Global sensitivity analysis in probabilistic graphical models

TL;DR

This paper introduces an efficient method for global sensitivity analysis in Bayesian networks using Sobol's indices, leveraging network structure for exact or approximate inference, applicable to cyclic and acyclic models.

Contribution

It presents a novel tensor network-inspired algorithm that generalizes tensor sensitivity techniques to cyclic Bayesian networks, enabling efficient sensitivity analysis.

Findings

Exact sensitivity indices can be computed with the proposed method.

The method significantly reduces computational cost compared to Monte Carlo approaches.

Demonstrated effectiveness on medium to large Bayesian networks in risk and reliability domains.

Abstract

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.