Making Sensitivity Analysis Computationally Efficient
This work addresses a computational bottleneck for researchers and practitioners using Bayesian networks, offering incremental improvements in efficiency for sensitivity analysis.
The paper tackles the computational inefficiency of sensitivity analysis in Bayesian networks by introducing a method that reduces the required number of network evaluations to just a single outward propagation in a junction tree for establishing coefficients, with an inward propagation for evidence processing, and extends this to n-way analysis for sets of parameters.
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.