Inference and Learning in Multi-dimensional Bayesian Network Classifiers

Authors:
Peter R. Waal;Linda C. Gaag
Affiliations:
Department of Information and Computing Sciences, Faculty of Sciences, Utrecht University, Utrecht, The Netherlands 3508TB;Department of Information and Computing Sciences, Faculty of Sciences, Utrecht University, Utrecht, The Netherlands 3508TB
Venue:
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2007

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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.