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I am watching this lecture on VAE:

https://www.youtube.com/watch?v=uaaqyVS9-rM&t=1507s

and at 26:00, it is stated that the goal is the minimize the KL div. between the distribution we are trying to find - p(z|x) by approximating it with another distribution: q(z). but why aren't we using q(z|x)?

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The evidence lower bound we're trying to maximize is valid for any choice of $q(z)$, so for example, you could just arbitrarily choose $q(z) = \mathcal{N}(0,1)$, but this wouldn't yield a very good bound.

Since we can use any $q(z)$ for any given $x$, we might as well have our $q(z)$ depend on $x$, and this is written as $q(z|x)$ -- admittedly maybe some notation like $q(z) = r(z;x)$ would be less confusing.

TLDR: $q(z|x)$ is just a special case of all the possible $q(z)$'s that we could choose from.

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