Sensitivity analysis measures the influence of a Bayesian network’s parameters on a
quantity of interest defined by the network, such as the probability of a variable taking
a specific value. In the literature, this influence is often measured by computing the
partial derivative with respect to the network parameters. However, this can become
computationally expensive in large networks with thousands of parameters. We propose
an algorithm combining automatic differentiation and exact inference to calculate the
sensitivity measures in a single pass efficiently. It first marginalizes the whole network
once, using e.g. variable elimination, and then backpropagates this operation to obtain
the gradient with respect to all input parameters. Our method can be used for one-way
and multi-way sensitivity analysis and the derivation of admissible regions. Simulation
studies highlight the efficiency of our algorithm by scaling it to massive networks with
up to 100,000 parameters and investigate the feasibility of generic multi-way analyses.
Our routines are also showcased over two medium-sized Bayesian networks: the first
modeling the country risks of a humanitarian crisis, the second studying the relationship
between the use of technology and the psychological effects of forced social isolation
during the COVID-19 pandemic. An implementation of the methods using the popular
machine learning library PyTorch is freely available.