Abstract
In this paper an adaptive strategy to learn graphical Markov models is proposed to construct two algorithms. A statistical model complexity index (SMCI) is defined and used to classify models in complexity classes, sparse, medium and dense. The first step of both algorithms is to fit a tree using the Chow and Liu algorithm. The second step begins calculating SMCI and using it to evaluate an index (EMUBI) to predict the edges to add to the model. The first algorithm adds the predicted edges and stop, and the second, decides to add an edge when the fitting improves. The two algorithms are compared by an experimental design using models of different complexity classes. The samples to test the models are generated by a random sampler (MSRS). For the sparse class both algorithms obtain always the correct model. For the other two classes, efficiency of the algorithms is sensible to complexity.
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
Adami, C.N., Cerf, J.: Physical Complexity of Symbolic Sequences. Physica D 137, 62–69 (2000)
Akaike, H.: A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control 19, 716–723 (1974)
Chickering, M.C., Heckerman, D., Meck, C.: Large-Sample Learning of Bayesian Network is NP-Hard. Journal of Machine Learning Research 5, 1287–1330 (2004)
Chow, C.K., Liu, W.: Approximating Discrete Probability Distributions with Dependency Trees. IEEE Trans. Inf. Theory IT-14(3), 462–467 (1968)
Deming, W.E., Stephan, F.F.: On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known. Ann. of Math. Static. 11, 427–444 (1940)
Diaz, E.: Metaheurísticas Híbridas para el Aprendizaje de Modelos Gráficos Markovianos y Aplicaciones. Tesis para optar por el Grado de Doctor en Ciencias de la Computación. Universidad Autónoma de Aguascalientes, Ags., Mexico (2008)
Diaz, E., Ponce de Leon, E.: Discrete Markov model selection by a genetic algorithm. In: Sossa-Azuela, J.H., Aguilar-IbaÑÉz, C., Alvarado-Mentado, M., Gelbukh, A. (eds.) Avances en Ciencias de la Computación e Ingeniería de Cómputo, Mexico, vol. 2, pp. 315–324 (2002)
Diaz, E., Ponce de Leon, E.: Markov Structure Random Sampler (MSRS) algorithm from unrestricted discrete graphic Markov models. In: Gelbukh, A., Reyes, C.A. (eds.) Proceedings of the Fifth Mexican International Conference on Artificial Intelligence, pp. 199–206. IEEE Computer Society, Mexico (2006)
Haberman, S.J.: The Analysis of Frequency Data. The University of Chicago Press (1974)
Koller, D., Freedman, N., Getoor, L., Taskar, B.: Graphical models in a nutshell in Introduction to Statistical Relational Learning. In: Getoor, L., Taskar, B. (eds.) Stanford (2007)
Kruskal, J.B.: On the Shortest Spanning Tree of a Graph and the Traveling Salesman Problem. Proc. Amer. Math. Soc. 7, 48–50 (1956)
Kuratowski, K.: Introduction to Calculus. Pergamon Press, Warsaw (1961)
Lauritzen, S.L.: Graphical models. Oxford University Press, USA (1996)
Li, M., Vitanyi, P.M.B.: An Introduction to Kolmogorov Complexity and its Applications. Springer, Heidelberg (1993)
MacKay, J.C.: Information Theory Inference and Learning Algorithms. Cambridge Press (2003)
Zvonkin, A.K., Levin, L.A.: The Complexity of Finite Objects and the Development of the Concepts of Information and Randomness by Means of the Theory of Algorithms. Russ. Math. Surv. 256, 83–124 (1970)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Diaz, E., Ponce-de-Leon, E., Larrañaga, P., Bielza, C. (2009). Probabilistic Graphical Markov Model Learning: An Adaptive Strategy. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds) MICAI 2009: Advances in Artificial Intelligence. MICAI 2009. Lecture Notes in Computer Science(), vol 5845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05258-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-05258-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05257-6
Online ISBN: 978-3-642-05258-3
eBook Packages: Computer ScienceComputer Science (R0)