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.Comment: 19 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:0909.168
