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A Bayesian network is a widely used probabilistic graphical model withapplications in knowledge discovery and prediction. Learning a Bayesian network(BN) from data can be cast as an optimization problem using the well-knownscore-and-search approach. However, selecting a single model (i.e., the bestscoring BN) can be misleading or may not achieve the best possible accuracy. Analternative to committing to a single model is to perform some form of Bayesianor frequentist model averaging, where the space of possible BNs is sampled orenumerated in some fashion. Unfortunately, existing approaches for modelaveraging either severely restrict the structure of the Bayesian network orhave only been shown to scale to networks with fewer than 30 random variables.In this paper, we propose a novel approach to model averaging inspired byperformance guarantees in approximation algorithms. Our approach has twoprimary advantages. First, our approach only considers credible models in thatthey are optimal or near-optimal in score. Second, our approach is moreefficient and scales to significantly larger Bayesian networks than existingapproaches.

Finding All Bayesian Network Structures within a Factor of Optimal