What do the tilde and the set E refer to here?

Question

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.

Answer 1

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.