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Graphical Models

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Encyclopedia of Machine Learning and Data Mining

Definition

Graphical models are a means of compactly representing multivariate distributions, allowing for efficient algorithms to be developed when dealing with high-dimensional data. At their core, graphical models make use of the fact that high-dimensional distributions tend to factorize around local interactions, meaning that they can be expressed as a product of low-dimensional terms.

The notation we shall use is defined in Table 1, and some core definitions are presented in Table 2.

Graphical Models, Table 1 Notation

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  • Amir E (2001) Efficient approximation for triangulation of minimum treewidth. In: Proceedings of the 17th conference on uncertainty in artificial intelligence. Morgan Kaufmann, San Francisco, pp 7–15

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  • Cowell RG, Dawid PA, Lauritzen SL, Spiegelhalter DJ (2003) Probabilistic networks and expert systems. Springer, Berlin

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  • Edwards D (2000) Introduction to graphical modelling. Springer, New York

    Book  MATH  Google Scholar 

  • Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6:721–741

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  • Getoor L, Taskar B (eds) (2007) An introduction to statistical relational learning. MIT Press, Cambridge

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  • Ihler AT, Fischer III JW, Willsky AS (2005) Loopy belief propagation: convergence and effects of message errors. J Mach Learn Res 6:905–936

    MathSciNet  MATH  Google Scholar 

  • Jensen FV (2001) Bayesian networks and decision graphs. Springer, Berlin

    Book  MATH  Google Scholar 

  • Jordan M (ed) (1998) Learning in graphical models. MIT Press, Cambridge

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  • Koller D, Friedman N (2009) Probabilistic graphical models: principles and techniques. MIT Press, Cambridge

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  • Kschischang FR, Frey BJ, Loeliger HA (2001) Factor graphs and the sum-product algorithm. IEEE Trans Inf Theory 47(2):498–519

    Article  MathSciNet  MATH  Google Scholar 

  • Lauritzen SL (1996) Graphical models. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Lauritzen SL, Spiegelhalter DJ (1988) Local computations with probabilities on graphical structures and their application to expert systems. J R Stat Soc Ser B 50:157–224

    MathSciNet  MATH  Google Scholar 

  • Murphy K (1998) A brief introduction to graphical models and Bayesian networks. Morgan Kaufmann, San Francisco

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  • Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Francisco

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  • Pearl J (2000) Causality. Cambridge University Press, Cambridge

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  • Roweis S, Ghahramani Z (1997) A unifying review of linear Gaussian models. Neural Comput 11:305–345

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  • Smyth P (1998) Belief networks, hidden Markov models, and Markov random fields: a unifying view. Pattern Recogn Lett 18:1261–1268

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  • Wainwright MJ, Jordan MI (2008) Graphical models, exponential families, and variational inference. Found Trends Mach Learn 1:1–305

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Correspondence to Julian McAuley .

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McAuley, J., Caetano, T., Buntine, W.L. (2017). Graphical Models. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_119

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