Learning Bayesian Network Models from Incomplete Data using Importance Sampling

We propose a Bayesian approach to learning Bayesian network models from incomplete data. The objective is to obtain the posterior distribution of models, given the observed part of the data. We describe a new algorithm, called eMC, to simulate draws from this posterior distribution. One of the new ideas in our algorithm is to use importance sampling to approximate the posterior distribution of models given the observed data and the current imputation model. The importance sampler is constructed by defining an approximate predictive distribution for the unobserved part of the data. In this way existing (heuristic) imputation methods can be used that don’t require exact inference for generating imputations. We illustrate eMC by its application to modeling the risk factors of coronary heart disease. In the experiments we consider different missing data mechanisms and different fractions of missing data.