Making Sensitivity Analysis Computationally Efficient

TL;DR

This paper introduces a computationally efficient method for sensitivity analysis in Bayesian networks, reducing the number of network evaluations needed by using a single outward propagation for multiple parameters and evidence processing.

Contribution

The paper presents a novel approach that significantly reduces computational effort in sensitivity analysis of Bayesian networks by leveraging a single outward propagation for multiple parameters.

Findings

Requires only one outward propagation for all parameters

Extends to n-way sensitivity analysis

Efficiently computes posterior marginals in Bayesian networks

Abstract

To investigate the robustness of the output probabilities of a Bayesian network, a sensitivity analysis can be performed. A one-way sensitivity analysis establishes, for each of the probability parameters of a network, a function expressing a posterior marginal probability of interest in terms of the parameter. Current methods for computing the coefficients in such a function rely on a large number of network evaluations. In this paper, we present a method that requires just a single outward propagation in a junction tree for establishing the coefficients in the functions for all possible parameters; in addition, an inward propagation is required for processing evidence. Conversely, the method requires a single outward propagation for computing the coefficients in the functions expressing all possible posterior marginals in terms of a single parameter. We extend these results to an n-way sensitivity analysis in which sets of parameters are studied.