Overview
In a Gaussian Latent Variable model, the model assumes a latent variable (or vector of variables) that is drawn from the Gaussian distribution.
{% p(\vec{z}_i) = \mathcal{N} (\vec{z}_i | \vec{\mu}_0, \boldsymbol{\Sigma}) %}
The observed variables, labeled here as a vector {% \vec{x} %} are then drawn from a distribution
(often from the Gaussian distribution, but not always) that is dependent on the value of the
latent variable {% \vec{z} %}.
{% p(\vec{x} | \vec{z}_i, \theta) = \mathcal{N}(\textbf{W} \vec{z}_i + \vec{\mu}, \boldsymbol{\Psi} ) %}
(see Murphy chpt 12)