Confused by qλ(z) #25
Description
Reading the following paragraphs in the VAE notes:
Next, we introduce a variational family Q of distributions that approximate the true, but intractable posterior p(z∣x). Further henceforth, we will assume a parameteric setting where any distribution in the model family Px,z is specified via a set of parameters θ∈Θ and distributions in the variational family Q are specified via a set of parameters λ∈Λ.
Given Px,z and Q, we note that the following relationships hold true1 for any x and all variational distributions qλ(z)∈Q
If "qλ(z)" is intended to approximate the distribution "p(z∣x)", then I'm confused as to why "qλ(z)" doesn't include "x". Should it be "qλ(z∣x)", or it is actually approximating the distribution "p(z)"?
Apologies if this sounds like an ignorant question--my understanding of probability notation isn't too sharp.