mlsanityData to 7 Oct 2026

Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning

arXiv 2110.14049 ↗First posted 26 Oct 2021cs.LG stat.MLcited by 162

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Abstract (arXiv)

Data Shapley has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. It can effectively identify helpful or harmful data points for a learning algorithm. In this paper, we propose Beta Shapley, which is a substantial generalization of Data Shapley. Beta Shapley arises naturally by relaxing the efficiency axiom of the Shapley value, which is not critical for machine learning settings. Beta Shapley unifies several popular data valuation methods and includes data Shapley as a special case. Moreover, we prove that Beta Shapley has several desirable statistical properties and propose efficient algorithms to estimate it. We demonstrate that Beta Shapley outperforms state-of-the-art data valuation methods on several downstream ML tasks such as: 1) detecting mislabeled training data; 2) learning with subsamples; and 3) identifying points whose addition or removal have the largest positive or negative impact on the model.

Key facts. Cited by 162 papers in the map (data through 7 Oct 2026). Builds on 25 of its 61 references that are in the map. First posted on arXiv 26 Oct 2021.

Builds on

25 of 61 references.

References · 25

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  7. 2019Data Shapley: Equitable Valuation of Data for Machine Learningcited by 617
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  9. 2021Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarkscited by 388
  10. 2019The many Shapley values for model explanationcited by 341
  11. 2019Towards Efficient Data Valuation Based on the Shapley Valuecited by 279
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13 more
  1. 2020Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regressioncited by 153
  2. 2018L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Datacited by 100
  3. 2020Neuron Shapley: Discovering the Responsible Neuronscited by 98
  4. 2020A Distributional Framework for Data Valuationcited by 79
  5. 2020Collaborative Machine Learning with Incentive-Aware Model Rewardscited by 71
  6. 2019Explainable AI for Trees: From Local Explanations to Global Understandingcited by 64
  7. 2013Bounding the Estimation Error of Sampling-based Shapley Value Approximationcited by 56
  8. 2021Shapley Explanation Networkscited by 41
  9. 2020Efficient computation and analysis of distributional Shapley valuescited by 38
  10. 2021The Shapley Value of Classifiers in Ensemble Gamescited by 23
  11. 2018Revisiting the Gelman-Rubin Diagnosticcited by 18
  12. 2017Optimal Sub-sampling with Influence Functionscited by 11
  13. 2018A Feature Selection Method Based on Shapley Value to False Alarm Reduction in ICUs, A Genetic-Algorithm Approachcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 12; 2023: 26; 2024: 56; 2025: 35; 2026: 33.

162 papers.

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  1. 2022Training Data Influence Analysis and Estimation: A Surveycited by 134
  2. 2022Data Banzhaf: A Robust Data Valuation Framework for Machine Learningcited by 126
  3. 2023DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Modelscited by 121
  4. 2022The Shapley Value in Machine Learningcited by 97
  5. 2024What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functionscited by 88
  6. 2022MetaShift: A Dataset of Datasets for Evaluating Contextual Distribution Shifts and Training Conflictscited by 81
  7. 2024Data Shapley in One Training Runcited by 76
  8. 2023LAVA: Data Valuation without Pre-Specified Learning Algorithmscited by 69
  9. 2023OpenDataVal: a Unified Benchmark for Data Valuationcited by 55
  10. 2022Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experimentscited by 50
  11. 2023Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Valuecited by 38
  12. 2022WeightedSHAP: analyzing and improving Shapley based feature attributionscited by 36
38 more
  1. 2024Training Data Attribution via Approximate Unrolled Differentiationcited by 33
  2. 2022A Data-Based Perspective on Transfer Learningcited by 32
  3. 2022CS-Shapley: Class-wise Shapley Values for Data Valuation in Classificationcited by 32
  4. 2024Rethinking Data Shapley for Data Selection Tasks: Misleads and Meritscited by 29
  5. 2024Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Modelscited by 29
  6. 2023Data Selection for Fine-tuning Large Language Models Using Transferred Shapley Valuescited by 21
  7. 2024Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attributioncited by 21
  8. 2024Do Influence Functions Work on Large Language Models?cited by 20
  9. 2023Threshold KNN-Shapley: A Linear-Time and Privacy-Friendly Approach to Data Valuationcited by 19
  10. 2025Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Valuescited by 19
  11. 2022Fair and efficient contribution valuation for vertical federated learningcited by 18
  12. 2024Efficient Data Shapley for Weighted Nearest Neighbor Algorithmscited by 18
  13. 2023Data Valuation and Detections in Federated Learningcited by 17
  14. 2022Variance reduced Shapley value estimation for trustworthy data valuationcited by 16
  15. 2023Performance Scaling via Optimal Transport: Enabling Data Selection from Partially Revealed Sourcescited by 16
  16. 2024The Mirrored Influence Hypothesis: Efficient Data Influence Estimation by Harnessing Forward Passescited by 16
  17. 2024Helpful or Harmful Data? Fine-tuning-free Shapley Attribution for Explaining Language Model Predictionscited by 13
  18. 2023DU-Shapley: A Shapley Value Proxy for Efficient Dataset Valuationcited by 12
  19. 2025LayerIF: Estimating Layer Quality for Large Language Models using Influence Functionscited by 12
  20. 2025From Points to Coalitions: Hierarchical Contrastive Shapley Values for Prioritizing Data Samplescited by 12
  21. 2023A Note on "Towards Efficient Data Valuation Based on the Shapley Value''cited by 11
  22. 2023A Note on "Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms"cited by 11
  23. 2024Dissecting Sample Hardness: A Fine-Grained Analysis of Hardness Characterization Methods for Data-Centric AIcited by 11
  24. 2023Sample based Explanations via Generalized Representerscited by 10
  25. 2024Outlier Gradient Analysis: Efficiently Identifying Detrimental Training Samples for Deep Learning Modelscited by 10
  26. 2024Scaling Laws for the Value of Individual Data Points in Machine Learningcited by 10
  27. 2023Data Acquisition: A New Frontier in Data-centric AIcited by 9
  28. 2024Towards Explainable Artificial Intelligence (XAI): A Data Mining Perspectivecited by 9
  29. 2024One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficientlycited by 9
  30. 2024BWS: Best Window Selection Based on Sample Scores for Data Pruning across Broad Rangescited by 8
  31. 2025What Data Enables Optimal Decisions? An Exact Characterization for Linear Optimizationcited by 8
  32. 2023Towards Algorithmic Fairness by means of Instance-level Data Re-weighting based on Shapley Valuescited by 7
  33. 20232D-Shapley: A Framework for Fragmented Data Valuationcited by 7
  34. 2024HyperINF: Unleashing the HyperPower of the Schulz's Method for Data Influence Estimationcited by 7
  35. 2024Dissecting Representation Misalignment in Contrastive Learning via Influence Functioncited by 7
  36. 2025Source Attribution in Retrieval-Augmented Generationcited by 7
  37. 2022Probably Approximate Shapley Fairness with Applications in Machine Learningcited by 6
  38. 2024Precedence-Constrained Winter Value for Effective Graph Data Valuationcited by 6

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