# The Distributional Uncertainty of the SHAP score in Explainable Machine Learning

arXiv: https://arxiv.org/abs/2401.12731 · HTML: https://mlsanity.com/paper/2401.12731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [Model Interpretability through the Lens of Computational Complexity](https://mlsanity.com/paper/2010.12265/) (2020)
- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
- [Causality-based Explanation of Classification Outcomes](https://mlsanity.com/paper/2003.06868/) (2020)
- [Declarative Approaches to Counterfactual Explanations for Classification](https://mlsanity.com/paper/2011.07423/) (2020)
- [From Robustness to Explainability and Back Again](https://mlsanity.com/paper/2306.03048/) (2023)
- [Efficient Computation of Shap Explanation Scores for Neural Network Classifiers via Knowledge Compilation](https://mlsanity.com/paper/2303.06516/) (2023)

## Built on by (most cited first, 1 of 1)

- [UbiQTree: Uncertainty Quantification in XAI with Tree Ensembles](https://mlsanity.com/paper/2508.09639/) (2025)

## Abstract (arXiv)

Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley value used in coalition game theory. The definition of this score relies on a probability distribution on the entity population. Since the exact distribution is generally unknown, it needs to be assigned subjectively or be estimated from data, which may lead to misleading feature scores. In this paper, we propose a principled framework for reasoning on SHAP scores under unknown entity population distributions. In our framework, we consider an uncertainty region that contains the potential distributions, and the SHAP score of a feature becomes a function defined over this region. We study the basic problems of finding maxima and minima of this function, which allows us to determine tight ranges for the SHAP scores of all features. In particular, we pinpoint the complexity of these problems, and other related ones, showing them to be NP-complete. Finally, we present experiments on a real-world dataset, showing that our framework may contribute to a more robust feature scoring.