Estimation of convergence rate for multi-regression learning algorithm

作     者：XU ZongBen1,2, ZHANG YongQuan3,1,2 & CAO FeiLong3 1Institute for Information and System Sciences, Xi’an Jiaotong University, Xi’an 710049, China 2MOE Key Labratory for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an 710049, China 3Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou 310018, China 

作者机构：Institute for Information and System Sciences Xi’an Jiaotong University Xi’an China MOE Key Labratory for Intelligent Networks and Network Security Xi’an Jiaotong University Xi’an China Department of Information and Mathematics Sciences China Jiliang University Hangzhou China 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2012年第55卷第3期

页      面：701-713页

核心收录：

学科分类：0810[工学-信息与通信工程] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by National Basic Research Program of China (Grant No. 2007CB311002) National Natural Science Foundation of China (Grant Nos. 90818020, 60873206) 

主　　题：learning theory covering number rate of convergence entropy number 

摘      要：In many applications, the pre-information on regression function is always unknown. Therefore, it is necessary to learn regression function by means of some valid tools. In this paper we investigate the regression problem in learning theory, i.e., convergence rate of regression learning algorithm with least square schemes in multi-dimensional polynomial space. Our main aim is to analyze the generalization error for multi-regression problems in learning theory. By using the famous Jackson operators in approximation theory, covering number, entropy number and relative probability inequalities, we obtain the estimates of upper and lower bounds for the convergence rate of learning algorithm. In particular, it is shown that for multi-variable smooth regression functions, the estimates are able to achieve almost optimal rate of convergence except for a logarithmic factor. Our results are significant for the research of convergence, stability and complexity of regression learning algorithm.