Note to bounty hunters, since it’s come up twice: An “approximately deterministic function of X” is one where, conditional on X, the entropy of F(X) is very small, though possibly nonzero. I.e. you have very nearly pinned down the value that F(X) takes on once you learn X. For conceptual intuition on the graphical representation, X approximately mediating between F(X) and F(X) (two random variables which always take on the same value as each other) means as always that there is approximately no further update on the value of either given the other, (despite them being perfectly informative about the value of the other,) if one already knows the value of X. See this for more.
Note to bounty hunters, since it’s come up twice: An “approximately deterministic function of X” is one where, conditional on X, the entropy of F(X) is very small, though possibly nonzero. I.e. you have very nearly pinned down the value that F(X) takes on once you learn X. For conceptual intuition on the graphical representation, X approximately mediating between F(X) and F(X) (two random variables which always take on the same value as each other) means as always that there is approximately no further update on the value of either given the other, (despite them being perfectly informative about the value of the other,) if one already knows the value of X. See this for more.
(Note that F, in David’s notation here, is a stochastic function in general.)