Evaluating the difference between graph structures in Gaussian Bayesian networks

In this work, we evaluate the sensitivity of Gaussian Bayesian networks to perturbations or uncertainties in the regression coefficients of the network arcs and the conditional distributions of the variables. The Kullback–Leibler divergence measure is used to compare the original network to its perturbation. By setting the regression coefficients to zero or non-zero values, the proposed method can remove or add arcs, making it possible to compare different network structures. The methodology is implemented with some case studies.

► A new methodology to deal with perturbations in the conditional specification of Gaussian Bayesian networks is proposed.
► We can remove or add arcs, making it possible to compare different network structures.
► Some practical examples and a case study in metrology demonstrate the feasibility of the procedure.