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Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature…

Machine Learning · Computer Science 2023-10-31 Fabian Fumagalli , Maximilian Muschalik , Patrick Kolpaczki , Eyke Hüllermeier , Barbara Hammer

Addressing the limitations of individual attribution scores via the Shapley value (SV), the field of explainable AI (XAI) has recently explored intricate interactions of features or data points. In particular, extensions of the SV, such as…

Computer Science and Game Theory · Computer Science 2024-03-04 Patrick Kolpaczki , Maximilian Muschalik , Fabian Fumagalli , Barbara Hammer , Eyke Hüllermeier

While shallow decision trees may be interpretable, larger ensemble models like gradient-boosted trees, which often set the state of the art in machine learning problems involving tabular data, still remain black box models. As a remedy, the…

Machine Learning · Computer Science 2024-06-21 Maximilian Muschalik , Fabian Fumagalli , Barbara Hammer , Eyke Hüllermeier

Originally rooted in game theory, the Shapley Value (SV) has recently become an important tool in machine learning research. Perhaps most notably, it is used for feature attribution and data valuation in explainable artificial intelligence.…

Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has…

Artificial Intelligence · Computer Science 2026-05-14 Fabian Fumagalli , R. Teal Witter , Christopher Musco

In Explainable AI (XAI), Shapley values are a popular model-agnostic framework for explaining predictions made by complex machine learning models. The computation of Shapley values requires estimating non-trivial contribution functions…

Machine Learning · Computer Science 2026-01-27 Lars Henry Berge Olsen , Martin Jullum

The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the…

Machine Learning · Computer Science 2021-04-26 Ian Covert , Su-In Lee

Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to…

Machine Learning · Statistics 2022-05-27 Siu Lun Chau , Robert Hu , Javier Gonzalez , Dino Sejdinovic

This study proposes Interaction Tensor SHAP (IT-SHAP), a tensor algebraic formulation of the Shapley Taylor Interaction Index (STII) that makes its computational structure explicit. STII extends the Shapley value to higher order…

Machine Learning · Computer Science 2026-01-06 Hiroki Hasegawa , Yukihiko Okada

Besides accuracy, recent studies on machine learning models have been addressing the question on how the obtained results can be interpreted. Indeed, while complex machine learning models are able to provide very good results in terms of…

Machine Learning · Computer Science 2022-11-07 Guilherme Dean Pelegrina , Leonardo Tomazeli Duarte , Michel Grabisch

Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…

Machine Learning · Statistics 2020-02-07 Kjersti Aas , Martin Jullum , Anders Løland

Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation…

Machine Learning · Computer Science 2023-01-10 Jianhong Wang , Yuan Zhang , Yunjie Gu , Tae-Kyun Kim

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature…

Explainable artificial intelligence (XAI) is essential for trustworthy machine learning (ML), particularly in high-stakes domains such as healthcare and finance. Shapley value (SV) methods provide a principled framework for feature…

Machine Learning · Statistics 2025-10-03 Wangxuan Fan , Siqi Li , Doudou Zhou , Yohei Okada , Chuan Hong , Molei Liu , Nan Liu

The Shapley value (SV) and Least core (LC) are classic methods in cooperative game theory for cost/profit sharing problems. Both methods have recently been proposed as a principled solution for data valuation tasks, i.e., quantifying the…

Machine Learning · Computer Science 2022-04-08 Tianhao Wang , Yu Yang , Ruoxi Jia

Originally introduced in game theory, Shapley values have emerged as a central tool in explainable machine learning, where they are used to attribute model predictions to specific input features. However, computing Shapley values exactly is…

Machine Learning · Computer Science 2025-03-11 Christopher Musco , R. Teal Witter

Shapley values, which were originally designed to assign attributions to individual players in coalition games, have become a commonly used approach in explainable machine learning to provide attributions to input features for black-box…

Machine Learning · Computer Science 2023-03-24 Che-Ping Tsai , Chih-Kuan Yeh , Pradeep Ravikumar

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…

Machine Learning · Statistics 2025-08-19 Michael Mayer , Mario V. Wüthrich

The Shapley value (SV) is adopted in various scenarios in machine learning (ML), including data valuation, agent valuation, and feature attribution, as it satisfies their fairness requirements. However, as exact SVs are infeasible to…

Machine Learning · Computer Science 2022-12-02 Zijian Zhou , Xinyi Xu , Rachael Hwee Ling Sim , Chuan Sheng Foo , Kian Hsiang Low

Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so…

Machine Learning · Computer Science 2023-08-01 Vincent Lemaire , Fabrice Clérot , Marc Boullé
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