Suppose I trained a neural network with standardisation of the data following (X-EX)/std(X). The input is x(t) and output is y(t). How can I calculate the sensitivity of this trained network (basically the dy/dx)? if I multiply (1+epsilon) to X, the 1+epsilon will disappear after standardisation. So what should I do? I tried to add a perturbation to the standardized input X' which is (X-mean(X))/(std(X)). But after the perturbation what I got is dy/d(standard(x)) rather than dy/dx. So I also need the ratio of dx/d(standard(x)) where standard(x) is (x(t) - mean(x(t)))/std(x(t)).
We can assume x(t) and y(t) the is N-order Markov process.
So how to calculate the dx/d(standard(x))? thanks a lot!