mlsanityData to 7 Oct 2026

The Shapley Value in Machine Learning

arXiv 2202.05594 ↗First posted 11 Feb 2022cs.LG cs.AI cs.GTcited by 97

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Abstract (arXiv)

Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic properties of the Shapley value. Then we give an overview of the most important applications of the Shapley value in machine learning: feature selection, explainability, multi-agent reinforcement learning, ensemble pruning, and data valuation. We examine the most crucial limitations of the Shapley value and point out directions for future research.

Key facts. Cited by 97 papers in the map (data through 7 Oct 2026). Builds on 32 of its 83 references that are in the map. First posted on arXiv 11 Feb 2022.

Builds on

32 of 83 references.

References · 32

  1. 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
  2. 2017Understanding Black-box Predictions via Influence Functionscited by 1,714
  3. 2019Data Shapley: Equitable Valuation of Data for Machine Learningcited by 617
  4. 2019The many Shapley values for model explanationcited by 341
  5. 2021On Explainability of Graph Neural Networks via Subgraph Explorationscited by 280
  6. 2019Towards Efficient Data Valuation Based on the Shapley Valuecited by 279
  7. 2020Problems with Shapley-value-based explanations as feature importance measurescited by 198
  8. 2021Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learningcited by 162
  9. 2020Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regressioncited by 153
  10. 2019The Shapley Taylor Interaction Indexcited by 143
  11. 2020A Principled Approach to Data Valuation for Federated Learningcited by 127
  12. 2019Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximationcited by 115
20 more
  1. 2019Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainabilitycited by 114
  2. 2020Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Modelscited by 107
  3. 2021Sampling Permutations for Shapley Value Estimationcited by 101
  4. 2018L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Datacited by 100
  5. 2020Neuron Shapley: Discovering the Responsible Neuronscited by 98
  6. 2020Shapley explainability on the data manifoldcited by 88
  7. 2020A Distributional Framework for Data Valuationcited by 79
  8. 2021GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learningcited by 73
  9. 2021GraphSVX: Shapley Value Explanations for Graph Neural Networkscited by 63
  10. 2020Efficient nonparametric statistical inference on population feature importance using Shapley valuescited by 61
  11. 2013Bounding the Estimation Error of Sampling-based Shapley Value Approximationcited by 56
  12. 2021Shapley values for feature selection: The good, the bad, and the axiomscited by 54
  13. 2020Shapley Flow: A Graph-based Approach to Interpreting Model Predictionscited by 51
  14. 2020Efficient computation and analysis of distributional Shapley valuescited by 38
  15. 2021Shapley Counterfactual Credits for Multi-Agent Reinforcement Learningcited by 37
  16. 2020A Multilinear Sampling Algorithm to Estimate Shapley Valuescited by 33
  17. 2021The Shapley Value of Classifiers in Ensemble Gamescited by 23
  18. 2018Finding Influential Training Samples for Gradient Boosted Decision Treescited by 15
  19. 2019Estimation of the Shapley value by ergodic samplingcited by 15
  20. 2018Antithetic and Monte Carlo kernel estimators for partial rankingscited by 10

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Citing papers per year: 2022: 10; 2023: 18; 2024: 21; 2025: 27; 2026: 21.

97 papers.

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  1. 2022Training Data Influence Analysis and Estimation: A Surveycited by 134
  2. 2022Algorithms to estimate Shapley value feature attributionscited by 114
  3. 2024Unified Gradient-Based Machine Unlearning with Remain Geometry Enhancementcited by 43
  4. 2024shapiq: Shapley Interactions for Machine Learningcited by 42
  5. 2023Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Valuecited by 38
  6. 2022WeightedSHAP: analyzing and improving Shapley based feature attributionscited by 36
  7. 2023Approximating the Shapley Value without Marginal Contributionscited by 34
  8. 2023The Inadequacy of Shapley Values for Explainabilitycited by 30
  9. 2023Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learningcited by 17
  10. 2023MultiModN- Multimodal, Multi-Task, Interpretable Modular Networkscited by 14
  11. 2025Lost in Moderation: How Commercial Content Moderation APIs Over- and Under-Moderate Group-Targeted Hate Speech and Linguistic Variationscited by 12
  12. 2024Interpretable Machine Learning for TabPFNcited by 10
38 more
  1. 2024Towards Explainable Artificial Intelligence (XAI): A Data Mining Perspectivecited by 9
  2. 2024One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficientlycited by 9
  3. 2022Differentially Private Shapley Values for Data Evaluationcited by 8
  4. 2022SHAP-XRT: The Shapley Value Meets Conditional Independence Testingcited by 6
  5. 2022Probably Approximate Shapley Fairness with Applications in Machine Learningcited by 6
  6. 2023A comparative assessment of deep learning models for day-ahead load forecasting: Investigating key accuracy driverscited by 6
  7. 2025A Unified Gradient-based Framework for Task-agnostic Continual Learning-Unlearningcited by 6
  8. 2025Explaining Similarity in Vision-Language Encoders with Weighted Banzhaf Interactionscited by 6
  9. 2023Generating Explanations to Understand and Repair Embedding-based Entity Alignmentcited by 5
  10. 2024A Survey on Contribution Evaluation in Vertical Federated Learningcited by 5
  11. 2025CAMs as Shapley Value-based Explainerscited by 5
  12. 2025Where on Earth? A Vision-Language Benchmark for Probing Model Geolocation Skills Across Scalescited by 5
  13. 2026An Odd Estimator for Shapley Valuescited by 5
  14. 2024Explanatory Model Monitoring to Understand the Effects of Feature Shifts on Performancecited by 4
  15. 2025HyperSHAP: Shapley Values and Interactions for Explaining Hyperparameter Optimizationcited by 4
  16. 2025Souper-Model: How Simple Arithmetic Unlocks State-of-the-Art LLM Performancecited by 4
  17. 2022Unsupervised Features Ranking via Coalitional Game Theory for Categorical Datacited by 3
  18. 2023For Better or Worse: The Impact of Counterfactual Explanations' Directionality on User Behavior in xAIcited by 3
  19. 2023Learning Channel Importance for High Content Imaging with Interpretable Deep Input Channel Mixingcited by 3
  20. 2023CopyScope: Model-level Copyright Infringement Quantification in the Diffusion Workflowcited by 3
  21. 2024Explaining Probabilistic Models with Distributional Valuescited by 3
  22. 2024Using Stratified Sampling to Improve LIME Image Explanationscited by 3
  23. 2024CHG Shapley: Efficient Data Valuation and Selection towards Trustworthy Machine Learningcited by 3
  24. 2024Explainable Post hoc Portfolio Management Financial Policy of a Deep Reinforcement Learning agentcited by 3
  25. 2026Exactly Computing do-Shapley Valuescited by 3
  26. 2023Beyond Demographic Parity: Redefining Equal Treatmentcited by 2
  27. 2023Incentive Allocation in Vertical Federated Learning Based on Bankruptcy Problemcited by 2
  28. 2023Sensitivity analysis of AI-based algorithms for autonomous driving on optical wavefront aberrations induced by the windshieldcited by 2
  29. 2024Explainable Adaptive Tree-based Model Selection for Time Series Forecastingcited by 2
  30. 2024Multi-Excitation Projective Simulation with a Many-Body Physics Inspired Inductive Biascited by 2
  31. 2024A Comprehensive Study of Shapley Value in Data Analyticscited by 2
  32. 2025Decomposing Interventional Causality into Synergistic, Redundant, and Unique Componentscited by 2
  33. 2025Shapley Value Approximation Based on k-Additive Gamescited by 2
  34. 2025Adaptive Prompting: Ad-hoc Prompt Composition for Social Bias Detectioncited by 2
  35. 2025Efficient Data Valuation Approximation in Federated Learning: A Sampling-based Approachcited by 2
  36. 2025Newfluence: Boosting Model interpretability and Understanding in High Dimensionscited by 2
  37. 2025Shift-Invariant Attribute Scoring for Kolmogorov-Arnold Networks via Shapley Valuecited by 2
  38. 2025Modality-Aware SAM: Sharpness-Aware-Minimization Driven Gradient Modulation for Harmonized Multimodal Learningcited by 2

50 most cited of 97 All 97 (JSON)