# Factor Analysis
Very similar to probabilistic PCA, just the conditional distribution is different:
$
p(\mathbf{x|z} = \mathcal{N}(\mathbf{x|Wz}+\boldsymbol{\mu},\boldsymbol{\Psi})
$
where
$
\mathbf{x}= \mathbf{Wz}+\boldsymbol{\mu}+\boldsymbol{\epsilon}\quad \boldsymbol{\epsilon}~\mathcal{N}(\mathbf{z}|0,\boldsymbol{\Psi})
$
- ***W*** - factor loading matrix, explains covariance between observed variables
- ***Ψ*** - uniqueness, independent noise variances for each observed variable