Measures of Variability for Bayesian Network Graphical Structures

TL;DR

This paper introduces statistical measures and tests for assessing the variability of Bayesian network structures, aiding in comparing learning algorithms and evaluating arc subset strength.

Contribution

It presents new descriptive statistics and tests for the undirected graph of Bayesian networks, modeled as multivariate Bernoulli variables, with practical examples.

Findings

New variability measures for Bayesian network structures

Performance comparison of structure learning algorithms

Application of tests on small sample data

Abstract

The structure of a Bayesian network includes a great deal of information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study its variability, which can be used to compare the performance of different learning algorithms and to measure the strength of any arbitrary subset of arcs. In this paper we will introduce some descriptive statistics and the corresponding parametric and Monte Carlo tests on the undirected graph underlying the structure of a Bayesian network, modeled as a multivariate Bernoulli random variable. A simple numeric example and the comparison of the performance of some structure learning algorithm on small samples will then illustrate their use.