(Barber 2012):

Placeholder for my notes on probabilistic graphical models.
In general graphical models are a particular type of way of handling
multivariate data based on working out *what* is
conditionally independent of *what else*.

Thematically, this is scattered across graphical models in inference, learning graphs from data, learning causation from data plus graphs, quantum graphical models because it all looks a bit different with noncommutative probability.

See also diagramming graphical models.

## Directed graphs

Graphs of conditional, directed independence are a convenient formalism for many models. These are also called Bayes nets (not to be confused with Bayesian inference.)

## Undirected, a.k.a. Markov graphs

a.k.a Markov random fields, Markov random networks. (other types?)

## Factor graphs

A unifying formalism for the directed and undirected graphical models. I have not really used these. See factor graphs.

## Implementations

Pedagogically useful, although probably not industrial-grade, David Barber’s discrete graphical model code (Julia) can do queries over graphical models.

Barber, David. 2012. *Bayesian Reasoning and Machine Learning*. Cambridge ; New York: Cambridge University Press. http://www.cs.ucl.ac.uk/staff/d.barber/brml/.

Bishop, Christopher M. 2006. *Pattern Recognition and Machine Learning*. Information Science and Statistics. New York: Springer.

Charniak, Eugene. 1991. “Bayesian Networks Without Tears.” *AI Magazine* 12 (4): 50.

Dawid, A. Philip. 1979. “Conditional Independence in Statistical Theory.” *Journal of the Royal Statistical Society. Series B (Methodological)* 41 (1): 1–31. http://people.csail.mit.edu/tdanford/discovering-causal-graphs-papers/dawid-79.pdf.

———. 1980. “Conditional Independence for Statistical Operations.” *The Annals of Statistics* 8 (3): 598–617. https://doi.org/10.1214/aos/1176345011.

Jordan, Michael Irwin. 1999. *Learning in Graphical Models*. Cambridge, Mass.: MIT Press.

Koller, Daphne, and Nir Friedman. 2009. *Probabilistic Graphical Models : Principles and Techniques*. Cambridge, MA: MIT Press.

Lauritzen, Steffen L. 1996. *Graphical Models*. Clarendon Press.

Montanari, Andrea. 2011. “Lecture Notes for Stat 375 Inference in Graphical Models.” http://www.stanford.edu/~montanar/TEACHING/Stat375/handouts/notes_stat375_1.pdf.

Murphy, Kevin P. 2012. *Machine Learning: A Probabilistic Perspective*. 1 edition. Adaptive Computation and Machine Learning Series. Cambridge, MA: MIT Press.

Pearl, Judea. 2008. *Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference*. Rev. 2. print., 12. [Dr.]. The Morgan Kaufmann Series in Representation and Reasoning. San Francisco, Calif: Kaufmann.

———. 2009. *Causality: Models, Reasoning and Inference*. Cambridge University Press.

Pearl, Judea, Dan Geiger, and Thomas Verma. 1989. “Conditional Independence and Its Representations.” *Kybernetika* 25 (7): 33–44. http://dml.cz/bitstream/handle/10338.dmlcz/125413/Kybernetika_25-1989-7_6.pdf.