Abstract
We describe the family of multi-dimensional Bayesian network classifiers which include one or more class variables and multiple feature variables. The family does not require that every feature variable is modelled as being dependent on every class variable, which results in better modelling capabilities than families of models with a single class variable. For the family of multidimensional classifiers, we address the complexity of the classification problem and show that it can be solved in polynomial time for classifiers with a graphical structure of bounded treewidth over their feature variables and a restricted number of class variables. We further describe the learning problem for the subfamily of fully polytree-augmented multi-dimensional classifiers and show that its computational complexity is polynomial in the number of feature variables.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bodlaender, H.L., van den Eijkhof, F., van der Gaag, L.C.: On the complexity of the MPA problem in probabilistic networks. In: Proceedings of the 15th European Conference on Artificial Intelligence, pp. 675–679. IOS Press, Amsterdam (2002)
Bodlaender, H.L., Möhring, R.H.: The pathwidth and treewidth of cographs. Siam Journal of Discrete Methods 6, 181–188 (1993)
Cooper, G.F.: The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence 42, 393–405 (1990)
Friedman, N., Geiger, D., Goldszmidt, M.: Bayesian network classifiers. Machine Learning 29, 131–163 (1997)
van der Gaag, L.C., Renooij, S., Witteman, C.L.M., Aleman, B.M.P., Taal, B.G.: Probabilities for a probabilistic network: a case study in oesophageal cancer. Artificial Intelligence in Medicine 25, 123–148 (2002)
van der Gaag, L.C., de Waal, P.R.: Multi-dimensional Bayesian network classifiers. In: Studeny, M., Vomlel, J. (eds.) Proceedings of the Third European Workshop in Probabilistic Graphical Models, Prague, pp. 107–114 (2006)
Kruskal, J.B.: On the shortest spanning subtree of a graph and the travelling salesman problem. Proc. Amer. Math. Soc. 7, 48–50 (1956)
Lucas, P.J.F.: Restricted Bayesian network structure learning. In: Gámez, G.A., Moral, S., Salmerón, A. (eds.) Advances in Bayesian Network, Studies in Fuzziness and Soft Computing, vol. 146, pp. 217–232. Springer, Heidelberg (2004)
Rebane, G., Pearl, J.: The recovery of causal poly-trees from statistical data. In: Kanal, L.N., Levitt, T.S., Lemmer, J.F. (eds.) Proceedings of the 3rd Conference on Uncertainty in Artificial Intelligence. Elsevier, Amsterdam (1989)
Sahami, M.: Learning limited dependence Bayesian classifiers. In: KDD 1996, Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, pp. 335–338. AAAI Press, Menlo Park (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Waal, P.R., van der Gaag, L.C. (2007). Inference and Learning in Multi-dimensional Bayesian Network Classifiers. In: Mellouli, K. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2007. Lecture Notes in Computer Science(), vol 4724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75256-1_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-75256-1_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75255-4
Online ISBN: 978-3-540-75256-1
eBook Packages: Computer ScienceComputer Science (R0)