# Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs

arXiv: https://arxiv.org/abs/2101.08083 · HTML: https://mlsanity.com/paper/2101.08083/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2021.

## Built on by (most cited first, 4 of 4)

- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysis](https://mlsanity.com/paper/2202.07728/) (2022)
- [Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning models](https://mlsanity.com/paper/2209.11539/) (2022)

## Abstract (arXiv)

Reliability-oriented sensitivity analysis methods have been developed for understanding the influence of model inputs relative to events which characterize the failure of a system (e.g., a threshold exceedance of the model output). In this field, the target sensitivity analysis focuses primarily on capturing the influence of the inputs on the occurrence of such a critical event. This paper proposes new target sensitivity indices, based on the Shapley values and called "target Shapley effects", allowing for interpretable sensitivity measures under dependent inputs. Two algorithms (one based on Monte Carlo sampling, and a given-data algorithm based on a nearest-neighbors procedure) are proposed for the estimation of these target Shapley effects based on the ℓ2 norm. Additionally, the behavior of these target Shapley effects are theoretically and empirically studied through various toy-cases. Finally, the application of these new indices in two real-world use-cases (a river flood model and a COVID-19 epidemiological model) is discussed.