On Sensitivity of the MAP Bayesian Network Structure to the Equivalent Sample Size Parameter

TL;DR

This paper investigates how the choice of the equivalent sample size parameter affects Bayesian network structure learning using the BDeu score, revealing high sensitivity and proposing explanations and potential solutions.

Contribution

It demonstrates the high sensitivity of Bayesian network structures to the alpha parameter in the BDeu score and provides insights into the underlying causes.

Findings

Network structure solutions vary significantly with alpha.

The sensitivity impacts model selection reliability.

Proposes ideas to mitigate the sensitivity issue.

Abstract

BDeu marginal likelihood score is a popular model selection criterion for selecting a Bayesian network structure based on sample data. This non-informative scoring criterion assigns same score for network structures that encode same independence statements. However, before applying the BDeu score, one must determine a single parameter, the equivalent sample size alpha. Unfortunately no generally accepted rule for determining the alpha parameter has been suggested. This is disturbing, since in this paper we show through a series of concrete experiments that the solution of the network structure optimization problem is highly sensitive to the chosen alpha parameter value. Based on these results, we are able to give explanations for how and why this phenomenon happens, and discuss ideas for solving this problem.