In this short manuscript we introduce the Variational Autoencoder model as an extension of the well-known Gaussian Mixture Model. Various implementations of VAEs are introduced and we discuss the gap between the theory motivating the models and these implementations.
Mid 2021 Update I am currently investing a lot of time on this project recently; it is reworked as a review of VAEs proposed improvement upon the problems of simple VAES. I will post a new version on the web site soon enough.
Early 2022 Update Some of my recent work on this project lead me to investigate the evaluation of latent variable models which I have described in one of my recent paper. At the moment, this project is on the backburner until I complete my postdoc and get some feedback on the aforementionned paper.