On Sensitivity of the MAP Bayesian Network Structure to the Equivalent Sample Size Parameter
This addresses a critical problem for researchers and practitioners in machine learning and statistics who rely on Bayesian networks for model selection, as it highlights a significant sensitivity that can affect the reliability of results, making it an incremental contribution by identifying and analyzing a known bottleneck.
The paper tackles the sensitivity of Bayesian network structure selection to the equivalent sample size parameter (alpha) in the BDeu scoring criterion, showing through experiments that the optimal network structure is highly sensitive to alpha, and provides explanations and potential solutions for this issue.
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.