GMDH算法的终止法则研究

Research on Stopping Criterion of GMDH

为了从理论上说明GMDH(GroupMethodofDataHanding)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。

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.