#gaussian-likelihood

Question 1: Select all that apply

A VAE decoder outputs a mean vector $f_\theta(z)$ and models the data as $P(X \mid z) = \mathcal{N}\big(f_\theta(z), I\big)$ , a Gaussian with unit variance in every dimension. Which statements follow? Select all that apply.

The covariance matrix of $P(X \mid z)$ is the identity matrix1
Given $z$ , the components of $X$ (e.g. pixels) are independent of each other2
Maximising $\log P(X \mid z)$ amounts to minimising $\lVert X - f_\theta(z) \rVert^2$ 3
The decoder must also output a separate variance for every pixel4
Given $z$ , neighbouring pixels stay correlated through the covariance5

#gaussian-likelihood

Timed test