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Shapley-like values, including the Shapley and Banzhaf values, provide a principled way to quantify how individual tuples contribute to a query result. Their exact computation, however, is intractable because it requires aggregating…

Databases · Computer Science 2025-12-01 Amirhossein Alizad , Mostafa Milani

Structural Causal Models (SCM) are a powerful framework for describing complicated dynamics across the natural sciences. A particularly elegant way of interpreting SCMs is do-Shapley, a game-theoretic method of quantifying the average…

A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch…

Machine Learning · Computer Science 2024-10-28 Luca Franceschi , Michele Donini , Cédric Archambeau , Matthias Seeger

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 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

We propose in this paper a coinvestment plan between several stakeholders of different types, namely a physical network owner, operating network nodes, e.g. a network operator or a tower company, and a set of service providers willing to…

Computer Science and Game Theory · Computer Science 2022-10-04 Rosario Patanè , Andrea Araldo , Tijani Chahed , Diego Kiedanski , Daniel Kofman

Shapley effects are attracting increasing attention as sensitivity measures. When the value function is the conditional variance, they account for the individual and higher order effects of a model input. They are also well defined under…

Computation · Statistics 2021-10-13 Elmar Plischke , Giovanni Rabitti , Emanuele Borgonovo

The information decomposition problem requires an additive decomposition of the mutual information between the input and target variables into nonnegative terms. The recently introduced solution to this problem, Information Attribution,…

Information Theory · Computer Science 2022-07-13 Tomáš Kroupa , Sara Vannucci , Tomáš Votroubek

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

The idea of paying people for their data is increasingly seen as a promising direction for resolving privacy debates, improving the quality of online data, and even offering an alternative to labor-based compensation in a future dominated…

Social and Information Networks · Computer Science 2019-09-04 Marius Paraschiv , Nikolaos Laoutaris

The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…

Computer Science and Game Theory · Computer Science 2021-07-19 Vijay V. Vazirani

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…

Machine Learning · Computer Science 2020-10-05 Masayoshi Mase , Art B. Owen , Benjamin Seiler

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

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

In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing…

Databases · Computer Science 2023-06-27 Ahmet Kara , Dan Olteanu , Dan Suciu

Shapley value-based data valuation methods, originating from cooperative game theory, quantify the usefulness of each individual sample by considering its contribution to all possible training subsets. Despite their extensive applications,…

Machine Learning · Computer Science 2024-05-29 Ziao Yang , Han Yue , Jian Chen , Hongfu Liu

We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…

Machine Learning · Statistics 2023-05-25 Siu Lun Chau , Krikamol Muandet , Dino Sejdinovic

Originally rooted in game theory, the Shapley Value (SV) has recently become an important tool in machine learning research. Perhaps most notably, it is used for feature attribution and data valuation in explainable artificial intelligence.…

The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This…

Theoretical Economics · Economics 2024-07-23 André Casajus , Yukihiko Funaki , Frank Huettner

This paper introduces the shapr R package, a versatile tool for generating Shapley value-based prediction explanations for machine learning and statistical regression models. Moreover, the shaprpy Python library brings the core capabilities…

Machine Learning · Computer Science 2026-02-03 Martin Jullum , Lars Henry Berge Olsen , Jon Lachmann , Annabelle Redelmeier