Structure Variability in Bayesian Networks

TL;DR

This paper investigates the variability of Bayesian network structures using descriptive statistics and statistical tests, aiding in comparing learning algorithms and assessing arc subset strength.

Contribution

It introduces new descriptive statistics and tests for analyzing the structure variability of Bayesian networks modeled as multivariate Bernoulli variables.

Findings

Provides methods to quantify structure variability

Enables comparison of different learning algorithms

Offers tools to assess arc subset strength

Abstract

The structure of a Bayesian network encodes most of the information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study the variability of its network structure, 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.