# Global sensitivity analysis in probabilistic graphical models

arXiv: https://arxiv.org/abs/2110.03749 · HTML: https://mlsanity.com/paper/2110.03749/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 6 of 6)

- [Bayesian Networks in Healthcare: Distribution by Medical Condition](https://mlsanity.com/paper/2002.00224/) (2020)
- [Duality of Graphical Models and Tensor Networks](https://mlsanity.com/paper/1710.01437/) (2017)
- [Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R package](https://mlsanity.com/paper/2107.11785/) (2021)
- [Making Sensitivity Analysis Computationally Efficient](https://mlsanity.com/paper/1301.3868/) (2013)
- [A geometric characterisation of sensitivity analysis in monomial models](https://mlsanity.com/paper/1901.02058/) (2018)
- [Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition](https://mlsanity.com/paper/1407.3023/) (2014)

## Abstract (arXiv)

We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to transform the problem of Sobol index estimation into that of marginalization inference. This way, we can efficiently compute indices for networks where brute-force or Monte Carlo based estimators for variance-based sensitivity analysis would require millions of costly samples. Moreover, our method gives exact results when exact inference is used, and also supports the case of correlated inputs. The proposed algorithm is inspired by the field of tensor networks, and generalizes earlier tensor sensitivity techniques from the acyclic to the cyclic case. We demonstrate the method on three medium to large Bayesian networks that cover the areas of project risk management and reliability engineering.