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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

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

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

Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…

Machine Learning · Computer Science 2021-12-21 Thomas W. Campbell , Heinrich Roder , Robert W. Georgantas , Joanna Roder

Shapley Values (SV) are widely used in explainable AI, but their estimation and interpretation can be challenging, leading to inaccurate inferences and explanations. As a starting point, we remind an invariance principle for SV and derive…

Machine Learning · Statistics 2023-06-01 Salim I. Amoukou , Nicolas J-B. Brunel , Tangi Salaün

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

Shapley values have seen widespread use in machine learning as a way to explain model predictions and estimate the importance of covariates. Accurately explaining models is critical in real-world models to both aid in decision making and to…

Machine Learning · Statistics 2024-08-19 Daniel de Marchi , Michael Kosorok , Scott de Marchi

The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world…

Computer Science and Game Theory · Computer Science 2014-02-05 Tomasz Pawel Michalak , Karthik V Aadithya , Piotr L. Szczepanski , Balaraman Ravindran , Nicholas R. Jennings

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

The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about…

Machine Learning · Computer Science 2019-06-24 Marco Ancona , Cengiz Öztireli , Markus Gross

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…

Computer Science and Game Theory · Computer Science 2025-11-20 Xi Zheng , Xiangyu Chang , Ruoxi Jia , Yong Tan

"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…

Machine Learning · Computer Science 2023-03-07 Ruoxi Jia , David Dao , Boxin Wang , Frances Ann Hubis , Nick Hynes , Nezihe Merve Gurel , Bo Li , Ce Zhang , Dawn Song , Costas Spanos

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

Machine Learning · Computer Science 2020-02-28 Amirata Ghorbani , Michael P. Kim , James Zou

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. The Shapley framework for explainability has strength in its general applicability combined with its…

Machine Learning · Statistics 2021-12-21 Christopher Frye , Colin Rowat , Ilya Feige

The Shapley Additive Global Importance (SAGE) value is a theoretically appealing interpretability method that fairly attributes global importance to a model's features. However, its exact calculation requires the computation of the…

Machine Learning · Statistics 2023-04-07 Christoph Luther , Gunnar König , Moritz Grosse-Wentrup

Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several…

Machine Learning · Statistics 2024-04-15 Lars Henry Berge Olsen , Ingrid Kristine Glad , Martin Jullum , Kjersti Aas

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

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

SHAP (SHapley Additive exPlanations) has become a popular method to attribute the prediction of a machine learning model on an input to its features. One main challenge of SHAP is the computation time. An exact computation of Shapley values…

Machine Learning · Statistics 2023-09-06 Linwei Hu , Ke Wang

Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the…

Machine Learning · Statistics 2022-04-15 Indranil Basu , Subhadip Maji
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