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 particular, the so-called sensitivity value measures the quantity of interest's partial derivative with respect to the network's conditional probabilities. However, finding such values in large networks with thousands of parameters can become computationally very expensive. We propose to use automatic differentiation combined with exact inference to obtain all sensitivity values in a single pass. Our method 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. We demonstrate our routines by ranking all parameters by importance on a Bayesian network modeling humanitarian crises and disasters, and then show the method's efficiency by scaling it to huge networks with up to 100'000 parameters. An implementation of the methods using the popular machine learning library PyTorch is freely available.

该研究提出一种基于自动微分和精确推断的方法，通过一遍推断来获得贝叶斯网络的所有敏感度值，并用 PyTorch 实现。该方法可用于大型网络，以提高计算效率并排名各参数的重要性。

You Only Derive Once (YODO): 贝叶斯网络中的高效敏感度分析自动差分