Global sensitivity analysis in probabilistic graphical models
This work addresses the computational bottleneck in sensitivity analysis for probabilistic graphical models, which is incremental by generalizing earlier tensor-based techniques to cyclic networks.
The authors tackled the problem of efficiently computing global sensitivity indices for Bayesian networks, enabling exact or approximate results with significantly reduced computational cost compared to brute-force or Monte Carlo methods, as demonstrated on medium to large networks in project risk management and reliability engineering.
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.