Probabilistic graphical models

(Barber 2012):

Taxonomy of graphical models

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.)

See directed graphical models.

Undirected, a.k.a. Markov graphs

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

See undirected graphical models.

Factor graphs

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


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.
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.
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———. 1980. “Conditional Independence for Statistical Operations.” The Annals of Statistics 8 (3): 598–617.
Jordan, Michael Irwin. 1999. Learning in Graphical Models. Cambridge, Mass.: MIT Press.
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Obermeyer, Fritz, Eli Bingham, Martin Jankowiak, Du Phan, and Jonathan P. Chen. 2020. “Functional Tensors for Probabilistic Programming.” arXiv:1910.10775 [cs, Stat], March.
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.
Sadeghi, Kayvan. 2020. “On finite exchangeability and conditional independence.” Electronic Journal of Statistics 14 (2): 2773–97.

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