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階層型ニューラルネットによる非線形多変量データ解析に関する研究

利用分层神经网络进行非线性多元数据分析的研究

基本信息

批准号：
09680317
负责人：
TSUJITANI Masaaki
金额：
$ 0.58万
依托单位：
Osaka Electronic-Communication University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

项目摘要

In application of feed-forward neural network models to regression and classification problems, we introduce the probabilistic interpretations of network outputs and construct the likelihood principle of the models. We first, present a feed-forward neural network model for a single binary output, which can be regarded as an extension of ordinal logistic regression models. With the arc-sine transformation for binary response, we provide the likelihood function of network models and the learning algorithm. It is proved that maximizing the likelihood function based on the arc-sine transformation results in minimizing the sum-of-squares error function in the neural network model. The proposed method is evaluated by comparison with ordinal logistic regression model through the index plots of the residuals.Non-linear discriminant analysis in classification problems is also investigated by using feed-forward neural networks with a single or multiple outputs. We derive the theorem of the relat … More ionship of two types of error function, i. e., the sum-of-squares error function and the Kullback-Leibler measure. Statistical inference based on the likelihood approach is then formulated in order to optimize a complex network model. AIC with the sum-of-squares, which is based on the assumption that the noise is normally distributed, has been used for selection of a best model among several competing models. We suggest an alternative information criterion based on the bootstrap method for determination of the appropriate number of hidden units. We also present the bootstrap estimates of the actual error rates because excess error estimation is important when the training sample is small relative to the number of parameters. It is shown that the proposed method has smaller error rates than those by Fisher's discriminant analysis and CART (Classification And Regression Trees).Complex network models do not always achieve good generalization due to the learning of the noise. We thus develop the pruning algorithm of the connection weights using the likelihood-ratio statistic in order to test the significance of the connection weights. We also use the likelihood-ratio statistic for selecting the best subset of predictor variables. From the point of dimensionality reduction, we finally study the relationship between discriminant analysis and fee-forward neural networks used for classification. By analogy with the technique for the canonical scores in the multi-dimensional canonical discriminant analysis, we derive the compression scores as the linear combination of predictor variables. It allows us to reduce the dimensions of the information due to graphical presentation of the data. Less

在前馈神经网络模型的回归和分类问题的应用中，我们引入了网络输出的概率解释，并构造了模型的似然原理。首先，我们提出了一个前馈神经网络模型的一个单一的二进制输出，它可以被视为有序逻辑回归模型的扩展。通过对二值响应的反正弦变换，给出了网络模型的似然函数和学习算法。证明了基于反正弦变换的似然函数的最大化使得神经网络模型中的误差平方和函数最小。通过残差指数图与有序逻辑回归模型的比较，对该方法进行了评价，并利用单输出或多输出前馈神经网络研究了非线性判别分析在分类问题中的应用。我们导出了关系定理， ...更多信息两类误差函数的独立性，即：例如，平方和误差函数和Kullback-Leibler测度。基于似然方法的统计推断，然后制定，以优化复杂的网络模型。AIC与平方和，这是基于假设的噪声是正态分布的，已被用于选择一个最好的模型之间的几个竞争模型。我们提出了一种替代的信息准则的基础上的自举方法确定适当数量的隐藏单元。我们还提出了实际错误率的自举估计，因为当训练样本相对于参数的数量较小时，过量的错误估计是很重要的。实验结果表明，该方法比Fisher判别分析和CART（Classification And Regression Trees）方法具有更小的错误率，但复杂网络模型由于噪声的影响，并不总是具有很好的泛化能力。因此，我们开发的修剪算法的连接权重使用似然比统计，以测试的显着性的连接权重。我们还使用似然比统计量来选择预测变量的最佳子集。最后，从降维的角度研究了判别分析与前馈神经网络用于分类的关系。通过与多维典型判别分析中的典型分数的技术类比，我们将压缩分数导出为预测变量的线性组合。由于数据的图形表示，它使我们能够减少信息的维度。少