Variational autoencoder: Difference between revisions

Revision as of 10:25, 21 December 2021

Revision as of 10:27, 21 December 2021

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The main assumption about the latent space is that it can be considered as a set of multivariate Gaussian distributions, and thus can be described as

: <math>\mathbf{z} \sim q_\phiPhi(\mathbf{z}\mid\mathbf{x}) = \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\sigma}^2)</math>[[File:Reparameterized Variational Autoencoder.png|thumb|The scheme of a variational autoencoder after the reparameterization trick. |300x300px]]

Given <math>\boldsymbol{\varepsilon} \sim \mathcal{N}(0, \boldsymbol{I})</math> and <math>\odot</math> defined as the element-wise product, the reparameterization trick modifies the above equation as