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)