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We argue that using the Shapley value of cooperative game theory as the scheme for risk allocation among non-orthogonal risk factors is a natural way of interpreting the contribution made by each of such factors to overall portfolio risk.…

Computational Finance · Quantitative Finance 2021-03-10 Patrick S. Hagan , Andrew Lesniewski , Georgios E. Skoufis , Diana E. Woodward

Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important…

Machine Learning · Computer Science 2022-10-14 Jianhong Wang , Yuan Zhang , Tae-Kyun Kim , Yunjie Gu

Shapley values has established itself as one of the most appropriate and theoretically sound frameworks for explaining predictions from complex machine learning models. The popularity of Shapley values in the explanation setting is probably…

Machine Learning · Statistics 2021-06-24 Martin Jullum , Annabelle Redelmeier , Kjersti Aas

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

Despite the popularity of Shapley Values in explaining neural text classification models, computing them is prohibitive for large pretrained models due to a large number of model evaluations. In practice, Shapley Values are often estimated…

Computation and Language · Computer Science 2023-06-01 Chenghao Yang , Fan Yin , He He , Kai-Wei Chang , Xiaofei Ma , Bing Xiang

Shapley Values (SV) are widely used in explainable AI, but their estimation and interpretation can be challenging, leading to inaccurate inferences and explanations. As a starting point, we remind an invariance principle for SV and derive…

Machine Learning · Statistics 2023-06-01 Salim I. Amoukou , Nicolas J-B. Brunel , Tangi Salaün

The Shapley value provides a natural means of quantifying the contributions of facts to database query answers. In this work, we seek to broaden our understanding of Shapley value computation (SVC) in the database setting by revealing how…

Databases · Computer Science 2024-03-26 Meghyn Bienvenu , Diego Figueira , Pierre Lafourcade

Data-management-as-a-service systems are increasingly being used in collaborative settings, where multiple users access common datasets. Cloud providers have the choice to implement various optimizations, such as indexing or materialized…

Databases · Computer Science 2015-03-20 Prasang Upadhyaya , Magdalena Balazinska , Dan Suciu

We study a class of probabilistic cooperative games which can be treated as an extension of the classical cooperative games with transferable utilities. The coalitions have an exogenous probability of being realized. This probability…

Theoretical Economics · Economics 2023-08-08 Surajit Borkotokey , Sujata Gowala , Rajnish Kumar

Shapley-based data valuation provides a principled way to quantify the contribution of training data, but its high computational cost makes it impractical in dynamic settings where tasks and training players evolve. Existing methods treat…

Machine Learning · Computer Science 2026-05-21 Xuan Yang , Hsi-Wen Chen , Ming-Syan Chen , Jian Pei

Shapley value is a widely used tool in explainable artificial intelligence (XAI), as it provides a principled way to attribute contributions of input features to model outputs. However, estimation of Shapley value requires capturing…

Machine Learning · Computer Science 2025-11-05 Cheng Lu , Jiusun Zeng , Yu Xia , Jinhui Cai , Shihua Luo

Although Game Theory principles have been used extensively in developing analytical models for access pricing in Internet networks, transmission pricing in electric power networks and access pricing in telephone/cable networks, most of the…

Computer Science and Game Theory · Computer Science 2020-01-29 Michael C. Nwogugu

Understanding the decision-making process of machine learning models is crucial for ensuring trustworthy machine learning. Data Shapley, a landmark study on data valuation, advances this understanding by assessing the contribution of each…

Computer Science and Game Theory · Computer Science 2025-01-23 Huaiguang Cai

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 values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley…

Computer Science and Game Theory · Computer Science 2024-09-11 Ilya Rozenfeld

For feature selection and related problems, we introduce the notion of classification game, a cooperative game, with features as players and hinge loss based characteristic function and relate a feature's contribution to Shapley value based…

Machine Learning · Statistics 2021-04-27 Sandhya Tripathi , N. Hemachandra , Prashant Trivedi

The coefficient of determination, the $R^2$, is often used to measure the variance explained by an affine combination of multiple explanatory covariates. An attribution of this explanatory contribution to each of the individual covariates…

Methodology · Statistics 2020-08-11 Daniel Fryer , Inga Strumke , Hien Nguyen

Feature attributions based on the Shapley value are popular for explaining machine learning models; however, their estimation is complex from both a theoretical and computational standpoint. We disentangle this complexity into two factors:…

Machine Learning · Computer Science 2022-07-18 Hugh Chen , Ian C. Covert , Scott M. Lundberg , Su-In Lee

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

Measuring individual productivity (or equivalently distributing the overall productivity) in a network structure of workers displaying peer effects has been a subject of ongoing interest in many areas ranging from academia to industry. In…

Computer Science and Game Theory · Computer Science 2024-02-07 N. Allouch , Luis A. Guardiola , A. Meca