Robust Learning with Missing Data

Bayesian methods are becoming increasingly popular in the development of intelligent machines. Bayesian Belief Networks (BBNs) are nowaday a prominent reasoning method and, during the past few years, several efforts have been addressed to develop methods able to learn BBNs directly from databases. However, all these methods assume that the database is complete or, at least, that unreported data are missing at random. Unfortunately, real-world databases are rarely complete and the "Missing at Random" assumption is often unrealistic. This paper shows that this assumption can dramatically affect the reliability of the learned BBN and introduces a robust method to learn conditional probabilities in a BBN, which does not rely on this assumption. In order to drop this assumption, we have to change the overall learning strategy used by traditional Bayesian methods: our method bounds the set of all posterior probabilities consistent with the database and proceed by refining this set as more information becomes available. An experimental comparison - using both an artificial example and a real medical application - of our method with a powerful stochastic simulator will show a dramatic gain in robustness and the computational advantages of our deterministic method.

1. Knowledge Media Institute, The Open University.

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