Efficient Approximations for the Marginal Likelihood of Incomplete Data Given a Bayesian Network

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/M DL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz ( 1995). These approximations are as efficient as BIC/M DL, 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 Hayes models having a hidden root node, we find that (1) the BIC/M DL measure is the least accurate, having a bias in favor of simple models, and (2) the Draper and CS measures are the most accurate, having a bias in favor of simple and complex models, respectively.