Learning All Credible Bayesian Network Structures for Model Averaging
  A Bayesian network is a widely used probabilistic graphical model with
applications in knowledge discovery and prediction. Learning a Bayesian network
(BN) from data can be cast as an optimization problem using the well-known
score-and-search approach. However, selecting a single model (i.e., the best
scoring BN) can be misleading or may not achieve the best possible accuracy. An
alternative to committing to a single model is to perform some form of Bayesian
or frequentist model averaging, where the space of possible BNs is sampled or
enumerated in some fashion. Unfortunately, existing approaches for model
averaging either severely restrict the structure of the Bayesian network or
have 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 by
performance guarantees in approximation algorithms. Our approach has two
primary advantages. First, our approach only considers credible models in that
they are optimal or near-optimal in score. Second, our approach is more
efficient and scales to significantly larger Bayesian networks than existing
approaches.
