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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

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's…

General Mathematics · Mathematics 2007-09-03 Vladislav Kargin

M\"obius inversion and Shapley values are two mathematical tools for characterizing and decomposing higher-order structure in complex systems. The former defines higher-order interactions as discrete derivatives over a partial order; the…

Computer Science and Game Theory · Computer Science 2026-04-23 Patrick Forré , Abel Jansma

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

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

Explainable artificial intelligence promises to yield insights into relevant features, thereby enabling humans to examine and scrutinize machine learning models or even facilitating scientific discovery. Considering the widespread technique…

Machine Learning · Computer Science 2026-03-30 Jörg Martin , Stefan Haufe

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

As machine learning (ML) systems take a more prominent and central role in contributing to life-impacting decisions, ensuring their trustworthiness and accountability is of utmost importance. Explanations sit at the core of these desirable…

Machine Learning · Computer Science 2021-06-16 Sahil Verma , Aditya Lahiri , John P. Dickerson , Su-In Lee

Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and…

Machine Learning · Computer Science 2026-02-23 Shahaf Bassan , Xuanxiang Huang , Guy Katz

As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method…

Machine Learning · Statistics 2024-07-30 Mengmeng Wu , Zhihong Liu , Xiang Li , Ruoxi Jia , Xiangyu Chang

Feature attribution (FA) methods are widely used in explainable AI (XAI) to help users understand how the inputs of a machine learning model contribute to its outputs. However, different FA models often provide disagreeing importance scores…

Explainability in yield prediction helps us fully explore the potential of machine learning models that are already able to achieve high accuracy for a variety of yield prediction scenarios. The data included for the prediction of yields…

Machine Learning · Computer Science 2023-04-17 Florian Huber , Hannes Engler , Anna Kicherer , Katja Herzog , Reinhard Töpfer , Volker Steinhage

Recent work demonstrated the existence of critical flaws in the current use of Shapley values in explainable AI (XAI), i.e. the so-called SHAP scores. These flaws are significant in that the scores provided to a human decision-maker can be…

Artificial Intelligence · Computer Science 2025-02-18 Joao Marques-Silva , Xuanxiang Huang , Olivier Letoffe

Many important questions about a model cannot be answered just by explaining how much each feature contributes to its output. To answer a broader set of questions, we generalize a popular, mathematically well-grounded explanation technique,…

Machine Learning · Computer Science 2020-06-16 Dillon Bowen , Lyle Ungar

Explaining the decisions of black-box models is a central theme in the study of trustworthy ML. Numerous measures have been proposed in the literature; however, none of them take an axiomatic approach to causal explainability. In this work,…

Machine Learning · Computer Science 2024-02-20 Gagan Biradar , Vignesh Viswanathan , Yair Zick

Model interpretability has become an important problem in machine learning (ML) due to the increased effect that algorithmic decisions have on humans. Counterfactual explanations can help users understand not only why ML models make certain…

Machine Learning · Computer Science 2021-12-20 Ana Lucic , Harrie Oosterhuis , Hinda Haned , Maarten de Rijke

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

Shapley values have become one of the most popular feature attribution explanation methods. However, most prior work has focused on post-hoc Shapley explanations, which can be computationally demanding due to its exponential time complexity…

Machine Learning · Computer Science 2021-04-07 Rui Wang , Xiaoqian Wang , David I. Inouye

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

We consider the dataset valuation problem, that is, the problem of quantifying the incremental gain, to some relevant pre-defined utility of a machine learning task, of aggregating an individual dataset to others. The Shapley value is a…

Artificial Intelligence · Computer Science 2025-02-25 Felipe Garrido-Lucero , Benjamin Heymann , Maxime Vono , Patrick Loiseau , Vianney Perchet
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