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psanch21 / VAE-GMVAE

This repository contains the implementation of the VAE and Gaussian Mixture VAE using TensorFlow and several network architectures
Apache License 2.0
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The expression of conditional prior and y-prior terms in the code. #2

Closed BobXWu closed 5 years ago

BobXWu commented 5 years ago

Hello, thanks for sharing. I've read the original paper about GMVAE. But I still don't know how to derive the conditional prior and y-prior terms as you did in the code. Can you explain more about the derivation?

psanch21 commented 5 years ago

Hi. In Section 4 of my Bachelor's dissertation you may find a description of the model proposed by Nat Dilokthanakul et al. Please, notice the naming of the variables we use differs from the one of the original paper. Then, in Appendix D of the dissertation you may find the full derivation of all the terms of the ELBO. Hope this helps!

BobXWu commented 5 years ago

Thanks a lot for your reply. That helps much. And what is the "log det" when simplify the terms D.1 in the Appendix D?

psanch21 commented 5 years ago

It refers to the log of the determinant of the covariance matrix (represented as sigma squared). Since we consider a mean field approximation for the distributions, the determinant of the covariance matrix is just the product of the terms in the diagonal. Hope this helps!