Probablistic PCA

Individual observations (single samples) are vectors: $$\mathbf{x} \in \mathbb{R}^d$$

$n$ samples produce a matrix $X$: $$\mathbb{R}^{n \times d}$$

The generative model is for a single observation: $$\mathbf{x} = \mathbf{W}\mathbf{z} + \boldsymbol{\mu} + \boldsymbol{\epsilon}$$

note: $x$ is used for observations AND generations in the generative model. This is because the model is saying "this is the process that generated what you observed".

??i am assuming this changes under bayesian PCA??