TITLE: What do the tilde and the set E refer to here?
QUESTION [5 upvotes]: I'm wondering what the subscript means here, specifically the tilde, and if the set E
is a known set in Math that I'm unfamiliar with.
This is a definition that I found in the description of a generative adversarial network.

REPLY [4 votes]: The $\mathbb{E}$ means "expected value," or average. The other stuff, $x, y \sim  p_{\text{data}(x, y) }$ may mean that the variables $x$ and $y$ follow the distribution described by $p_\text{data}$.
To learn more, find any elementary probability theory text, although they'll use some different notation.