# On the Connection between Game-Theoretic Feature Attributions and Counterfactual Explanations

arXiv: https://arxiv.org/abs/2307.06941 · HTML: https://mlsanity.com/paper/2307.06941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 50 of its 99 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 30 of 50)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective](https://mlsanity.com/paper/2202.01602/) (2022)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Artificial Intelligence: the global landscape of ethics guidelines](https://mlsanity.com/paper/1906.11668/) (2019)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [The role of explainability in creating trustworthy artificial intelligence for health care: a comprehensive survey of the terminology, design choices, and evaluation strategies](https://mlsanity.com/paper/2007.15911/) (2020)

## Abstract (arXiv)

Explainable Artificial Intelligence (XAI) has received widespread interest in recent years, and two of the most popular types of explanations are feature attributions, and counterfactual explanations. These classes of approaches have been largely studied independently and the few attempts at reconciling them have been primarily empirical. This work establishes a clear theoretical connection between game-theoretic feature attributions, focusing on but not limited to SHAP, and counterfactuals explanations. After motivating operative changes to Shapley values based feature attributions and counterfactual explanations, we prove that, under conditions, they are in fact equivalent. We then extend the equivalency result to game-theoretic solution concepts beyond Shapley values. Moreover, through the analysis of the conditions of such equivalence, we shed light on the limitations of naively using counterfactual explanations to provide feature importances. Experiments on three datasets quantitatively show the difference in explanations at every stage of the connection between the two approaches and corroborate the theoretical findings.