Overview: Probabilistic and Graphical Models

Every probabilistic model built in this unit so far — Naive Bayes's independence assumption, the Gaussian mixture's latent structure, linear regression's Gaussian-noise assumption — has an implicit dependency structure between its variables that has, until now, been stated in prose. Graphical models make that structure explicit and visual: a graph whose nodes are random variables and whose edges (or absence of edges) encode exactly which conditional-independence assumptions the model makes. This short topic — compressed here relative to the depth given at Imperial, Oxford, and Cambridge per the profile's length-flex note — introduces directed and undirected graphical models, revisits Gaussian processes with a fuller Bayesian framing, and closes with a pointer to variational inference.