Mixed-Distribution-Based Robust Stochastic Configuration Networks for Prediction Interval Construction

It is challenging to develop point prediction models with high accuracy due to that outliers and noise are commonly present in the real-world data. In this context, this article proposes a novel robust stochastic configuration network (SCN) and uses the bootstrap ensemble strategy to construct prediction intervals (PIs). Since the output weights of the original SCN are computed by the least-squares method, which is sensitive to noise with an unknown distribution or outliers, a robust SCN based on a mixture of the Gaussian and Laplace distributions (MoGL-SCN) in the Bayesian framework is proposed. The mixed distributions can effectively characterize the complex distributions of the real-world data, and their heavy-tailed properties can improve the robustness of SCNs. Furthermore, there are no analytical solutions available to obtain the network parameters due to the assumption on the mixed distributions, hence, the parameters of the MoGL-SCN are estimated by the expectation-maximization algorithm. In addition, considering the uncertainties caused by both the model mismatch and noise in the real-world data, a bootstrap ensemble strategy using MoGL-SCN is designed to construct the PIs. The experimental results on two benchmark datasets and a real-world dataset demonstrate the effectiveness of the proposed method in terms of the quality of PIs, prediction accuracy, and robustness.