Factor graphs

A unifying formalism for the directed and undirected graphical models. How does that work then?


A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to represent factorization of a probability distribution function, enabling efficient computations, such as the computation of marginal distributions through the sum-product algorithm.

To discuss: relation to message passing via factor graph decompositions? e.g. via (Cox, van de Laar, and de Vries 2019). Forney-vs-classic-style factor graphs etc.


Abbeel, Pieter, Daphne Koller, and Andrew Y. Ng. 2006. “Learning Factor Graphs in Polynomial Time and Sample Complexity.” Journal of Machine Learning Research 7 (December): 1743–88. http://machinelearning.wustl.edu/mlpapers/paper_files/AbbeelKN06.pdf.
Cox, Marco, Thijs van de Laar, and Bert de Vries. 2019. “A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms.” International Journal of Approximate Reasoning 104 (January): 185–204. https://doi.org/10.1016/j.ijar.2018.11.002.
Forney, G.D. 2001. “Codes on Graphs: Normal Realizations.” IEEE Transactions on Information Theory 47 (2): 520–48. https://doi.org/10.1109/18.910573.
Frey, Brendan J. 2003. “Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models.” In Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence, 257–64. UAI’03. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc. http://arxiv.org/abs/1212.2486.
Kschischang, F.R., B.J. Frey, and H.-A. Loeliger. 2001. “Factor Graphs and the Sum-Product Algorithm.” IEEE Transactions on Information Theory 47 (2): 498–519. https://doi.org/10.1109/18.910572.
Laar, Thijs van de, Marco Cox, Ismail Senoz, Ivan Bocharov, and Bert de Vries. n.d. “ForneyLab: A Toolbox for Biologically Plausible Free Energy Minimization in Dynamic Neural Models,” 3.
Loeliger, H.-A. 2004. “An Introduction to Factor Graphs.” IEEE Signal Processing Magazine 21 (1): 28–41. https://doi.org/10.1109/MSP.2004.1267047.
Loeliger, Hans-Andrea, Justin Dauwels, Junli Hu, Sascha Korl, Li Ping, and Frank R. Kschischang. 2007. “The Factor Graph Approach to Model-Based Signal Processing.” Proceedings of the IEEE 95 (6): 1295–1322. https://doi.org/10.1109/JPROC.2007.896497.
Mao, Yongyi, Frank R. Kschischang, and Brendan J. Frey. 2004. “Convolutional Factor Graphs As Probabilistic Models.” In Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence, 374–81. UAI ’04. Arlington, Virginia, United States: AUAI Press. http://arxiv.org/abs/1207.4136.

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