PPCA: The Minimal Generative Model
PCA is one of those algorithms you learn early and then treat as a black box: center the data, compute the top eigenvectors of the sample covariance, project. But PCA feels algebraic, where does it come from probabilistically? Probabilistic PCA (PPCA) answers that question: it is the maximum-likelihood solution of a simple linear Gaussian latent-variable model. Understanding PPCA is a tiny, high-value step on the path to modern generative models (VAEs, normalizing flows): it isolates the linear + Gaussian case where every calculation is analytic, so you can see clearly how inference and likelihood tie together.
