Confidence and prediction intervals for neural network ensembles

In this paper we propose a new technique that uses the bootstrap to estimate conndence and prediction intervals for neural network (regression) ensembles. Our proposed technique can be applied to any ensemble technique that uses the bootstrap to generate the training sets for the ensemble, such as bagging 1] and balancing 5]. Conndence and prediction intervals are estimated that include a signiicantly improved estimate of underlying model uncertainty (i.e.) the uncertainty of our estimate of the \true" regression. Unlike existing techniques, this estimate of uncertainty will vary according to which ensemble technique is used { if the eeect of using a speciic ensemble technique is to produce less model uncertainty than using another ensemble technique, then this will be reeected in the conndence and prediction intervals. Preliminary results illustrate how our technique can provide more accurate conndence and prediction intervals (intervals that better reeect the desired level of conndence (e.g.) 90%, 95%, etc.) for neural network ensembles than previous attempts.