# Algorithms to estimate Shapley value feature attributions

arXiv: https://arxiv.org/abs/2207.07605 · HTML: https://mlsanity.com/paper/2207.07605/

## Key facts

- Cited by 115 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 95 references that are in the map.
- First posted on arXiv 15 Jul 2022.

## Builds on (most cited first, 30 of 46)

- [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)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [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)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [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)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers](https://mlsanity.com/paper/1604.00825/) (2016)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [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)
- [XRAI: Better Attributions Through Regions](https://mlsanity.com/paper/1906.02825/) (2019)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [Neuron Shapley: Discovering the Responsible Neurons](https://mlsanity.com/paper/2002.09815/) (2020)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [On Using Very Large Target Vocabulary for Neural Machine Translation](https://mlsanity.com/paper/1412.2007/) (2014)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)

## Built on by (most cited first, 30 of 115)

- [Explainability for Large Language Models: A Survey](https://mlsanity.com/paper/2309.01029/) (2023)
- [What does a platypus look like? Generating customized prompts for zero-shot image classification](https://mlsanity.com/paper/2209.03320/) (2022)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [Adversarial attacks and defenses in explainable artificial intelligence: A survey](https://mlsanity.com/paper/2306.06123/) (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)
- [Approximating the Shapley Value without Marginal Contributions](https://mlsanity.com/paper/2302.00736/) (2023)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [Feature Importance: A Closer Look at Shapley Values and LOCO](https://mlsanity.com/paper/2303.05981/) (2023)
- [Explainability is NOT a Game](https://mlsanity.com/paper/2307.07514/) (2023)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution](https://mlsanity.com/paper/2401.15866/) (2024)
- [On the Robustness of Removal-Based Feature Attributions](https://mlsanity.com/paper/2306.07462/) (2023)
- [FaithLM: Towards Faithful Explanations for Large Language Models](https://mlsanity.com/paper/2402.04678/) (2024)
- [HarsanyiNet: Computing Accurate Shapley Values in a Single Forward Propagation](https://mlsanity.com/paper/2304.01811/) (2023)
- [A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Them](https://mlsanity.com/paper/2305.09536/) (2023)
- [CausalArmor: Efficient Indirect Prompt Injection Guardrails via Causal Attribution](https://mlsanity.com/paper/2602.07918/) (2026)
- [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)
- [Explanation Shift: Detecting distribution shifts on tabular data via the explanation space](https://mlsanity.com/paper/2210.12369/) (2022)
- [Interpretable machine learning for time-to-event prediction in medicine and healthcare](https://mlsanity.com/paper/2303.09817/) (2023)
- [Who Deserves the Reward? SHARP: Shapley Credit-based Optimization for Multi-Agent System](https://mlsanity.com/paper/2602.08335/) (2026)
- [Explanation Shift: How Did the Distribution Shift Impact the Model?](https://mlsanity.com/paper/2303.08081/) (2023)
- [Model-agnostic variable importance for predictive uncertainty: an entropy-based approach](https://mlsanity.com/paper/2310.12842/) (2023)
- [Practical do-Shapley Explanations with Estimand-Agnostic Causal Inference](https://mlsanity.com/paper/2509.20211/) (2025)
- [Shapley-based Explainable AI for Clustering Applications in Fault Diagnosis and Prognosis](https://mlsanity.com/paper/2303.14581/) (2023)
- [Four Axiomatic Characterizations of the Integrated Gradients Attribution Method](https://mlsanity.com/paper/2306.13753/) (2023)
- [Improving the Weighting Strategy in KernelSHAP](https://mlsanity.com/paper/2410.04883/) (2024)
- [shapr: Explaining Machine Learning Models with Conditional Shapley Values in R and Python](https://mlsanity.com/paper/2504.01842/) (2025)

## Abstract (arXiv)

Feature attributions based on the Shapley value are popular for explaining machine learning models; however, their estimation is complex from both a theoretical and computational standpoint. We disentangle this complexity into two factors: (1)~the approach to removing feature information, and (2)~the tractable estimation strategy. These two factors provide a natural lens through which we can better understand and compare 24 distinct algorithms. Based on the various feature removal approaches, we describe the multiple types of Shapley value feature attributions and methods to calculate each one. Then, based on the tractable estimation strategies, we characterize two distinct families of approaches: model-agnostic and model-specific approximations. For the model-agnostic approximations, we benchmark a wide class of estimation approaches and tie them to alternative yet equivalent characterizations of the Shapley value. For the model-specific approximations, we clarify the assumptions crucial to each method's tractability for linear, tree, and deep models. Finally, we identify gaps in the literature and promising future research directions.