🏭 Linear Factor Model

Linear factor models are simple models that capture the distribution with latent variables, called factors , that model

where is some form of noise.

Factor Analysis §

With , we have

where is a diagonal covariance matrix. This form is known as factor analysis

Probabilistic PCA §

If we force all variances to be equal to each other, we get probabilistic PCA,

or

where is Gaussian noise. With , we get the standard 🗜️ Principle Component Analysis.