Improving Accuracy of Constraint-Based Structure Learning

Hybrid algorithms for learning the structure of Bayesian networks combine techniques from both the constraintbased and search-and-score paradigms of structure learning. One class of hybrid approaches uses a constraintbased algorithm to learn an undirected skeleton identifying edges that should appear in the final network. This skeleton is used to constrain the model space considered by a search-and-score algorithm to orient the edges and produce a final model structure. At small sample sizes, the performance of models learned using this hybrid approach do not achieve likelihood as high as models learned by unconstrained search. Low performance is a result of errors made by the skeleton identification algorithm, particularly false negative errors, which lead to an over-constrained search space. These errors are often attributed to “noisy” hypothesis tests that are run during skeleton identification. However, at least three specific sources of error have been identified in the literature: unsuitable hypothesis tests, lowpower hypothesis tests, and unexplained d-separation. No previous work has considered these sources of error in combination. We determine the relative importance of each source individually and in combination. We identify that low-power tests are the primary source of false negative errors, and show that these errors can be corrected by a novel application of statistical power analysis. The result is a new hybrid algorithm for learning the structure of Bayesian networks which produces models with equivalent likelihood to models produced by unconstrained greedy search, using only a fraction of the time.