# SHAP-XRT: The Shapley Value Meets Conditional Independence Testing

arXiv: https://arxiv.org/abs/2207.07038 · HTML: https://mlsanity.com/paper/2207.07038/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 95 references that are in the map.
- First posted on arXiv 14 Jul 2022.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [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 Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [Shapley explainability on the data manifold](https://mlsanity.com/paper/2006.01272/) (2020)
- [A Distributional Framework for Data Valuation](https://mlsanity.com/paper/2002.12334/) (2020)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [Do Input Gradients Highlight Discriminative Features?](https://mlsanity.com/paper/2102.12781/) (2021)
- [Interpretable to Whom? A Role-based Model for Analyzing Interpretable Machine Learning Systems](https://mlsanity.com/paper/1806.07552/) (2018)
- [Learning to Estimate Shapley Values with Vision Transformers](https://mlsanity.com/paper/2206.05282/) (2022)

## Built on by (most cited first, 6 of 6)

- [I Bet You Did Not Mean That: Testing Semantic Importance via Betting](https://mlsanity.com/paper/2405.19146/) (2024)
- [Sufficient and Necessary Explanations (and What Lies in Between)](https://mlsanity.com/paper/2409.20427/) (2024)
- [MinShap: A Shapley-Based Framework for Feature Redundancy](https://mlsanity.com/paper/2604.15107/) (2026)
- [A Saliency-based Clustering Framework for Identifying Aberrant Predictions](https://mlsanity.com/paper/2311.06454/) (2023)
- [Shapley-PC: Constraint-based Causal Structure Learning with a Shapley Inspired Framework](https://mlsanity.com/paper/2312.11582/) (2023)
- [Direct Preference Optimization for Adaptive Concept-based Explanations](https://mlsanity.com/paper/2505.15626/) (2025)

## Abstract (arXiv)

The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation methods for machine learning models. More traditionally, from a statistical perspective, feature importance is defined in terms of conditional independence. So far, these two approaches to interpretability and feature importance have been considered separate and distinct. In this work, we show that Shapley-based explanation methods and conditional independence testing are closely related. We introduce the SHAPley EXplanation Randomization Test (SHAP-XRT), a testing procedure inspired by the Conditional Randomization Test (CRT) for a specific notion of local (i.e., on a sample) conditional independence. With it, we prove that for binary classification problems, the marginal contributions in the Shapley value provide lower and upper bounds to the expected p-values of their respective tests. Furthermore, we show that the Shapley value itself provides an upper bound to the expected p-value of a global (i.e., overall) null hypothesis. As a result, we further our understanding of Shapley-based explanation methods from a novel perspective and characterize the conditions under which one can make statistically valid claims about feature importance via the Shapley value.