Abstract
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.
Highlights
It is important for a predictor to be able to estimate the reliability of the prediction results
The models adopted for prediction mainly include fuzzy model [3], support vector machine (SVM) [4, 5], and neural networks (NNs) [6,7,8], in which NNs-based models are the most commonly used for prediction intervals (PIs) construction
As for the drawbacks of the conventional ensemble structure analysed in the introduction, the contribution of this study lies in a distributed NNs ensemble, which consists of several local Gaussian granular NNs (GGNNs) whose connections are described by Gaussian probability density function (PDF)
Summary
It is important for a predictor to be able to estimate the reliability of the prediction results. Compared to the point-oriented methods, PIs construction can be employed to quantify the modelling uncertainty and the data noise It becomes more popular in the field of data-based prediction [1, 2]. At present, there is still a lack of some relative research on the granular NNs ensemble-based PIs. In this study, a Map-Reduce based distributed computing structure composed of a number of local Gaussian granular NNs (GGNNs) is proposed in this study for PIs construction. The coefficient can be estimated by evaluating the performance of PIs constructed by the local networks, where a new evaluation principle is designed here with the consideration of the interval width, the coverage probability, and the accuracy. To simultaneously estimate the uncertainties due to modelling and data noises, GGNNs are constructed as the local networks, and the neurons connections and the outputs are represented by Gaussian distributions.
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