non-linear regression, bootstrap estimation, and maximum likelihood were coded in Visual Basic. The neural network used the backpropagation algorithm with an input layer, one hidden layer and an output layer with one unit. The hidden layer had a logistic or binary sigmoidal activation function and the output layer had a linear activation function. These techniques were tested on various data sets with and without additional noise. Out of eight cases studied, non-linear regression and bootstrapping each had the four lowest values for the average coverage probability minus the nominal probability. For the average coverage probabilities minus the nominal probabilities of all data sets, the bootstrapping estimation obtained the lowest values. The ranges and standard deviations of the coverage probabilities over 15 simulations for the three techniques were computed, and it was observed that the non-linear regression obtained consistent results with the least range and standard deviation, and bootstrapping had the largest ranges and standard deviations. The bootstrapping estimation technique gave a slightly better average coverage probability (CP) minus nominal values than the non-linear regression method, but it had considerably more variation in individual simulations. The maximum likelihood estimation had the poorest results with respect to the average CP minus nominal values