Robust Parameter Learning in Bayesian Networks with Missing Data

Bayesian belief Networks (BBNs) are a powerful formalism for knowledge representation and reasoning under uncertainty. During the past few years, Artificial Intelligence met Statistics in the quest to develop effective methods to learn BBNs directly from real-world databases. Unfortunately, real-world databases include missing and/or unreported data whose presence challenges traditional learning techniques, from both the theoretical and computational point of view. This paper outlines a new method to learn the probabilities defining a BBNs from incomplete databases. The basic assumption of this method is that the BBN generated by the learning process should enable the problem solver to reason and make decisions on the basis of the currently available information. This assumption requires the learning method to return results whose precision is a monotonic increasing function of the available information. The intuition behind our method is close to the robust sensitivity analysis interpretation of probability: the method computes the convex set of possible distributions defined by the available information and proceeds by refining this set as more information becomes available. Finally, experimental results will be presented comparing this approach to a popular Monte Carlo method.

1. Knowledge Media Institute, The Open University.

2. Department of Actuarial Science and Statistics, City University.