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

Abstract

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.