# Graphical models

An introduction to directed and undirected probabilistic graphical models, including inference (belief propagation and the junction tree algorithm), parameter learning and structure learning, variational approximations, and approximate inference.

- Introduction to graphical models: (directed, undirected and factor graphs; conditional independence; d-separation; plate notation)
- Inference and propagation algorithms: (belief propagation; factor graph propagation; forward-backward and Kalman smoothing; the junction tree algorithm)
- Learning parameters and structure: maximum likelihood and Bayesian parameter learning for complete and incomplete data; EM; Dirichlet distributions; score-based structure learning; Bayesian structural EM; brief comments on causality and on learning undirected models)
- Approximate Inference: (Laplace approximation; BIC; variational Bayesian EM; variational message passing; VB for model selection)
- Bayesian information retrieval using sets of items: (Bayesian Sets; Applications)
- Foundations of Bayesian inference: (Cox Theorem; Dutch Book Theorem; Asymptotic consensus and certainty; choosing priors; limitations)

*Author: Zoubin Ghahramani, University Of Cambridge*