# The many Shapley values for model explanation

arXiv: https://arxiv.org/abs/1908.08474 · HTML: https://mlsanity.com/paper/1908.08474/

## Key facts

- Cited by 344 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2019.

## Built on by (most cited first, 30 of 344)

- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Foundation Models and Fair Use](https://mlsanity.com/paper/2303.15715/) (2023)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [The Out-of-Distribution Problem in Explainability and Search Methods for Feature Importance Explanations](https://mlsanity.com/paper/2106.00786/) (2021)
- [Impossibility Theorems for Feature Attribution](https://mlsanity.com/paper/2212.11870/) (2022)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Synthetic Benchmarks for Scientific Research in Explainable Machine Learning](https://mlsanity.com/paper/2106.12543/) (2021)
- [Additive MIL: Intrinsically Interpretable Multiple Instance Learning for Pathology](https://mlsanity.com/paper/2206.01794/) (2022)
- [Don't Say No: Jailbreaking LLM by Suppressing Refusal](https://mlsanity.com/paper/2404.16369/) (2024)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [Post-Hoc Explanations Fail to Achieve their Purpose in Adversarial Contexts](https://mlsanity.com/paper/2201.10295/) (2022)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Shapley Explanation Networks](https://mlsanity.com/paper/2104.02297/) (2021)
- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [Shapley Counterfactual Credits for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2106.00285/) (2021)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [MultiViz: Towards Visualizing and Understanding Multimodal Models](https://mlsanity.com/paper/2207.00056/) (2022)
- [WeightedSHAP: analyzing and improving Shapley based feature attributions](https://mlsanity.com/paper/2209.13429/) (2022)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [LINe: Out-of-Distribution Detection by Leveraging Important Neurons](https://mlsanity.com/paper/2303.13995/) (2023)
- [Neural Response Interpretation through the Lens of Critical Pathways](https://mlsanity.com/paper/2103.16886/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)

## Abstract (arXiv)

The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing [16] showing that it is the unique method that satisfies certain good properties (axioms). There are, however, a multiplicity of ways in which the Shapley value is operationalized in the attribution problem. These differ in how they reference the model, the training data, and the explanation context. These give very different results, rendering the uniqueness result meaningless. Furthermore, we find that previously proposed approaches can produce counterintuitive attributions in theory and in practice---for instance, they can assign non-zero attributions to features that are not even referenced by the model. In this paper, we use the axiomatic approach to study the differences between some of the many operationalizations of the Shapley value for attribution, and propose a technique called Baseline Shapley (BShap) that is backed by a proper uniqueness result. We also contrast BShap with Integrated Gradients, another extension of Shapley value to the continuous setting.