The accuracy of a Bayesian Network

Abstract

A Bayesian network is a construct that represents a joint probability distribution, and can be used in order to model a given joint probability distribution. A principal characteristic of a Bayesian network is the degree to which it models the given joint probability distribution accurately; the accuracy of a Bayesian network. Although the accuracy of a Bayesian network can be well defined in theory, it is rarely possible to determine the accuracy of a Bayesian network in practice for real-world applications. Instead, alternative characteristics of a Bayesian network, which relate to and reflect the accuracy, are used to model the accuracy of a Bayesian network, and appropriate measures are devised. A popular formalism that adopts such methods to study the accuracy of a Bayesian network is the Minimum Description Length (MDL) formalism, which models the accuracy of a Bayesian network as the probability of the Bayesian network given the data set that describes the joint probability distribution the Bayesian network models. However, in the context of Bayesian Networks, the MDL formalism is flawed, exhibiting several shortcomings, and thus inappropriate for examining the accuracy of a Bayesian network. An alternative framework for Bayesian Networks is proposed, which models the accuracy of a Bayesian network as the accuracy of the conditional independencies implied by the structure of the Bayesian network, and specifies an appropriate measure called the Network Conditional Independencies Mutual Information (NCIMI) measure. The proposed framework is inspired by the principles governing the field of Bayesian Networks, and is based on formal theoretical foundations. Experiments have been conducted, using real-world problems, that evaluate both the MDL formalism and the proposed framework for Bayesian Networks. The experimental results support the theoretical claims, and confirm the significance of the proposed framework