Improving Bayesian Network Structure Search with Random Variable Aggregation Hierarchies

Abstract

Bayesian network structure identification is known to be NP-Hard in the general case. We demonstrate a heuristic search for structure identification based on aggregation hierarchies . The basic idea is to perform initial exhaustive searches on composite “high-level” random variables (RVs) that are created via aggregations of atomic RVs. The results of the high-level searches then constrain a refined search on the atomic RVs. We demonstrate our methods on a challenging real-world neuroimaging domain and show that they consistently yield higher scoring networks when compared to traditional searches, provided sufficient topological complexity is permitted. On simulated data, where ground truth is known and controllable, our methods yield improved classification accuracy and structural precision, but can also result in reduced structural recall on particularly noisy datasets.