Assigning Confidence Intervals to Neural Network Predictions 1
Richard Dybowski · 1997
This report reviews three possible approaches to the assignment of confidence intervals to feed-forward neural networks, namely, bootstrap estimation, maximum likelihood estimation, and Bayesian statistics. The report concludes with a proposal for mixture modelling via Markov Chain Monte Carlo sampling to enable non-Gaussian variances to be modelled without introducing the bias caused by maximum likelihood. 1. Regression models Regression analysis is a common approach to modelling the relationship between a variable t and a vector of variables x. The method assumes that t is related to x by stochastic and deterministic elements: the stochastic element is a probability function p(t|x) with mean E[t|x]; the deterministic element is E[t|x] as a function of x. The aim of the modelling process is to estimate the functional relationship between E[t|x] and x (the regression model) from a given dataset. Even if the type of regression model selected (i.e. linear, polynomial, etc.) is appropriate for the data, deriving a regression model from a dataset is prone to variation. This is due to intrinsic noise resulting from the variance of p(t|x) coupled with the fact that the dataset is finite and subject to sampling variation. Because of this variation, two types of confidence intervals are traditionally associated with a regressionbased