Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Graphical Models

  • Julian McAuley
  • Tibério Caetano
  • Wray Buntine
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_351


The notation we shall use is defined in Table 1, and some core definitions are presented in Table 2. In each of the examples presented in Fig. 1, we are simply asserting that
$$\underbrace{p({x}_{A},{x}_{B}\vert {x}_{C})}_{\text{ function of three variables}} =\underbrace{ p({x}_{A}\vert {x}_{C})p({x}_{B}\vert {x}_{C})}_{\text{ functions of two variables}},$$
This is a preview of subscription content, log in to check access.


  1. Aji, S. M., & McEliece, R. J. (2000). The generalized distributive law. IEEE transactions on information theory, 46(2): 325-343.MathSciNetMATHCrossRefGoogle Scholar
  2. Amir, E. (2001). Efficient approximation for triangulation of minimum treewidth. In Proceedings of the 17th conference on uncertainty in artificial intelligence (pp. 7–15). San Francisco: Morgan Kaufmann.Google Scholar
  3. Cowell, R. G., Dawid, P. A., Lauritzen, S. L., & Spiegelhalter, D. J. (2003). Probabilistic networks and expert systems. Berlin: Springer.Google Scholar
  4. Edwards, D. (2000). Introduction to graphical modelling. New York: Springer.MATHGoogle Scholar
  5. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the bayesian restoration of images. In IEEE transactions on pattern analysis and machine intelligence, 6, 721–741.Google Scholar
  6. Getoor, L., & Taskar, B. (Eds.). (2007). An introduction to statistical relational learning. Cambridge, MA: MIT Press.Google Scholar
  7. Ihler, A. T., Fischer III, J. W., & Willsky, A. S. (2005). Loopy belief propagation: Convergence and effects of message errors. Journal of Machine Learning Research, 6, 905–936.Google Scholar
  8. Jensen, F. V. (2001). Bayesian networks and decision graphs. Berlin: Springer.MATHGoogle Scholar
  9. Jordan, M. (Ed.). (1998). Learning in graphical models. Cambridge, MA: MIT Press.Google Scholar
  10. Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. Cambridge, MA: MIT Press.Google Scholar
  11. Kschischang, F. R., Frey, B. J., & Loeliger, H. A. (2001). Factor graphs and the sum-product algorithm. IEEE transactions on information theory, 47(2), 498–519.MathSciNetMATHCrossRefGoogle Scholar
  12. Lauritzen, S. L. (1996). Graphical models. Oxford: Oxford University Press.Google Scholar
  13. Lauritzen, S. L., & Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society, Series B, 50, 157–224.MathSciNetMATHGoogle Scholar
  14. Murphy, K. (1998). A brief introduction to graphical models and Bayesian networks. San Francisco: Morgan Kaufmann.Google Scholar
  15. Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Francisco: Morgan Kaufmann.Google Scholar
  16. Pearl, J. (2000). Causality. Cambridge: Cambridge University Press.MATHGoogle Scholar
  17. Roweis, S., & Ghahramani, Z. (1997). A unifying review of linear Gaussian models. Neural Computation, 11, 305–345.CrossRefGoogle Scholar
  18. Smyth, P. (1998). Belief networks, hidden Markov models, and Markov random fields: A unifying view. Pattern Recognition Letters, 18, 1261–1268.CrossRefGoogle Scholar
  19. Wainwright, M. J., & Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends in Machine Learning, 1, 1–305.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Julian McAuley
    • 1
  • Tibério Caetano
    • 1
  • Wray Buntine
    • 1
  1. 1.Statistical Machine Learning ProgramNICTACanberraAustralia