An introduction to graphical models

"An introduction to graphical models," Kevin Murphy, 2001.

Graphical models are the combination of probability theory and graph theory. They can be directed or undirected models. The directed graphical models are known as Bayesian networks, where the ancestor/parent relationship is with respect to some fixed topological ordering of the nodes, and the undirected graphical models are known as Markov networks. There are some hidden causes in the graph, and their values must be estimated from observation, that is inference. There are some popular approximate inference methods: sampling(Monte Carlo) methods, variational methods, and loopy brief propagation. According to the structure and the observation, Learning methods are simply classified into four category:

  observability
structure\ full  partial
known    closed form EM
unknown  local search structural EM

Finally, computing the optimal actions to perform to get the maximum expected utility and making decisions under uncertainty. The decision algorithm is similar to inference algorithm.