Is there any theoretical work on how to measure posterior collapse? One can measure decoder output, but it is not clear if the degradation (if any) happened due to posterior collapse or due to failing to match the data distribution. Therefore I'm interested in measuring "how informative latent variable z is". Thank you.
By "posterior collapse" I meant an event when signal from input x to posterior parameters is either too weak or too noisy, and as a result, decoder starts ignoring z samples drawn from the posterior $q_\theta(z_d | x)$. If z is too noisy then decoder ignores it during x' generation. If z too weak, then we observe that $\mu$ and $\sigma$ become constant regardless of the input x.