Global Sensitivity Analysis with Dependence Measures
This work addresses a theoretical and practical problem in sensitivity analysis for researchers and practitioners in fields like statistics and machine learning, offering a novel approach that is incremental but builds on recent advances in dependence measures.
The paper tackles the limitations of variance-based global sensitivity analysis by introducing a new class of sensitivity indices based on dependence measures, such as distance correlation and the Hilbert-Schmidt independence criterion, which overcome issues with handling multivariate variables and focusing only on output variance.
Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which overcomes these insufficiencies. Our approach originates from the idea to compare the output distribution with its conditional counterpart when one of the input variables is fixed. We establish that this comparison yields previously proposed indices when it is performed with Csiszar f-divergences, as well as sensitivity indices which are well-known dependence measures between random variables. This leads us to investigate completely new sensitivity indices based on recent state-of-the-art dependence measures, such as distance correlation and the Hilbert-Schmidt independence criterion. We also emphasize the potential of feature selection techniques relying on such dependence measures as alternatives to screening in high dimension.