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.

本文的目的是提出一种基于深度神经网络集成的新型预测模型，该模型适应最初为随机森林开发的极度随机树方法。集成中引入的额外随机性降低了预测的方差并提高了样本外的准确性。作为副产品，我们能够计算模型预测的不确定性并构建区间预测。与基于引导的算法相关的一些限制可以通过不执行数据重采样来克服，因此，通过确保该方法在低维和中维设置中的适用性，或者当$\mathrm{一世}.\mathrm{一世}.d.$假设不成立。广泛的蒙特卡罗模拟练习表明，这种新型预测方法在均方预测误差和预测区间在样本外预测区间覆盖概率方面的准确性方面具有良好的性能。先进的方法在实验设置中提供了更好的样本外准确性，改进了最先进的方法，如 MC dropout 和 bootstrap 程序。