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Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…

Machine Learning · Statistics 2025-06-18 Marouane Il Idrissi , Agathe Fernandes Machado , Arthur Charpentier

Shapley value is a concept from game theory. Recently, it has been used for explaining complex models produced by machine learning techniques. Although the mathematical definition of Shapley value is straight-forward, the implication of…

Machine Learning · Computer Science 2020-08-13 Sisi Ma , Roshan Tourani

This paper focuses on the fundamental challenge of partitioning input variables in attribution methods for Explainable AI, particularly in Shapley value-based approaches. Previous methods always compute attributions given a predefined…

Machine Learning · Computer Science 2026-02-25 Xinhao Zheng , Huiqi Deng , Quanshi Zhang

Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley…

Artificial Intelligence · Computer Science 2024-08-14 Santiago Cifuentes , Leopoldo Bertossi , Nina Pardal , Sergio Abriola , Maria Vanina Martinez , Miguel Romero

Shapley value has recently become a popular way to explain the predictions of complex and simple machine learning models. This paper is discusses the factors that influence Shapley value. In particular, we explore the relationship between…

Machine Learning · Statistics 2021-11-24 Harsh Kumar , Jithu Chandran

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking…

Artificial Intelligence · Computer Science 2025-05-20 Marouane Il Idrissi , Agathe Fernandes Machado , Ewen Gallic , Arthur Charpentier

Shapley value is a concept in cooperative game theory for measuring the contribution of each participant, which was named in honor of Lloyd Shapley. Shapley value has been recently applied in data marketplaces for compensation allocation…

Machine Learning · Computer Science 2020-03-24 Jinfei Liu

Feature selection is a classical problem in statistics and machine learning, and it continues to remain an extremely challenging problem especially in the context of unknown non-linear relationships with dependent features. On the other…

Machine Learning · Statistics 2026-04-17 Chenghui Zheng , Garvesh Raskutti

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 complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation…

Machine Learning · Computer Science 2023-12-29 Jacopo Teneggi , Beepul Bharti , Yaniv Romano , Jeremias Sulam

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…

Optimization and Control · Mathematics 2014-12-18 Ramón Flores , Elisenda Molina , Juan Tejada

Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…

Machine Learning · Computer Science 2023-06-21 Joran Michiels , Maarten De Vos , Johan Suykens

This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the…

Machine Learning · Statistics 2022-12-09 Andreas Brandsæter , Ingrid K. Glad

Explainability in yield prediction helps us fully explore the potential of machine learning models that are already able to achieve high accuracy for a variety of yield prediction scenarios. The data included for the prediction of yields…

Machine Learning · Computer Science 2023-04-17 Florian Huber , Hannes Engler , Anna Kicherer , Katja Herzog , Reinhard Töpfer , Volker Steinhage

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

We consider MultiCriteria Decision Analysis models which are defined over discrete attributes, taking a finite number of values. We do not assume that the model is monotonically increasing with respect to the attributes values. Our aim is…

Computer Science and Game Theory · Computer Science 2017-04-10 Mustapha Ridaoui , Michel Grabisch , Christophe Labreuche

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…

Probability · Mathematics 2017-04-04 Riccardo Colini-Baldeschi , Marco Scarsini , Stefano Vaccari

As diffusion models are deployed in real-world settings, and their performance is driven by training data, appraising the contribution of data contributors is crucial to creating incentives for sharing quality data and to implementing…

Machine Learning · Computer Science 2025-03-05 Chris Lin , Mingyu Lu , Chanwoo Kim , Su-In Lee

M\"obius inversion and Shapley values are two mathematical tools for characterizing and decomposing higher-order structure in complex systems. The former defines higher-order interactions as discrete derivatives over a partial order; the…

Computer Science and Game Theory · Computer Science 2026-04-23 Patrick Forré , Abel Jansma

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

Machine Learning · Statistics 2021-02-19 Yongchan Kwon , Manuel A. Rivas , James Zou