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Related papers: Shapley Values: Paired-Sampling Approximations

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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…

Machine Learning · Computer Science 2022-05-27 Benedek Rozemberczki , Lauren Watson , Péter Bayer , Hao-Tsung Yang , Olivér Kiss , Sebastian Nilsson , Rik Sarkar

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

Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…

Machine Learning · Computer Science 2021-12-21 Thomas W. Campbell , Heinrich Roder , Robert W. Georgantas , Joanna Roder

The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The…

Machine Learning · Computer Science 2021-02-23 Daniel Fryer , Inga Strümke , Hien Nguyen

Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the…

Machine Learning · Statistics 2022-02-04 Rory Mitchell , Joshua Cooper , Eibe Frank , Geoffrey Holmes

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

Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…

Machine Learning · Statistics 2023-09-19 Liuqing Yang , Yongdao Zhou , Haoda Fu , Min-Qian Liu , Wei Zheng

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…

Machine Learning · Computer Science 2020-06-29 Luke Merrick , Ankur Taly

The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing [16] showing that it is the \emph{unique} method…

Artificial Intelligence · Computer Science 2020-02-10 Mukund Sundararajan , Amir Najmi

Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different…

Artificial Intelligence · Computer Science 2020-11-04 Tom Heskes , Evi Sijben , Ioan Gabriel Bucur , Tom Claassen

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

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…

Artificial Intelligence · Computer Science 2020-07-01 I. Elizabeth Kumar , Suresh Venkatasubramanian , Carlos Scheidegger , Sorelle Friedler

Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work…

Computer Science and Game Theory · Computer Science 2025-10-16 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…

Computer Science and Game Theory · Computer Science 2025-11-20 Xi Zheng , Xiangyu Chang , Ruoxi Jia , Yong Tan

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is…

Machine Learning · Computer Science 2024-01-31 Patrick Kolpaczki , Viktor Bengs , Maximilian Muschalik , Eyke Hüllermeier

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

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

Feature attribution methods help make machine learning-based inference explainable by determining how much one or several features have contributed to a model's output. A particularly popular attribution method is based on the Shapley value…

Artificial Intelligence · Computer Science 2025-11-04 Filip Naudot , Tobias Sundqvist , Timotheus Kampik

Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…

Machine Learning · Computer Science 2020-10-26 Ramin Okhrati , Aldo Lipani

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning…

Machine Learning · Computer Science 2022-09-28 Yongchan Kwon , James Zou
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