Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks

TL;DR

This paper introduces a global variance-based sensitivity analysis method for Bayesian networks, capturing the joint effects of multiple uncertain parameters using tensor decomposition and Sobol indices, providing a more comprehensive understanding than traditional OAT methods.

Contribution

The paper presents a novel approach combining tensor decomposition and Sobol indices for global sensitivity analysis in Bayesian networks, addressing limitations of one-at-a-time methods.

Findings

Sobol indices differ significantly from OAT indices

The method reveals true influence and interactions of parameters

Demonstrated effectiveness on benchmark Bayesian networks

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.