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The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…

Computational Geometry · Computer Science 2020-02-14 Shuhao Tan

We study the complexity of computing the Shapley value in games with externalities. We focus on two representations based on marginal contribution nets (embedded MC-nets and weighted MC-nets). Our results show that while weighted MC-nets…

Computer Science and Game Theory · Computer Science 2022-12-01 Oskar Skibski

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

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…

Machine Learning · Computer Science 2023-04-03 Raoul Heese , Sascha Mücke , Matthias Jakobs , Thore Gerlach , Nico Piatkowski

Interpretability of learning algorithms is crucial for applications involving critical decisions, and variable importance is one of the main interpretation tools. Shapley effects are now widely used to interpret both tree ensembles and…

Machine Learning · Statistics 2022-02-03 Clément Bénard , Gérard Biau , Sébastien da Veiga , Erwan Scornet

Measuring the value of individual samples is critical for many data-driven tasks, e.g., the training of a deep learning model. Recent literature witnesses the substantial efforts in developing data valuation methods. The primary data…

Machine Learning · Computer Science 2024-06-06 Ou Wu , Weiyao Zhu , Mengyang Li

In healthcare, making the best possible predictions with complex models (e.g., neural networks, ensembles/stacks of different models) can impact patient welfare. In order to make these complex models explainable, we present DeepSHAP for…

Machine Learning · Computer Science 2019-11-28 Hugh Chen , Scott Lundberg , Su-In Lee

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional…

Machine Learning · Computer Science 2020-06-30 Hugh Chen , Joseph D. Janizek , Scott Lundberg , Su-In Lee

The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…

Statistics Theory · Mathematics 2020-02-14 Baptiste Broto , François Bachoc , Marine Depecker

Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely…

Machine Learning · Computer Science 2025-08-21 Majid Mohammadi , Krikamol Muandet , Ilaria Tiddi , Annette Ten Teije , Siu Lun Chau

Feature attribution maps are a popular approach to highlight the most important pixels in an image for a given prediction of a model. Despite a recent growth in popularity and available methods, little attention is given to the objective…

Computer Vision and Pattern Recognition · Computer Science 2024-08-12 Arne Gevaert , Axel-Jan Rousseau , Thijs Becker , Dirk Valkenborg , Tijl De Bie , Yvan Saeys

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…

Computer Science and Game Theory · Computer Science 2026-05-13 Guilherme Dean Pelegrina , Patrick Kolpaczki , Eyke Hüllermeier

In causal inference, confounders are variables that influence both treatment decisions and outcomes. However, unlike as in randomized clinical trials, the treatment assignment mechanism in observational studies is not known, and it is thus…

The Shapley value is the solution concept in cooperative game theory that is most used in both theoretical as practical settings. Unfortunately, computing the Shapley value is computationally intractable in general. This paper focuses on…

Computer Science and Game Theory · Computer Science 2022-08-30 Tom C. van der Zanden , Hans L. Bodlaender , Herbert J. M. Hamers

Understanding why a model makes a certain prediction can be as crucial as the prediction's accuracy in many applications. However, the highest accuracy for large modern datasets is often achieved by complex models that even experts struggle…

Artificial Intelligence · Computer Science 2017-11-28 Scott Lundberg , Su-In Lee

This paper analyses properties of conceptual hierarchy obtained via incremental concept formation method called "flexible prediction" in order to determine what kind of "relevance" of participating attributes may be requested for meaningful…

Artificial Intelligence · Computer Science 2020-05-26 Mieczyslaw A. Klopotek , Andrzej Matuszewski

Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has…

Artificial Intelligence · Computer Science 2026-05-14 Fabian Fumagalli , R. Teal Witter , Christopher Musco

Shapley values are ubiquitous in interpretable Machine Learning due to their strong theoretical background and efficient implementation in the SHAP library. Computing these values previously induced an exponential cost with respect to the…

Machine Learning · Computer Science 2022-12-06 Gabriel Laberge , Yann Pequignot

Given an unexpected change in the output metric of a large-scale system, it is important to answer why the change occurred: which inputs caused the change in metric? A key component of such an attribution question is estimating the…

Machine Learning · Computer Science 2022-08-18 Amit Sharma , Hua Li , Jian Jiao

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