| 基于投影算子的正则化最小二乘回归 |
| |
| 引用本文： | 杨运中,冯云龙.基于投影算子的正则化最小二乘回归[J].武汉大学学报(理学版),2012,58(2):100-104. |
| |
| 作者姓名： | 杨运中 冯云龙 |
| |
| 作者单位： | 1. 南京机电职业技术学院机械工程系,江苏南京,211135
2. 中国科学技术大学-香港城市大学联合高等研究中心,江苏苏州,215123 |
| |
| 摘 要： | 通过引入经验覆盖数（empirical covering number）和投影算子（projection-operator）,从理论上研究正则化最小二乘回归学习算法.与已有的方法相比,一方面简化了回归分析的过程;另一方面,提高了最小二则回归学习算法的误差收敛阶.即,通过引入投影算子,得到了O（m-1）型的收敛阶,这是统计学习理论中关于泛化误差的最佳逼近阶.
|
| 关 键 词： | 学习理论 正则化最小二乘回归 投影算子 经验覆盖数 |
The Regularized Least-Square Regression via the Projection Operator |
| |
| YANG Yunzhong,FENG Yunlong.The Regularized Least-Square Regression via the Projection Operator[J].JOurnal of Wuhan University:Natural Science Edition,2012,58(2):100-104. |
| |
| Authors: | YANG Yunzhong FENG Yunlong |
| |
| Institution: | 1.Department of Mechanical Engineering,Nanjing Institute of Mechatronic Technology,Nanjing 211135,Jiangsu,China; 2.Joint Advanced Research Center of University of Science and Technology of China and City University of Hong Kong,Suzhou 215123,Jiangsu,China) |
| |
| Abstract: | In this paper,we investigate the regularized least-square regression problem by making use of empirical covering numbers and the projection operator.Learning rates are conducted based on these techniques.Comparing with existing results,we simplify the theoretical analysis.Moreover,learning rates are also improved under mild conditions.Concretely speaking,the learning rates we obtained are of type O(m-1),which are regarded as the optimal learning rates on the generalization errors in learning theory literature.Meanwhile,we abandon the widely adopted iteration methods when deriving the generalization errors. |
| |
| Keywords: | learning theory regularized least-square regression projection operator empirical covering number |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
