Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks

• URL: http://arxiv.org/abs/2406.05764v1
• Date: Sun, 9 Jun 2024 12:36:38 GMT
• Title: Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks
• Authors: Rafael Ballester-Ripoll, Manuele Leonelli,
• Abstract summary: We propose to conduct global variance-based sensitivity analysis of $n$ parameters. Our method works by encoding the uncertainties as $n$ additional variables of the network. Last, we apply the method of Sobol to the resulting network to obtain $n$ global sensitivity indices.
• Score: 4.404496835736175
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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