Parameter Estimation in Bayesian Networks from Incomplete Databases

Current methods to learn Bayesian Networks from incomplete databases share the common assumption that the unreported data are missing at random. This paper describes a method – called Bound and Collapse (BC) – to learn Bayesian Networks from incomplete databases which allows the analyst to efficiently integrate information provided by the observed data and exogenous knowledge about the pattern of missing data. BC starts by bounding the set of estimates consistent with the available information and then collapses the resulting set to a point estimate via a convex combination of the extreme points, with weights depending on the assumed pattern of missing data. Experiments comparing BC to Gibbs Sampling are provided.