Distributed Gaussian Granular Neural Networks Ensemble for Prediction Intervals Construction

To overcome the weakness of generic neural networks (NNs) ensemble for prediction intervals (PIs) construction, a novel Map-Reduce framework-based distributed NN ensemble consisting of several local Gaussian granular NN (GGNNs) is proposed in this study. Each local network is weighted according to its contribution to the ensemble model. The weighted coefficient is estimated by evaluating the performance of the constructed PIs from each local network. A new evaluation principle is reported with the consideration of the predicting indices. To estimate the modelling uncertainty and the data noise simultaneously, the Gaussian granular is introduced to the numeric NNs. The constructed PIs can then be calculated by the variance of output distribution of each local NN, i.e., the summation of the model uncertainty variance and the data noise variance. To verify the effectiveness of the proposed model, a series of prediction experiments, including two classical time series with additive noise and two industrial time series, are carried out here. The results indicate that the proposed distributed GGNNs ensemble exhibits a good performance for PIs construction.