基于M-estimator的鲁棒宽度学习系统  

M-estimator-based robust broad learning system

作　　者：郭威 徐涛[3] GUO Wei;XU Tao(Jiangsu Provincial Key Constructive Laboratory for Big Data of Psychology and Cognitive Science,Yancheng Teachers University,Yancheng 224002,China;College of Information Engineering,Yancheng Teachers University,Yancheng 224002,China;College of Computer Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]盐城师范学院江苏省心理与认知科学大数据重点建设实验室,江苏盐城224002 [2]盐城师范学院信息工程学院,江苏盐城224002 [3]南京航空航天大学计算机科学与技术学院,南京210016

出　　处：《控制与决策》2023年第4期1039-1046,共8页Control and Decision

基　　金：国家自然科学基金项目(61603326);江苏省心理与认知科学大数据重点建设实验室开放基金项目(72591962004G)。

摘　　要：宽度学习系统(BLS)是最近提出的一种准确且高效的新兴机器学习算法,已在分类、回归等问题中展现出优越的学习性能.然而,传统BLS以最小二乘作为学习准则,易受到离群值的干扰从而生成不准确的学习模型.鉴于此,提出一种基于M-estimator的鲁棒宽度学习系统(RBLS).与BLS不同,RBLS在学习模型中使用具有鲁棒特性的M-estimator代价函数替代传统的最小二乘代价函数,并采用拉格朗日乘子法和迭代加权最小二乘方法进行优化求解.在迭代学习过程中,正常样本和离群值样本将根据其训练误差的大小而被逆向赋予不同的权重,从而有效地抑制或消除离群值误差对学习模型的不利影响.实验结果表明,作为一种统一的鲁棒学习框架,RBLS可以融合使用不同的M-estimator加权策略,且能够取得更好的泛化性能和鲁棒性.The broad learning system(BLS)is an accurate and efficient machine learning algorithm proposed recently,which has shown excellent performance in classification,regression and other problems.However,the traditional BLS takes least squares as learning criterion,which is prone to be affected by outliers and thus generates inaccurate learning models.To solve this problem,this paper proposes a robust broad learning system(RBLS)based on an M-estimator.Different from the BLS,the RBLS uses a robust M-estimator cost function to replace the traditional least squares cost function in the learning model,and adopts the Lagrange multiplier method and the iteratively reweighted least squares method to seek for an optimal solution.In the iterative learning process,the normal sample and the outlier sample will be reversely assigned different weights according to the size of their training errors,so as to effectively suppress or eliminate the adverse effects of the outlier residual on the learning model.Experimental results show that,as a unified robust learning framework,the RBLS can combine different M-estimator weighting strategies and achieve better generalization performance and robustness than the comparison algorithms.

关 键 词：宽度学习系统 离群值 鲁棒性 M估计 迭代加权最小二乘 拉格朗日乘子法 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]