论文标题:随机意义下依概率测度收敛的偏导数的定义及在RBFNN的敏感性分析中的应用
A Definition of Partial Derivative of Random Functions and Its Application to RBFNN Sensitivity Analysis
论文作者
论文导师 王熙照,论文学位 硕士,论文专业 基础数学
论文单位 河北大学,点击次数 91,论文页数 48页File Size1646K
论文网 http://www.lw23.com/lunwen_765513742/
Probability Measure; Partial Derivative; Sensitivity Analysis; RBFNN
神经网络的敏感性分析一直是神经网络研究的热点之一。目前，国内外有许多学者都在研究神经网络对其各个参数的敏感性，其中，Zurada等人利用实数空间中的偏导数的几何意义定义的敏感性应用很广泛。本文旨在当把神经网络各输入变量看作随机变量时，把这种定义推广到概率测度空间。 本文首先在概率测度空间上，利用依概率测度收敛，定义了多随机变量函数的偏导数，并且偏导数的计算式可以通过替换实值函数的对应的偏导数中所有的实变量替换为随机变量得到。在此基础上，本文把各个输入变量为随机变量时神经网络对第i个输入变量的敏感性，定义为神经网络对第i个输入变量的偏导数平方的数学期望。当神经网络的类型已知，各个输入变量的联合分布函数已知，就可以明确的求出神经网络对各输入变量的敏感性计算式。本文把提出的敏感性定义应用到径向基函数神经网络的冗余属性删除中。当网络的各输入变量相互独立、均服从正态分布时，本文给出了网络对输入变量的敏感性的计算式。把本文的敏感性定义与Zurada等人提出的敏感性定义作比较，实验结果表明，在网络的冗余属性删除的过程中，在不降低网络的测试精度的前提下，本文提出的敏感性能更有效的选择删除网络的冗余属性。
The sensitivity analysis is one of the popular research points of neural networks. Among those who paid much attention to the sensitivity analysis, Zurada et al proposed one remarkable definition of the sensitivity of the input variable of the differential feed-forward neural network. Considering the inputs of neural networks as random variables, this thesis aims at extending this definition to the probability measure space.First, the partial derivative is defined, based on the convergence in probability measure in the probability measure space. The partial derivative can be deduced according to replacing all the real variables of the corresponding partial derivative in real space with random variables. Consequently, the sensitivity of the input random variable of one neural network is defined as the mathematical expectation of the partial derivative in the probability measure space. If the model of the neural network and the distribution of the random variables are known, the calculating formula can be explicitly deduced. When applying the sensitivity definition to the Radial Basis Function Neural Networks (RBFNNs), the sensitivity calculating formulae of the variables are deduced assuming all the random variables are independently and normally distributed. When applying the sensitivity analysis to delete the redundant features of the neural network without losing any accuracy, the simulating results shows that it plays more effective than the sensitivity definition proposed by Zurada et al.
|
