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Sensitivity analysis measures the influence of a Bayesian network'sparameters on a quantity of interest defined by the network, such as theprobability of a variable taking a specific value. Various sensitivity measureshave been defined to quantify such influence, most commonly some function ofthe quantity of interest's partial derivative with respect to the network'sconditional probabilities. However, computing these measures in large networkswith thousands of parameters can become computationally very expensive. Wepropose an algorithm combining automatic differentiation and exact inference toefficiently calculate the sensitivity measures in a single pass. It firstmarginalizes the whole network once, using e.g. variable elimination, and thenbackpropagates this operation to obtain the gradient with respect to all inputparameters. Our method can be used for one-way and multi-way sensitivityanalysis and the derivation of admissible regions. Simulation studies highlightthe efficiency of our algorithm by scaling it to massive networks with up to100'000 parameters and investigate the feasibility of generic multi-wayanalyses. Our routines are also showcased over two medium-sized Bayesiannetworks: the first modeling the country-risks of a humanitarian crisis, thesecond studying the relationship between the use of technology and thepsychological effects of forced social isolation during the COVID-19 pandemic.An implementation of the methods using the popular machine learning libraryPyTorch is freely available.

The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks