Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks
This addresses the need for more comprehensive sensitivity analysis in Bayesian networks, particularly for applications relying on accurate uncertainty quantification, but it is incremental as it builds on existing global sensitivity methods.
The paper tackled the problem of sensitivity analysis in Bayesian networks by moving from one-at-a-time parameter modifications to a global variance-based approach, demonstrating that Sobol indices can significantly differ from traditional indices, revealing higher-order interactions among uncertain parameters.
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a comprehensive account of each inputs' relevance, since simultaneous perturbations in two or more parameters often entail higher-order effects that cannot be captured by an OAT analysis. We propose to conduct global variance-based sensitivity analysis instead, whereby $n$ parameters are viewed as uncertain at once and their importance is assessed jointly. Our method works by encoding the uncertainties as $n$ additional variables of the network. To prevent the curse of dimensionality while adding these dimensions, we use low-rank tensor decomposition to break down the new potentials into smaller factors. Last, we apply the method of Sobol to the resulting network to obtain $n$ global sensitivity indices. Using a benchmark array of both expert-elicited and learned Bayesian networks, we demonstrate that the Sobol indices can significantly differ from the OAT indices, thus revealing the true influence of uncertain parameters and their interactions.