You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks
This provides an efficient tool for researchers and practitioners in fields like disaster modeling to analyze parameter influences in large Bayesian networks, though it is incremental as it builds on existing automatic differentiation and inference techniques.
The paper tackles the computational expense of sensitivity analysis in large Bayesian networks by proposing a method that uses automatic differentiation combined with exact inference to compute all sensitivity values in a single pass, demonstrating efficiency on networks with up to 100,000 parameters.
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.