Abstract
This chapter introduces probabilistic graphical models and explain their use for modelling probabilistic relationships between variables in the context of optimisation with EDAs.We focus on Markov networksmodels and review different algorithms used to learn and sample Markov networks. Other probabilistic graphical models are also reviewed and their differences with Markov networks are analysed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abbeel, P., Koller, D., Ng, A.Y.: Learning factor graphs in polynomial time and sample complexity. Journal of Machine Learning Research 7, 1743–1788 (2006)
Bach, F.R., Jordan, M.I.: Thin junction trees. In: Proceedings of the Conference Advances in Neural Information Processing Systems 20, NIPS, pp. 569–576. MIT Press (2002)
Besag, J.: Spatial interactions and the statistical analysis of lattice systems (with discussions). Journal of the Royal Statistical Society 36, 192–236 (1974)
Bromberg, F., Margaritis, D., Honavar, V.: Efficient Markov network structure discovery using independence tests. Journal of Artificial Intelligence Research 35, 449–484 (2009)
Castillo, E., Gutierrez, J.M., Hadi, A.S.: Expert Systems and Probabilistic Network Models. Springer (1997)
Chechetka, A., Guestrin, C.: Efficient principled learning of thin junction trees. In: Proceedings of the Conference Advances in Neural Information Processing Systems 20, NIPS. MIT Press (2008)
Cox, D., Wermuth, N.: Linear dependencies represented by chain graphs. Statistical Science 8(3), 204–218 (1993)
d’Aspremont, A., Banerjee, O., Ghaoui, L.: First-order methods for sparse covariance selection. SIAM Journal on Matrix Analysis and Applications 30(1), 56–66 (2008)
Davis, J., Domingos, P.: Bottom-up learning of Markov network structure. In: Proceedings of the Twenty-Seventh International Conference on Machine Learning. ACM Press (2010)
Della Pietra, S., Della Pietra, V., Lafferty, J.: Inducing features of random fields. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(4), 380–393 (1997)
Duchi, J., Gould, S., Koller, D.: Projected subgradient methods for learning sparse Gaussians. In: Proceedings of the 24th Annual Conference on Uncertainty in Artificial Intelligence, UAI 2008 (2008)
Frey, B.: Graphical Models for Machine Learning and Digital Communication. MIT Press (1998)
Fung, R., Chang, K.: Weighting and integrating evidence for stochastic simulation in Bayesian networks. Uncertainty in Artificial Intelligence 5, 209–219 (1989)
Gandhi, P., Bromberg, F., Margaritis, D.: Learning Markov network structure using few independence tests. In: Proceedings of the SIAM Conference on Data Mining, pp. 680–691 (2008)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. In: Fischler, M.A., Firschein, O. (eds.) Readings in Computer Vision: Issues, Problems, Principles, and Paradigms, pp. 564–584. Kaufmann, Los Altos (1987)
Gogate, V., Austin, W., Domingos, W.: Learning efficient Markov networks. In: Proceedings of the Conference on Neural Information Processing Systems (NIPS 2010). MIT Press (2010)
Guo, J., Levina, E., Michailidis, G., Zhu, J.: Joint structure estimation for categorical Markov networks (2010) (summited), http://www.stat.lsa.umich.edu/~elevina
Hammersley, J.M., Clifford, P.: Markov fields on finite graphs and lattices (1971) (unpublished )
Kikuchi, R.: A theory of cooperative phenomena. Physical Review 81(6), 988–1003 (1951)
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)
Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47(2), 498–519 (2001)
Larrañaga, P.: An Introduction to probabilistic graphical models. In: Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation, pp. 25–54. Kluwer Academic Publishers, Boston (2002)
Larrañaga, P., Calvo, B., Santana, R., Bielza, C., Galdiano, J., Inza, I., Lozano, J.A., Armañanzas, R., Santafé, G., Pérez, A., Robles, V.: Machine learning in bioinformatics. Briefings in Bioinformatics 7, 86–112 (2006)
Lauritzen, S.L.: Graphical Models. Oxford Clarendon Press (1996)
Li, S.: Markov Random Field Modeling in Image Analysis. Springer-Verlag New York Inc. (2009)
Li, S.Z.: Markov Random Field modeling in computer vision. Springer (1995)
Margaritis, D., Bromberg, F.: Efficient Markov network discovery using particle filters. Computational Intelligence 25(4), 367–394 (2009)
McCallum, A.: Efficiently inducing features of conditional random fields. In: Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI 2003), pp. 403–410 (2003)
McLachlan, G., Peel, D.: Finite Mixture Models. John Wiley & Sons (2000)
Meinshausen, N., Bühlmann, P.: High-dimensional graphs and variable selection with the lasso. Annals of Statistics 34, 1436–1462 (2006)
Morita, T.: Formal structure of the cluster variation method. Progress of Theoretical Physics Supplements 115, 27–39 (1994)
Murphy, K.: Dynamic Bayesian Networks: Representation, Inference and Learning. PhD thesis, University of California, Berkeley (2002)
Neapolitan, R.E.: Learning Bayesian Networks. Prentice-Hall, Upper Saddle River (2003)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman Publishers, Palo Alto (1988)
Pearl, J., Paz, A.: Graphoids: A graph-based logic for reasoning about relevance relations. Technical Report R–53–L, Cognitive Systems Laboratory, University of California, Los Angeles (1985)
Pelikan, M.: Hierarchical Bayesian Optimization Algorithm. Toward a New Generation of Evolutionary Algorithms. STUDFUZZ, vol. 170. Springer, Heidelberg (2005)
Ravikumar, P., Wainwright, M., Lafferty, J.: High-dimensional ising model selection using l1-regularized logistic regression. The Annals of Statistics 38(3), 1287–1319 (2010)
Rue, H., Held, L.: Gaussian Markov Random Fields: Theory and Applications, vol. 104. Chapman & Hall (2005)
Scheinberg, K., Rish, I.: Learning sparse Gaussian Markov networks using a greedy coordinate ascent approach. In: Machine Learning and Knowledge Discovery in Databases, pp. 196–212 (2010)
Schlüter, F., Bromberg, F.: A survey on independence-based Markov networks learning, arXiv.org, arXiv:1108.2283 (2011)
Shachter, R., Peot, M.: Simulation approaches to general probabilistic inference on belief networks. In: Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence, pp. 221–234. North-Holland Publishing Co., Amsterdam (1990)
Shakya, S.: DEUM: A Framework for an Estimation of Distribution Algorithm based on Markov Random Fields. PhD thesis, The Robert Gordon University, Aberdeen, UK (April 2006)
Von Neumann, J.: Various techniques used in connection with random digits. Applied Math Series 12(36-38), 1 (1951)
Whittaker, J.: Graphical Models in Applied Multivariate Statistics. Wiley Series in Probability and Mathematical Statistics, New York (1991)
Yedidia, J.S., Freeman, W.T., Weiss, Y.: Constructing free energy approximations and generalized belief propagation algorithms. Technical Report TR-2002-35, Mitsubishi Electric Research Laboratories (August 2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Santana, R., Shakya, S. (2012). Probabilistic Graphical Models and Markov Networks. In: Shakya, S., Santana, R. (eds) Markov Networks in Evolutionary Computation. Adaptation, Learning, and Optimization, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28900-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-28900-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28899-9
Online ISBN: 978-3-642-28900-2
eBook Packages: EngineeringEngineering (R0)