A Permutation Genetic Algorithm For Variable Ordering In Learning Bayesian Networks From Data

Greedy score-based algorithms for learning the structure of Bayesian networks may produce very different models depending on the order in which variables are scored. These models often vary significantly in quality when applied to inference. Unfortunately, finding the optimal ordering of inputs entails search through the permutation space of variables. Furthermore, in real-world applications of structure learning, the gold standard network is typically unknown. In this paper, we first present a genetic algorithm (GA) that uses a well-known greedy algorithm for structure learning (K2) and approximate inference by importance sampling as primitives in searching this permutation space. We then develop a flexible fitness measure based upon inferential loss given a specification of evidence. Finally, we evaluate this GA wrapper using the well-known networks Asia and ALARM and show that it is competitive with exhaustive enumeration in finding good orderings for K2, resulting in structures with low inferential loss under importance sampling.