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Data valuation is an essential task in a data marketplace. It aims at fairly compensating data owners for their contribution. There is increasing recognition in the machine learning community that the Shapley value -- a foundational…

Cryptography and Security · Computer Science 2023-02-20 Zhihua Tian , Jian Liu , Jingyu Li , Xinle Cao , Ruoxi Jia , Jun Kong , Mengdi Liu , Kui Ren

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…

Computer Science and Game Theory · Computer Science 2014-09-19 Smriti Bhagat , Anthony Kim , S. Muthukrishnan , Udi Weinsberg

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

Data valuation, or the valuation of individual datum contributions, has seen growing interest in machine learning due to its demonstrable efficacy for tasks such as noisy label detection. In particular, due to the desirable axiomatic…

Machine Learning · Computer Science 2022-11-15 Stephanie Schoch , Haifeng Xu , Yangfeng Ji

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

While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For…

Machine Learning · Statistics 2022-04-07 Salim I. Amoukou , Nicolas J-B. Brunel , Tangi Salaün

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

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

Federated Learning (FL) wherein multiple institutions collaboratively train a machine learning model without sharing data is becoming popular. Participating institutions might not contribute equally, some contribute more data, some better…

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

As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been…

Machine Learning · Statistics 2019-06-11 Amirata Ghorbani , James Zou

Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian…

Machine Learning · Computer Science 2022-06-15 Lucas Agussurja , Xinyi Xu , Bryan Kian Hsiang Low

The Shapley value is arguably the most central normative solution concept in cooperative game theory. It specifies a unique way in which the reward from cooperation can be "fairly" divided among players. While it has a wide range of real…

Computer Science and Game Theory · Computer Science 2014-02-14 Sasan Maleki , Long Tran-Thanh , Greg Hines , Talal Rahwan , Alex Rogers

Various peer-to-peer energy markets have emerged in recent years in an attempt to manage distributed energy resources in a more efficient way. One of the main challenges these models face is how to create and allocate incentives to…

Computer Science and Game Theory · Computer Science 2019-03-27 Liyang Han , Thomas Morstyn , Malcolm McCulloch

Valuation problems, such as feature interpretation, data valuation and model valuation for ensembles, become increasingly more important in many machine learning applications. Such problems are commonly solved by well-known game-theoretic…

Machine Learning · Computer Science 2022-05-13 Yatao Bian , Yu Rong , Tingyang Xu , Jiaxiang Wu , Andreas Krause , Junzhou Huang

Facing the challenge of statistical diversity in client local data distribution, personalized federated learning (PFL) has become a growing research hotspot. Although the state-of-the-art methods with model similarity-based pairwise…

Artificial Intelligence · Computer Science 2022-02-09 Leijie Wu , Song Guo , Yaohong Ding , Yufeng Zhan , Jie Zhang

For reinforcement learning systems to be widely adopted, their users must understand and trust them. We present a theoretical analysis of explaining reinforcement learning using Shapley values, following a principled approach from game…

Machine Learning · Computer Science 2023-06-12 Daniel Beechey , Thomas M. S. Smith , Özgür Şimşek

The computation of a solution concept of a cooperative game usually depends on values of all coalitions. However, in some applications, values of some of the coalitions might be unknown due to various reasons. We introduce a method to…

Computer Science and Game Theory · Computer Science 2022-12-12 Martin Černý

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

Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives,…

Machine Learning · Computer Science 2020-10-27 Rachael Hwee Ling Sim , Yehong Zhang , Mun Choon Chan , Bryan Kian Hsiang Low