I have a question regarding the mutual information of conditionally independent random variables (observations).
Given $p(x,y|z) = p(x|z)p(y|z)$ where $z$ corresponds to a latent variable, I was wondering if an established approach exists for the decomposition of the mutual information $I(x;y)$ such that only quantities (MI / entropy / etc.) between one variable and the latent variable need to be calculated $I(x;y) = F(I(x;z), I(y;z))$?