Structural learning of Bayesian networks using local algorithms based on the space of orderings

Abstract

Structural learning of Bayesian networks (BNs) is an NP-hard problem which is generally addressed by means of heuristic search algorithms. Despite the fact that earlier proposals for dealing with this task were based on searching the space of Directed Acyclic Graphs (DAGs), there are some alternative approaches. One of these approaches for structural learning consists of searching the space of orderings, as given a certain topological order among the problem variables, it is relatively easy to build (and evaluate) a BN compatible with it. In practice, the latter methods make it possible to obtain good results, but they are still costly in terms of computation. In this article, we prove the correctness of the method used to evaluate each ordering, and we propose some efficient learning algorithms based on it. Our first proposal is based on the Hill-Climbing algorithm, and uses an improved neighbourhood definition. The second algorithm is an extension of the first one, and is based on the well-known Variable Neighbourhood Search metaheuristic. Finally, iterative versions of both algorithms are also proposed. The algorithms have been tested over a set of different domains, and have been compared with other methods such as Hill-Climbing in the space of DAGs or Greedy Equivalent Search, in order to study their behaviour in practice.