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.