# A simple algorithm for global sensitivity analysis with Shapley effects

arXiv: https://arxiv.org/abs/2009.00874 · HTML: https://mlsanity.com/paper/2009.00874/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Fast Approximation of the Shapley Values Based on Order-of-Addition Experimental Designs](https://mlsanity.com/paper/2309.08923/) (2023)
- [Cooperative effects in feature importance of individual patterns: application to air pollutants and Alzheimer disease](https://mlsanity.com/paper/2508.00930/) (2025)

## Abstract (arXiv)

Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sensitivity indices, so-called Shapley effects have recently gained popularity mainly because the Shapley effects for all the individual variables are summed up to the overall variance, which gives a better interpretability than the classical sensitivity indices called main effects and total effects. In this paper, assuming that all the input variables are independent, we introduce a quite simple Monte Carlo algorithm to estimate the Shapley effects for all the individual variables simultaneously, which drastically simplifies the existing algorithms proposed in the literature. We present a short Matlab implementation of our algorithm and show some numerical results. A possible extension to the case where the input variables are dependent is also discussed.