A Review on Distinct Methods and Approaches to Perform Triangulation for Bayesian Networks

Summary. Triangulation of a Bayesian network (BN) is somehow a necessary step in order to perform inference in a more efficient way, either if we use a secondary structure as the join tree (JT) or implicitly when we try to use other direct techniques on the network. If we focus on the first procedure, the goodness of the triangulation will affect on the simplicity of the join tree and therefore on a quicker and easier inference process. The task of obtaining an optimal triangulation (in terms of producing the minimum number of triangulation links a.k.a. fill-ins) has been proved as an NP-hard problem. That is why many methods of distinct nature have been used with the purpose of getting as good as possible triangulations for any given network, especially important for big structures, that is, with a large number of variables and links. In this chapter, we attempt to introduce the problem of triangulation, locating it in the compilation process and showing first its relevance for inference, and consequently for working with Bayesian networks. After this introduction, the most popular and used strategies to cope with the triangulation problem are reviewed, grouped into two main categories: heuristics and stochastic algorithms. Finally, another family of techniques could be understood as those based in decomposing the problem.