Learning Bayesian networks is known to be an NP-hard problem and that is the reason why the application of a heuristic search has proven advantageous in many domains. This learning approach is computationally efficient and, even though it does not guarantee an optimal result, many previous studies have shown that it obtains very good solutions. Hill climbing algorithms are particularly popular because of their good trade-off between computational demands and the quality of the models learned. In spite of this efficiency, when it comes to dealing with high-dimensional datasets, these algorithms can be improved upon, and this is the goal of this paper. Thus, we present an approach to improve hill climbing algorithms based on dynamically restricting the candidate solutions to be evaluated during the search process. This proposal, dynamic restriction, is new because other studies available in the literature about restricted search in the literature are based on two stages rather than only one as it is presented here. In addition to the aforementioned advantages of hill climbing algorithms, we show that under certain conditions the model they return is a minimal I-map of the joint probability distribution underlying the training data, which is a nice theoretical property with practical implications. In this paper we provided theoretical results that guarantee that, under these same conditions, the proposed algorithms also output a minimal I-map. Furthermore, we experimentally test the proposed algorithms Responsible editor: Charles Elkan. 123Learning Bayesian networks by hill climbing 107 over a set of different domains, some of them quite large (up to 800 variables), in order to study their behavior in practice.

One important approach to learning Bayesian networks (BNs) from data uses a scoring metric to evaluate the fitness of any given candidate network for the data base, and applies a search procedure to explore the set of candidate networks. The most usual search methods are greedy hill climbing, either deterministic or stochastic, although other techniques have also been used. In this paper we propose a new algorithm for learning BNs based on a recently introduced metaheuristic, which has been successfully applied to solve a variety of combinatorial optimization problems: ant colony optimization (ACO). We describe all the elements necessary to tackle our learning problem using this metaheuristic, and experimentally compare the performance of our ACObased algorithm with other algorithms used in the literature. The experimental work is carried out using three different domains: ALARM, INSURANCE and BOBLO.

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