Variational Autoencoders

Why

Definition

A variational autoencoder (VAE) from latent set $Z$ to observation set $X$ is an ordered pair $((p_{z}^{(\theta )}, p^{(\theta )}_{x \mid z}), q^{\phi }_{z \mid x})$ whose first coordinate is a deep latent generation pair from $Z$ to $X$ (with parameters $\theta $) and whose second coordinate is a deep conditional distribution from $X$ to $Z$ (with parameters $\phi $).

A VAE inherits its joint function from its deep latent generation pair. $p_z^{(\theta )}$ is called the latent distribution (or prior distribution, latent model). $p_{x \mid z}^{(\theta )}$ is called the decoder distribution. $q_{z \mid x}^{(\theta )}$ is called the encoder distribution (or inference distribution, recognition distribution).

A variational autoencoder family, from $Z$ to $X$, is a family of autoencoders $\set{ ((p_{z}^{(\theta )}, p^{(\theta )}_{x \mid z}) , q_{z \mid x}^{(\phi )}}_{(\theta , \phi ) \in \Theta \times \Phi }$.

1. Future editions will include. Future editions may also change the name of this sheet. It is also likely that there will be added prerequisite sheets on variational inference. ↩︎