# From Shapley Values to Generalized Additive Models and back

arXiv: https://arxiv.org/abs/2209.04012 · HTML: https://mlsanity.com/paper/2209.04012/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 67 references that are in the map.
- First posted on arXiv 8 Sep 2022.

## Builds on (most cited first, 30 of 38)

- [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)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (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)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Explaining the Explainer: A First Theoretical Analysis of LIME](https://mlsanity.com/paper/2001.03447/) (2020)
- [Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post Hoc Explanations](https://mlsanity.com/paper/2206.01254/) (2022)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Explainable k-Means and k-Medians Clustering](https://mlsanity.com/paper/2002.12538/) (2020)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Falling Rule Lists](https://mlsanity.com/paper/1411.5899/) (2014)
- [Post-Hoc Explanations Fail to Achieve their Purpose in Adversarial Contexts](https://mlsanity.com/paper/2201.10295/) (2022)
- [Towards the Unification and Robustness of Perturbation and Gradient Based Explanations](https://mlsanity.com/paper/2102.10618/) (2021)

## Built on by (most cited first, 30 of 60)

- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [Decoupling Pixel Flipping and Occlusion Strategy for Consistent XAI Benchmarks](https://mlsanity.com/paper/2401.06654/) (2024)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [ProxySPEX: Inference-Efficient Interpretability via Sparse Feature Interactions in LLMs](https://mlsanity.com/paper/2505.17495/) (2025)
- [Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks](https://mlsanity.com/paper/2501.16944/) (2025)
- [Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory](https://mlsanity.com/paper/2412.17152/) (2024)
- [Rethinking Explainable Machine Learning as Applied Statistics](https://mlsanity.com/paper/2402.02870/) (2024)
- [Data Science with LLMs and Interpretable Models](https://mlsanity.com/paper/2402.14474/) (2024)
- [Attention Mechanisms Don't Learn Additive Models: Rethinking Feature Importance for Transformers](https://mlsanity.com/paper/2405.13536/) (2024)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [LLMs Understand Glass-Box Models, Discover Surprises, and Suggest Repairs](https://mlsanity.com/paper/2308.01157/) (2023)
- [PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression](https://mlsanity.com/paper/2601.18608/) (2026)
- [Explaining Similarity in Vision-Language Encoders with Weighted Banzhaf Interactions](https://mlsanity.com/paper/2508.05430/) (2025)
- [Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithm](https://mlsanity.com/paper/2510.24815/) (2025)
- [On the Inflation of KNN-Shapley Value](https://mlsanity.com/paper/2405.17489/) (2024)
- [Fooling SHAP with Output Shuffling Attacks](https://mlsanity.com/paper/2408.06509/) (2024)
- [Fast Estimation of Partial Dependence Functions using Trees](https://mlsanity.com/paper/2410.13448/) (2024)
- [SHAP zero Explains Biological Sequence Models with Near-zero Marginal Cost for Future Queries](https://mlsanity.com/paper/2410.19236/) (2024)
- [Disentangling Interactions and Dependencies in Feature Attribution](https://mlsanity.com/paper/2410.23772/) (2024)
- [Towards Unified Attribution in Explainable AI, Data-Centric AI, and Mechanistic Interpretability](https://mlsanity.com/paper/2501.18887/) (2025)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [Exactly Computing do-Shapley Values](https://mlsanity.com/paper/2602.07203/) (2026)
- [HOPE: High-order Polynomial Expansion of Black-box Neural Networks](https://mlsanity.com/paper/2307.08192/) (2023)
- [Beyond Single-Feature Importance with ICECREAM](https://mlsanity.com/paper/2307.09779/) (2023)
- [Theoretical Evaluation of Asymmetric Shapley Values for Root-Cause Analysis](https://mlsanity.com/paper/2310.09961/) (2023)
- [How Well Do Feature-Additive Explainers Explain Feature-Additive Predictors?](https://mlsanity.com/paper/2310.18496/) (2023)

## Abstract (arXiv)

In explainable machine learning, local post-hoc explanation algorithms and inherently interpretable models are often seen as competing approaches. This work offers a partial reconciliation between the two by establishing a correspondence between Shapley Values and Generalized Additive Models (GAMs). We introduce n-Shapley Values, a parametric family of local post-hoc explanation algorithms that explain individual predictions with interaction terms up to order n. By varying the parameter n, we obtain a sequence of explanations that covers the entire range from Shapley Values up to a uniquely determined decomposition of the function we want to explain. The relationship between n-Shapley Values and this decomposition offers a functionally-grounded characterization of Shapley Values, which highlights their limitations. We then show that n-Shapley Values, as well as the Shapley Taylor- and Faith-Shap interaction indices, recover GAMs with interaction terms up to order n. This implies that the original Shapely Values recover GAMs without variable interactions. Taken together, our results provide a precise characterization of Shapley Values as they are being used in explainable machine learning. They also offer a principled interpretation of partial dependence plots of Shapley Values in terms of the underlying functional decomposition. A package for the estimation of different interaction indices is available at urlhttps://github.com/tml-tuebingen/nshap.