概率测度空间的随机变量函数偏导数研究

Research on Partial Derivatives of Random Variables in Probability Measure Space

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.