Triangulation of Bayesian networks with recursive estimation of distribution algorithms

AbstractBayesian networks can be used as a model to make inferences in domains with intrinsic uncertainty, that is, to determine the probability distribution of a set of variables given the instantiation of another set. The inference is an NP-hard problem. There are several algorithms to make exact and approximate inference. One of the most popular, and that is also an exact method, is the evidence propagation algorithm of Lauritzen and Spiegelhalter [S.L. Lauritzen, D.J. Spiegelhalter, Local computations with probabilities on graphical structures and their application on expert systems, Journal of the Royal Statistical Society B 50 (2) (1988) 157–224], improved later by Jensen et al. [F.V. Jensen, S.L. Lauritzen, K.G. Olesen, Bayesian updating in causal probalistic networks by local computations, In Computational Statistics Quaterly 4 (1990) 269–282]. This algorithm needs an ordering of the variables in order to make the triangulation of the moral graph associated with the original Bayesian network structure. The effectiveness of the inference depends on the variable ordering. In this paper, we will use a new paradigm for evolutionary computation, the estimation of distribution algorithms (EDAs), to get the optimal ordering of the variables to obtain the most efficient triangulation. We will also present a new type of evolutionary algorithm, the recursive EDAs (REDAs). We will prove that REDAs improve the behaviour of EDAs in this particular problem, and that their results are competitive with other triangulation techniques