In the third article of my series on variational auto-encoders, I want to discuss categorical variational auto-encoders. This variant allows to learn a latent space of discrete (e.g. categorical or Bernoulli) latent variables. Compared to regular variational auto-encoders, the main challenge lies in deriving a working reparameterization trick for discrete latent variables — the so-called Gumbel trick.
As part of my master thesis, I made heavy use of variational auto-encoders in order to learn latent spaces of shapes — to later perform shape completion. Overall, I invested a big portion of my time in understanding and implementing different variants of variational auto-encoders. This article, a first in a small series, will deal with the mathematics behind variational auto-encoders. The article covers variational inference in general, the concrete case of variational auto-encoder as well as practical considerations.