Title: Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tables,
Abstract: We present a novel approach for estimating conditional probability tables,
based on a joint, rather than independent, estimate of the conditional
distributions belonging to the same table. We derive exact analytical
expressions for the estimators and we analyse their properties both
analytically and via simulation. We then apply this method to the estimation of
parameters in a Bayesian network. Given the structure of the network, the
proposed approach better estimates the joint distribution and significantly
improves the classification performance with respect to traditional approaches.