Sensitivity indices for independent groups of variables

TL;DR

This paper investigates sensitivity indices for independent variable groups, especially in block-additive and Gaussian linear models, proposing efficient algorithms and improved estimation methods for Sobol and Shapley indices.

Contribution

It introduces a novel analysis of sensitivity indices for independent groups, demonstrating zero Sobol indices in block-additive models and providing an efficient algorithm for Gaussian models.

Findings

Most Sobol indices are zero in block-additive models

The proposed algorithm outperforms existing methods in efficiency

Improved estimation of Shapley effects for models with independent groups

Abstract

In this paper, we study sensitivity indices for independent groups of variables and we look at the particular case of block-additive models. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can be estimated more efficiently. We then apply this study to Gaussian linear models, and we provide an efficient algorithm to compute the theoretical sensitivity indices. In numerical experiments, we show that this algorithm compares favourably to other existing methods. We also use the theoretical results to improve the estimation of the Shapley effects for general models, when the inputs form independent groups of variables.