Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tables
This work addresses parameter estimation in Bayesian networks, offering a more accurate method for probabilistic modeling, though it appears incremental in nature.
The authors tackled the problem of estimating conditional probability tables by proposing a joint estimation approach for conditional distributions within the same table, which improved classification performance compared to traditional methods.
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.