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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05764 |
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| _version_ | 1866914830114357248 |
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| author | Ballester-Ripoll, Rafael Leonelli, Manuele |
| author_facet | Ballester-Ripoll, Rafael Leonelli, Manuele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks Ballester-Ripoll, Rafael Leonelli, Manuele Artificial Intelligence 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. |
| title | Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2406.05764 |