Prediction and structural uncertainty analyses of artificial neural networks using hierarchical Bayesian model averaging
Prediction and structural uncertainty analyses of artificial neural networks using hierarchical Bayesian model averaging
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DOI：
10.1016/j.jhydrol.2015.06.007
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发表时间：
2015-09-01
影响因子：
6.4
通讯作者：
Tsai, Frank T. -C.
中科院分区：
文献类型：
--
作者：
Chitsazan, Nima;Nadiri, Ata Allah;Tsai, Frank T. -C.
本研究采用层次贝叶斯模型平均（HBMA）方法对人工神经网络中不确定成分导致的预测不确定性进行分析。HBMA是一种集成预测方法，用于分离人工神经网络模型结构不确定性的来源，并研究其方差对总预测方差的贡献。人工神经网络中考虑的不确定性的具体来源包括神经网络权重和偏差（模型参数）的不确定性，为隐藏层选择激活函数的不确定性，以及选择隐藏层节点数量（模型结构）的不确定性。由不确定输入和人工神经网络模型参数引起的预测不确定性由模型内方差表示。由于激活函数不确定和隐层节点数不确定导致的预测不确定性由模型间方差表示。该方法通过一项利用人工神经网络预测伊朗阿扎尔拜詹马库地区含水层氟浓度的研究得到证明。结果表明，不确定输入和人工神经网络模型参数产生的预测方差最大，其次是不确定隐层节点数和不确定激活函数产生的预测方差。(C) 2015 Elsevier B.V.版权所有
This study adopts a hierarchical Bayesian model averaging (HBMA) method to analyze prediction uncertainty resulted from uncertain components in artificial neural networks (ANNs). The HBMA is an ensemble method for prediction and is used to segregate the sources of model structure uncertainty in ANNs and investigate their variance contributions to total prediction variance. Specific sources of uncertainty considered in ANNs include the uncertainty in neural network weights and biases (model parameters), uncertainty of selecting an activation function for the hidden layer, and uncertainty of selecting a number of hidden layer nodes (model structure). Prediction uncertainties due to uncertain inputs and ANN model parameters are represented by within-model variance. Prediction uncertainties due to uncertain activation function and uncertain number of nodes for the hidden layer are represented by between-model variance. The method is demonstrated through a study that employs ANNs to predict fluoride concentration in the aquifers of the Maku area, Azarbaijan, Iran. The results show that uncertain inputs and ANN model parameters produces the most prediction variance, followed by prediction variances from uncertain number of hidden layer nodes and uncertain activation function. (C) 2015 Elsevier B.V. All rights reserved.