A hybrid approach for learning parameters of probabilistic networks from incomplete databases

Probabilistic Inference Networks are becoming increasingly popular for modeling and reasoning in uncertain domains. In the past few years, many efforts have been made in learning the parameters of probabilistic network directly from databases. The learning techniques are based on the assumption that the database is complete. If there are missing values, these values are first estimated and then the modified database is used to learn the parameters of the network. During the estimation process, the missing values are assumed to be missing at random. This paper incorporates the concepts of the Dempster-Shafer theory of belief functions to learn the parameter of the inference network. Instead of filling the missing values by their estimates, we model these missing values as representing our ignorance or lack of belief in their state. The representation provides the possibility to obtain interval estimates of the marginal probabilities of each variable in the inference network. The representation also allows us to model evidence in terms of support functions as used in belief functions, thus providing a richer way to enter evidence or new findings in the probabilistic model.