Variational Autoencoders

Why

Definition

A variational autoencoder (VAE) from latent set $Z$ to observation set $X$ is an ordered pair $((p_z^{(\theta )},p_{x\mid z}^{(\theta )}),q_{z\mid x}^{\varphi })$ 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 $\varphi$).

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 $\{((p_z^{(\theta )},p_{x\mid z}^{(\theta )}),q_{z\mid x}^{(\varphi )}{\}}_{(\theta ,\varphi )\in \mathrm{\Theta }\times \mathrm{\Phi }}$.

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. ↩︎