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About the Derivation of Variational Lower Bound in Appendix A

Open Hannofdhu opened this issue 4 years ago • 3 comments

I read the derivation you provided in appendix A, but I don't know how the last approximation is obtained, I hope to get your answer, thank you very much

Hannofdhu avatar Mar 07 '22 10:03 Hannofdhu

It is very crude monte carlo approximation with sampling size 1 for z_x ~ q(z_x|x,c).

seanie12 avatar Mar 08 '22 12:03 seanie12

Thank you for your answer, I still don't understand something. Regarding the lower bound of the evidence derived in the paper, the coefficients in front of the KL divergence are all -1, why in the code, their coefficients become 0.1. Looking forward to your answer, thank you

Hannofdhu avatar Mar 22 '22 06:03 Hannofdhu

Hi, sorry for the late reply. If the coefficient is larger than -1 (beta=1 in the code), we cannot guarantee that it is lower bound of the marginal likelihood. But if we put the coefficient smaller than -1, we observe the posterior collapse. So, following [beta-vae],(https://openreview.net/forum?id=Sy2fzU9gl) we scale down the kl-divergence for training stability.

seanie12 avatar Jul 05 '22 04:07 seanie12