Find if a random variable is a proxy variable using neural networks

I have a probabilistic graphical model (a toy example):

where $B$ is a proxy variable to $A$.

I would like to understand: is $B$ a proxy to $A$?

My idea is to train a neural network with a single neuron in the input and output layer. And if it will be able to convert the random variable into $A$ into $B$, then I can conclude that B is the proxy to A.

Also, does somebody know where I can read more about similar problems (books, papers)…