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Cohort Shapley value is a model-free method of variable importance grounded in game theory that does not use any unobserved and potentially impossible feature combinations. We use it to evaluate algorithmic fairness, using the well known…

Machine Learning · Computer Science 2021-05-20 Masayoshi Mase , Art B. Owen , Benjamin B. Seiler

Over the recent years, Shapley value (SV), a solution concept from cooperative game theory, has found numerous applications in data analytics (DA). This paper presents the first comprehensive study of SV used throughout the DA workflow,…

Databases · Computer Science 2025-07-09 Hong Lin , Shixin Wan , Zhongle Xie , Ke Chen , Meihui Zhang , Lidan Shou , Gang Chen

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

Machine Learning · Computer Science 2026-01-14 R. Teal Witter , Yurong Liu , Christopher Musco

Shapley values are model-agnostic methods for explaining model predictions. Many commonly used methods of computing Shapley values, known as off-manifold methods, rely on model evaluations on out-of-distribution input samples. Consequently,…

Machine Learning · Statistics 2023-02-28 Muhammad Faaiz Taufiq , Patrick Blöbaum , Lenon Minorics

Shapley value and its priority-aware extensions are widely used for valuation in machine learning, but existing methods require pairwise priority to be binary and acyclic, a restriction spectacularly violated in real-data examples such as…

Machine Learning · Computer Science 2026-05-15 Kiljae Lee , Ziqi Liu , Weijing Tang , Yuan Zhang

The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and…

Machine Learning · Statistics 2022-02-11 Chris Harris , Richard Pymar , Colin Rowat

Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the…

Machine Learning · Statistics 2022-04-15 Indranil Basu , Subhadip Maji

When using machine learning techniques in decision-making processes, the interpretability of the models is important. In the present paper, we adopted the Shapley additive explanation (SHAP), which is based on fair profit allocation among…

Machine Learning · Computer Science 2022-03-03 Yasunobu Nohara , Koutarou Matsumoto , Hidehisa Soejima , Naoki Nakashima

In recent years, the Shapley value and SHAP explanations have emerged as one of the most dominant paradigms for providing post-hoc explanations of black-box models. Despite their well-founded theoretical properties, many recent works have…

Machine Learning · Computer Science 2025-02-21 James Enouen , Yan Liu

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central…

Computer Science and Game Theory · Computer Science 2013-08-29 Oskar Skibski , Tomasz P. Michalak , Michael Wooldridge

With the adoption of machine learning-based solutions in routine clinical practice, the need for reliable interpretability tools has become pressing. Shapley values provide local explanations. The method gained popularity in recent years.…

Methodology · Statistics 2023-06-27 Lucile Ter-Minassian , Sahra Ghalebikesabi , Karla Diaz-Ordaz , Chris Holmes

Shapley values are ubiquitous in interpretable Machine Learning due to their strong theoretical background and efficient implementation in the SHAP library. Computing these values previously induced an exponential cost with respect to the…

Machine Learning · Computer Science 2022-12-06 Gabriel Laberge , Yann Pequignot

Explainability in AI is crucial for model development, compliance with regulation, and providing operational nuance to predictions. The Shapley framework for explainability attributes a model's predictions to its input features in a…

Machine Learning · Computer Science 2021-12-21 Christopher Frye , Damien de Mijolla , Tom Begley , Laurence Cowton , Megan Stanley , Ilya Feige

"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…

Machine Learning · Computer Science 2023-03-07 Ruoxi Jia , David Dao , Boxin Wang , Frances Ann Hubis , Nick Hynes , Nezihe Merve Gurel , Bo Li , Ce Zhang , Dawn Song , Costas Spanos

The Shapley value is a prominent tool for interpreting black-box machine learning models thanks to its strong theoretical foundation. However, for models with structured inputs, such as graph neural networks, existing Shapley-based…

Machine Learning · Computer Science 2024-05-24 Ngoc Bui , Hieu Trung Nguyen , Viet Anh Nguyen , Rex Ying

In this paper we introduce a metric aimed at helping machine learning practitioners quickly summarize and communicate the overall importance of each feature in any black-box machine learning prediction model. Our proposed metric, based on a…

Methodology · Statistics 2019-08-27 Nickalus Redell

We study the efficient computation of Shapley values for \emph{product games} -- cooperative games in which the coalition value factorizes as a product of per-player terms. Such games arise in machine learning explainability whenever the…

Machine Learning · Computer Science 2026-05-19 Majid Mohammadi , Grigory Reznikov , Pavel Sinitcyn , Krikamol Muandet , Siu Lun Chau

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

Shapley values are widely used for model-agnostic data valuation and feature attribution, yet they implicitly assume contributors are interchangeable. This can be problematic when contributors are dependent (e.g., reused/augmented data or…

Machine Learning · Computer Science 2026-02-11 Kiljae Lee , Ziqi Liu , Weijing Tang , Yuan Zhang

Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward…

Artificial Intelligence · Computer Science 2019-04-18 Julian Stier , Gabriele Gianini , Michael Granitzer , Konstantin Ziegler
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