Learning parameters of Bayesian networks from incomplete data via importance sampling

We present an algorithm for learning parameters of Bayesian networks from incomplete data. By using importance sampling we are able to assign a score to imputation proposals depending on the quality of such a proposal in combination with the observed data. This in effect makes it possible to approximate the posterior parameter distribution given incomplete data by using a mixture distribution with a tractable number of components. The technique allows for different imputation methods, in particular we propose an imputation method that combines Gibbs sampling and a data augmentation derivative. We evaluate our algorithm, and we compare the results to those obtained with WinBUGS and the EM algorithm.