Minimum uncertainty as Bayesian network model selection principle

Bayesian Network (BN) modeling is a prominent methodology in computational systems biology. However, the incommensurability of datasets frequently encountered in life science domains gives rise to contextual dependence and numerical irregularities in the behavior of model selection criteria (such as MDL, Minimum Description Length) used in BN reconstruction. This renders model features, first and foremost dependency strengths, incomparable and difficult to interpret. In this study, we derive and evaluate a model selection principle that addresses these problems.

The objective of the study is attained by (i) approaching model evaluation as a misspecification problem, (ii) estimating the effect that sampling error has on the satisfiability of conditional independence criterion, as reflected by Mutual Information, and (iii) utilizing this error estimate to penalize uncertainty with the novel Minimum Uncertainty (MU) model selection principle. We validate our findings numerically and demonstrate the performance advantages of the MU criterion. Finally, we illustrate the advantages of the new model evaluation framework on real data examples.

The new BN model selection principle successfully overcomes performance irregularities observed with MDL, offers a superior average convergence rate in BN reconstruction, and improves the interpretability and universality of resulting BNs, thus enabling direct inter-BN comparisons and evaluations.