Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tables

TL;DR

This paper introduces a hierarchical multinomial-Dirichlet model that jointly estimates conditional probability tables in Bayesian networks, leading to improved accuracy and classification performance over traditional methods.

Contribution

The paper proposes a novel joint estimation approach for conditional probability tables using a hierarchical multinomial-Dirichlet model, with exact analytical estimators and demonstrated benefits.

Findings

Exact analytical expressions for estimators derived

Improved joint distribution estimation in Bayesian networks

Enhanced classification performance observed

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.