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# Learning Tractable Multidimensional Bayesian Network Classifiers

; Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:13-24, 2016.

#### Abstract

Multidimensional classification has become one of the most relevant topics in view of the many domains that require a vector of class values to be assigned to a vector of given features. The popularity of multidimensional Bayesian network classifiers has increased in the last few years due to their expressive power and the existence of methods for learning different families of these models. The problem with this approach is that the computational cost of using the learned models is usually high, especially if there are a lot of class variables. Class-bridge decomposability means that the multidimensional classification problem can be divided into multiple subproblems for these models. In this paper, we prove that class-bridge decomposability can also be used to guarantee the tractability of the models. We also propose a strategy for efficiently bounding their inference complexity, providing a simple learning method with an order-based search that obtains tractable multidimensional Bayesian network classifiers. Experimental results show that our approach is competitive with other methods in the state of the art and ensures the tractability of the learned models.