Extremely randomized neural networks for constructing prediction intervals

The aim of this paper is to propose a novel prediction model based on an ensemble of deep neural networks adapting the extremely randomized trees method originally developed for random forests. The extra-randomness introduced in the ensemble reduces the variance of the predictions and improves out-of-sample accuracy. As a byproduct, we are able to compute the uncertainty about our model predictions and construct interval forecasts. Some of the limitations associated with bootstrap-based algorithms can be overcome by not performing data resampling and thus, by ensuring the suitability of the methodology in low and mid-dimensional settings, or when the i.i.d. assumption does not hold. An extensive Monte Carlo simulation exercise shows the good performance of this novel prediction method in terms of mean square prediction error and the accuracy of the prediction intervals in terms of out-of-sample prediction interval coverage probabilities. The advanced approach delivers better out-of-sample accuracy in experimental settings, improving upon state-of-the-art methods like MC dropout and bootstrap procedures.