概率测度空间的随机变量函数偏导数研究
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摘要
提出了基于概率测度空间的随机变量函数偏导数分析方法.首先对概率测度收敛性进行分析,然后进行了随机变量函数的偏导数推理,给出随机变量偏导数的定义,并给出概率测度空间中随机变量函数的偏导数公式.将单随机变量函数的偏导数应用于神经网络的敏感性分析,实验结果支持了该方法的可行性和有效性.
A new method of partial derivative analysis of random variable function based on probabilistic measure space is proposed.Firstly,the convergence of probability measure is analyzed,and then the partial derivative reasoning of random variable function is carried out,the definition of partial derivative of random variable is given,and the partial derivative formula of random variable function in probabilistic measure space is given.The partial derivatives of variable functions are applied to the sensitivity analysis of neural networks.The experimental results show that the method is feasible and effective.
A new method of partial derivative analysis of random variable function based on probabilistic measure space is proposed.Firstly,the convergence of probability measure is analyzed,and then the partial derivative reasoning of random variable function is carried out,the definition of partial derivative of random variable is given,and the partial derivative formula of random variable function in probabilistic measure space is given.The partial derivatives of variable functions are applied to the sensitivity analysis of neural networks.The experimental results show that the method is feasible and effective.
引文
[1]Daniel S,Sun X Q.Usingfunction approximation to analyze the sensitivity of MLP with antisymmetric squashing activation function[J].IEEE Transactions on Neural Networks[J].2002,13(1):34-44.
[2]Wing W Y.Yeung:Selection ofweight quantization accuracy for radial basis function neural network using stochastic sensitivity measure[J].Electronics Letters,2003,39(10):787-789.
[3]Shi D,Yeung D S,Gao J.Sensitivity analysis applied to the construction of radial basis function networks[J].Neural Networks,2005,18(7):951-957.
[4]Wang X Z,Li C G.A new definition of sensitivity for RBFNN and its applications to feature reduction[J].Lecture Notes in Computer Science,2005,3496(19):81-86.
[5]张丹丹.随机变量分布函数的偏导数分析[J].内蒙古师范大学学报:自然科学汉文版,2017,46(5):650-652.
[2]Wing W Y.Yeung:Selection ofweight quantization accuracy for radial basis function neural network using stochastic sensitivity measure[J].Electronics Letters,2003,39(10):787-789.
[3]Shi D,Yeung D S,Gao J.Sensitivity analysis applied to the construction of radial basis function networks[J].Neural Networks,2005,18(7):951-957.
[4]Wang X Z,Li C G.A new definition of sensitivity for RBFNN and its applications to feature reduction[J].Lecture Notes in Computer Science,2005,3496(19):81-86.
[5]张丹丹.随机变量分布函数的偏导数分析[J].内蒙古师范大学学报:自然科学汉文版,2017,46(5):650-652.