I am reading about variational auto encoders, and there is the below loss function:

$l_i(\Theta,\phi) = - {\mathbb{E}}_{z\sim q} [log p_{\phi}(x_i|z)] + KL(q_{\phi}(z_i|x)||p(z))$

What does the notation $z\sim q$ under $\mathbb{E}$ mean? I just have seen notations like $E(X)$ or $ \langle X\rangle $ for expected value, $\mathbb{E}$.

What does this notation generally mean when using $\mathbb{E}_{x\sim y}$ for some $x$ and some $y$?

I am reading about variational auto encoders, and there is the below loss function:

$$l_i(\Theta,\phi) = - {\mathbb{E}}_{z\sim q} \left[\log p_\phi(x_i|z)\right] + KL(q_{\phi}(z_i|x)||p(z))$$

What does the notation $z\sim q$ under $\mathbb{E}$ mean? I just have seen notations like $E(X)$ or $ \langle X\rangle $ for expected value, $\mathbb{E}$.

What does this notation generally mean when using $\mathbb{E}_{x\sim y}$ for some $x$ and some $y$?

I am reading about variational auto encoders and there is the bellow loss function:
 $l_i(\Theta,\phi) = - {\mathbb{E}}_{z\sim q} [log p_{\phi}(x_i|z)] + KL(q_{\phi}(z_i|x)||p(z))$

My question is: What does the notation $z\sim q$ under $\mathbb{E}$ mean. I just have seen for expected value $\mathbb{E}$ notations like $E(X)$ or $ \langle X\rangle $.
Could someone explain what this notation generally means when using  $\mathbb{E}_{x\sim y}$ for some $x$ and some $y$?

I am reading about variational auto encoders, and there is the below loss function: 

$l_i(\Theta,\phi) = - {\mathbb{E}}_{z\sim q} [log p_{\phi}(x_i|z)] + KL(q_{\phi}(z_i|x)||p(z))$

What does the notation $z\sim q$ under $\mathbb{E}$ mean? I just have seen notations like $E(X)$ or $ \langle X\rangle $ for expected value, $\mathbb{E}$.

What does this notation generally mean when using $\mathbb{E}_{x\sim y}$ for some $x$ and some $y$?