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GMDH算法的终止法则研究
引用本文:张宾,贺昌政.GMDH算法的终止法则研究[J].吉林大学学报(信息科学版),2005,23(3):257-262.
作者姓名:张宾  贺昌政
作者单位:四川大学工商管理学院,成都,610064
摘    要:为了从理论上说明GMDH(Group Method of Data Handing)最优复杂度模型如何在推广能力与拟合精度之间达到平衡,用插值方法讨论了GMDH外准则值取得全局最小值时,对应的模型复杂度的位置.分析了模型在一定噪声水平下,已知训练集上的拟合能力与具有同一规律性的新数据上的推广能力关系,结果显示,GMDH最优模型的结构偏差与噪声影响的比值落在1的一个小领域内,其大小随噪声方差和外准则的变化而变化.说明,GMDH最优模型如何在拟合精度与推广能力之间达到平衡.

关 键 词:GMDH算法  终止法则  最优模型复杂度  GMDH  算法  终止法则  研究  Stopping  Criterion  变化  噪声方差  大小  比值  噪声影响  结构偏差  最优模型  显示  结果  关系  数据  规律  拟合  训练集  噪声水平
文章编号:1671-5896(2005)03-0257-06
修稿时间:2004年7月17日

Research on Stopping Criterion of GMDH
ZHANG Bin,HE Chang-zheng.Research on Stopping Criterion of GMDH[J].Journal of Jilin University:Information Sci Ed,2005,23(3):257-262.
Authors:ZHANG Bin  HE Chang-zheng
Abstract:It is studied theoretically how the trade-off is achieved between the closeness of fit and the generalization power of the optimal GMDH(Group Method of Data Handing) model.The position where the model complexity is corresponding to the minimum of the external criterion is discussed by interpolation method. It is demonstrated that the relationship of model quality on a given learning data set and its generalization power on new,not previously seen data,with the respect to the data sample's noise level,which shows that the ratio between the structural bias and the effect of noise of the optimal GMDH model is in a small domain around 1,and its value changes with the noise and external criterion.This can be explained the way by which the optimal GMDH model arrives at an optimal trade-off between its closeness of fit and the generalization power.
Keywords:group method of data handing(GMDH)  stopping criterion  optimal model complexity  
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