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Power indices are essential in assessing the contribution and influence of individual agents in multi-agent systems, providing crucial insights into collaborative dynamics and decision-making processes. While invaluable, traditional…

Multiagent Systems · Computer Science 2025-03-12 Benjamin Kempinski , Tal Kachman

Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…

Computer Science and Game Theory · Computer Science 2026-05-21 Piotr Kępczyński , Oskar Skibski

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

Quantifying the importance of each training point to a learning task is a fundamental problem in machine learning and the estimated importance scores have been leveraged to guide a range of data workflows such as data summarization and…

Machine Learning · Computer Science 2021-04-27 Ruoxi Jia , Fan Wu , Xuehui Sun , Jiacen Xu , David Dao , Bhavya Kailkhura , Ce Zhang , Bo Li , Dawn Song

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…

Statistics Theory · Mathematics 2017-03-22 Art B. Owen , Clémentine Prieur

Ride-sharing services are gaining popularity and are crucial for a sustainable environment. A special case in which such services are most applicable, is the last mile variant. In this variant it is assumed that all the passengers are…

Computer Science and Game Theory · Computer Science 2019-09-12 Chaya Levinger , Noam Hazon , Amos Azaria

This paper studies an incentive structure for cooperation and its stability in peer-assisted services when there exist multiple content providers, using a coalition game theoretic approach. We first consider a generalized coalition…

Computer Science and Game Theory · Computer Science 2015-03-17 Jeong-woo Cho , Yung Yi

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…

Computer Science and Game Theory · Computer Science 2013-07-02 Haris Aziz , Bart de Keijzer

Explainable AI (XAI) is critical for ensuring transparency, accountability, and trust in machine learning systems as black-box models are increasingly deployed within high-stakes domains. Among XAI methods, Shapley values are widely used…

Machine Learning · Computer Science 2025-02-19 Jiaxin Xu , Hung Chau , Angela Burden

We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score…

Machine Learning · Computer Science 2018-08-09 Jianbo Chen , Le Song , Martin J. Wainwright , Michael I. Jordan

The causal effect of showing an ad to a potential customer versus not, commonly referred to as "incrementality", is the fundamental question of advertising effectiveness. In digital advertising three major puzzle pieces are central to…

Machine Learning · Computer Science 2022-08-30 Randall Lewis , Jeffrey Wong

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy

The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e.,…

Computer Science and Game Theory · Computer Science 2018-10-04 Sascha Kurz , Stefan Napel

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

Predictive Business Process Monitoring is becoming an essential aid for organizations, providing online operational support of their processes. This paper tackles the fundamental problem of equipping predictive business process monitoring…

Machine Learning · Computer Science 2020-09-18 Riccardo Galanti , Bernat Coma-Puig , Massimiliano de Leoni , Josep Carmona , Nicolò Navarin

This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and…

Probability · Mathematics 2022-01-04 Tongseok Lim

Not all real-world data are labeled, and when labels are not available, it is often costly to obtain them. Moreover, as many algorithms suffer from the curse of dimensionality, reducing the features in the data to a smaller set is often of…

Machine Learning · Computer Science 2022-05-19 Chiara Balestra , Florian Huber , Andreas Mayr , Emmanuel Müller

In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the…

Data valuation has garnered increasing attention in recent years, given the critical role of high-quality data in various applications. Among diverse data valuation approaches, Shapley value-based methods are predominant due to their strong…

Machine Learning · Computer Science 2025-11-27 Xiaoling Zhou , Ou Wu , Michael K. Ng , Hao Jiang

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