I came across the following formula in a research paper and I am having a hard time understanding it.
$KL(q(z|x) || q(z)) = -H(q(z|x)) - \int q(z|x) \log \int q(z|x')p(x')dx'dz$
Could someone explain how this is derived and what is means? I've also attached a screenshot from the paper with the full proof.
