LEARNING BAYESIAN NETWORKS IN THE SPACE OF ORDERINGS WITH ESTIMATION OF DISTRIBUTION ALGORITHMS

Abstract

The search for the optimal ordering of a set of variables in order to solve a computational problem is a difficulty that can appear in several circumstances. One of these situations is the automatic learning of a network structure, for example, a Bayesian Network structure (BN) starting from a dataset. Searching in the space of structures is often unmanageable, especially if the number of variables is high. Popular heuristic approaches, like Cooper and Herskovits's K2 algorithm, depend on a given ordering of variables. Estimation of Distribution Algorithms (EDAs) are a new paradigm for Evolutionary Computation that have been used as a search engine in the BN structure learning problem. In this paper, we will use two different EDAs to obtain not the best structure, but the optimal ordering of variables for the K2 algorithm: UMDA and MIMIC, both of them in discrete and continuous domains. We will also check whether the individual representation and its relation to the corresponding ordering play important roles, and whether MIMIC outperforms the results of UMDA.