Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks
<|reference_start|>Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks: 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.<|reference_end|>
@article{ballester-ripoll2024global,
    title={Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks},
    author={Rafael Ballester-Ripoll and Manuele Leonelli},
    journal={arXiv preprint arXiv:2406.05764},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05764},
    primaryClass={cs.AI}
}