Local Sensitivity of Bayesian Networks to Multiple Simultaneous Parameter Shifts

The robustness of the performance of a Bayesian network to shifts in its parameters can be studied with a sensitivity analysis. For reasons of computational efficiency such an analysis is often limited to studying shifts in only one or two parameters at a time. The concept of sensitivity value, an important notion in sensitivity analysis, captures the effect of local changes in a single parameter. In this paper we generalise this concept to an n-way sensitivity value in order to capture the local effect of multiple simultaneous parameters changes. Moreover, we demonstrate that an n-way sensitivity value can be computed efficiently, even for large n. An n-way sensitivity value is direction dependent and its maximum, minimum, and direction of maximal change can be easily determined. The direction of maximal change can, for example, be exploited in network tuning. To this end, we introduce the concept of sliced sensitivity function for an n-way sensitivity function restricted to parameter shifts in a fixed direction. We moreover argue that such a function can be computed efficiently.