Multi-dimensional Bayesian network classifiers

We introduce the family of multi-dimensional Bayesian network classifiers. These clas-sifiers include one or more class variables and multiple feature variables, which need not be modelled as being dependent on every class variable. Our family of multi-dimensional classifiers includes as special cases the well-known naive Bayesian and tree-augmented classifiers, yet offers better modelling capabilities than families of models with a single class variable. We describe the learning problem for a subfamily of multi-dimensional classifiers and show that the complexity of the solution algorithm is polynomial in the number of variables involved. We further present some preliminary experimental results to illustrate the benefits of the multi-dimensionality of our classifiers.