(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 Barberβs discrete graphical model code (Julia) can do queries over graphical models.

All of the probabilistic programming languages end up needing to accound for graphical model structure in practice.

## References

*Bayesian Reasoning and Machine Learning*. Cambridge ; New York: Cambridge University Press.

*Pattern Recognition and Machine Learning*. Information Science and Statistics. New York: Springer.

*Journal of Artificial Intelligence Research*2 (1): 159β225.

*AI Magazine*12 (4): 50.

*arXiv:2106.13830 [Math-Ph, Physics:nlin, q-Bio]*, June.

*Journal of the Royal Statistical Society. Series B (Methodological)*41 (1): 1β31.

*The Annals of Statistics*8 (3): 598β617.

*Learning in Graphical Models*. Cambridge, Mass.: MIT Press.

*Probabilistic Graphical Models : Principles and Techniques*. Cambridge, MA: MIT Press.

*Graphical Models*. Oxford Statistical Science Series. Clarendon Press.

*arXiv:1805.00909 [Cs, Stat]*, May.

*Machine learning: a probabilistic perspective*. 1 edition. Adaptive computation and machine learning series. Cambridge, MA: MIT Press.

*arXiv:1910.10775 [Cs, Stat]*, March.

*Probabilistic reasoning in intelligent systems: networks of plausible inference*. Rev.Β 2. print., 12. [Dr.]. The Morgan Kaufmann series in representation and reasoning. San Francisco, Calif: Kaufmann.

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

*Kybernetika*25 (7): 33β44.

*Electronic Journal of Statistics*14 (2): 2773β97.

## No comments yet. Why not leave one?