Efficient Approximations for the Marginal Likelihood of Incomplete Data Given a Bayesian Network
This work addresses the challenge of efficient Bayesian learning for incomplete data, but it is incremental as it compares existing approximations without introducing new methods.
The paper tackled the problem of approximating the marginal likelihood for incomplete data in Bayesian network learning, finding that the CS measure was the most accurate in experiments with synthetic data from discrete naive-Bayes models with a hidden root node.
We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naive-Bayes models having a hidden root node, we find that the CS measure is the most accurate.