Regularized robust Broad Learning System for uncertain data modeling

Broad Learning System (BLS) has achieved outstanding performance in classification and regression problems. Specifically, the accuracy and efficiency can be balanced well by BLS. However, the presence of outliers in data may destroy the stability and generality of standard BLS. In this paper, we propose the robust version of BLS (RBLS) to treat the data modeling with outliers. By assuming the regression residual and output weights follow their respective distributions, the objective function for RBLS is derived and the output weights for robust modeling can be determined by maximum a posterior estimation. Then the robustness of RBLS can be enhanced further by integrating the regularization theory. The Augmented Lagrange Multiplier method is utilized to optimize the novel models efficiently, and a solid theoretical proof is given to guarantee that the proposed RBLS is more robust than the standard BLS. Extensive experiments on function approximation and real-world regression are carried out to demonstrate that our proposed RBLS model can achieve a better modeling performance in uncertain data environment than the standard BLS and other regression algorithms. (C) 2018 Elsevier B.V. All rights reserved.