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. β€œLearning Factor Graphs in Polynomial Time and Sample Complexity.” Journal of Machine Learning Research 7 (December): 1743–88.
Cox, Marco, Thijs van de Laar, and Bert de Vries. 2019. β€œA Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms.” International Journal of Approximate Reasoning 104 (January): 185–204.
Forney, G.D. 2001. β€œCodes on Graphs: Normal Realizations.” IEEE Transactions on Information Theory 47 (2): 520–48.
Frey, Brendan J. 2003. β€œExtending 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.
Kschischang, F.R., B.J. Frey, and H.-A. Loeliger. 2001. β€œFactor Graphs and the Sum-Product Algorithm.” IEEE Transactions on Information Theory 47 (2): 498–519.
Laar, Thijs van de, Marco Cox, Ismail Senoz, Ivan Bocharov, and Bert de Vries. n.d. β€œForneyLab: A Toolbox for Biologically Plausible Free Energy Minimization in Dynamic Neural Models,” 3.
Loeliger, H.-A. 2004. β€œAn Introduction to Factor Graphs.” IEEE Signal Processing Magazine 21 (1): 28–41.
Loeliger, Hans-Andrea, Justin Dauwels, Junli Hu, Sascha Korl, Li Ping, and Frank R. Kschischang. 2007. β€œThe Factor Graph Approach to Model-Based Signal Processing.” Proceedings of the IEEE 95 (6): 1295–1322.
Mao, Yongyi, Frank R. Kschischang, and Brendan J. Frey. 2004. β€œConvolutional 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.

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