#aggregate-posterior

Question 1: Select all that apply

A VAE with encoder $q_\phi(z \mid x) = \mathcal{N}(\mu(x), \sigma^2(x) I)$ is trained perfectly: the aggregate posterior $q_\phi(z) = \mathbb{E}_{x \sim p_{\text{data}}}[q_\phi(z \mid x)]$ equals the prior $\mathcal{N}(0, I)$ , and the model's marginal $p_\theta(x)$ equals $p_{\text{data}}$ . Which statements follow? Select all that apply.

Sampling $z \sim \mathcal{N}(0, I)$ and then $x \sim p_\theta(x \mid z)$ gives samples from $p_{\text{data}}$ 1
The encoder means $\mu(x)$ , for $x \sim p_{\text{data}}$ , are distributed as $\mathcal{N}(0, I)$ 2
Decoding only the means $\mu(x)$ of the data reproduces $p_{\text{data}}$ 3
Every individual posterior $q_\phi(z \mid x)$ equals $\mathcal{N}(0, I)$ 4

#aggregate-posterior

Timed test