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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…

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature…

Estimating feature importance is a significant aspect of explaining data-based models. Besides explaining the model itself, an equally relevant question is which features are important in the underlying data generating process. We present a…

Machine Learning · Computer Science 2021-09-21 Pål Vegard Johnsen , Inga Strümke , Signe Riemer-Sørensen , Andrew Thomas DeWan , Mette Langaas

With the widespread use of sophisticated machine learning models in sensitive applications, understanding their decision-making has become an essential task. Models trained on tabular data have witnessed significant progress in explanations…

Machine Learning · Computer Science 2022-06-16 Aditya Lahiri , Kamran Alipour , Ehsan Adeli , Babak Salimi

SHAP scores represent the proposed use of the well-known Shapley values in eXplainable Artificial Intelligence (XAI). Recent work has shown that the exact computation of SHAP scores can produce unsatisfactory results. Concretely, for some…

Machine Learning · Computer Science 2024-12-20 Olivier Letoffe , Xuanxiang Huang , Joao Marques-Silva

Explainability in AI is crucial for model development, compliance with regulation, and providing operational nuance to predictions. The Shapley framework for explainability attributes a model's predictions to its input features in a…

Machine Learning · Computer Science 2021-12-21 Christopher Frye , Damien de Mijolla , Tom Begley , Laurence Cowton , Megan Stanley , Ilya Feige

In Explainable AI (XAI), Shapley values are a popular model-agnostic framework for explaining predictions made by complex machine learning models. The computation of Shapley values requires estimating non-trivial contribution functions…

Machine Learning · Computer Science 2026-01-27 Lars Henry Berge Olsen , Martin Jullum

We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…

Computer Science and Game Theory · Computer Science 2016-01-26 Yuval Filmus , Joel Oren , Kannan Soundararajan

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

Local feature attribution methods are increasingly used to explain complex machine learning models. However, current methods are limited because they are extremely expensive to compute or are not capable of explaining a distributed series…

Machine Learning · Computer Science 2022-10-12 Hugh Chen , Scott M. Lundberg , Su-In Lee

Feature attributions based on the Shapley value are popular for explaining machine learning models; however, their estimation is complex from both a theoretical and computational standpoint. We disentangle this complexity into two factors:…

Machine Learning · Computer Science 2022-07-18 Hugh Chen , Ian C. Covert , Scott M. Lundberg , Su-In Lee

We introduce a new Shapley value approach for global sensitivity analysis and machine learning explainability. The method is based on the first-order partial derivatives of the underlying function. The computational complexity of the method…

Machine Learning · Computer Science 2023-03-28 Hui Duan , Giray Ökten

Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so…

Machine Learning · Computer Science 2023-08-01 Vincent Lemaire , Fabrice Clérot , Marc Boullé

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

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

For reinforcement learning systems to be widely adopted, their users must understand and trust them. We present a theoretical analysis of explaining reinforcement learning using Shapley values, following a principled approach from game…

Machine Learning · Computer Science 2023-06-12 Daniel Beechey , Thomas M. S. Smith , Özgür Şimşek

In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. Shapley allocation is regarded as…

Computer Science and Game Theory · Computer Science 2023-05-23 Mishal Assif P K , William Kennedy , Iraj Saniee

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

In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money…

Computer Science and Game Theory · Computer Science 2017-09-14 Francesco Lupia , Angelo Mendicelli , Andrea Ribichini , Francesco Scarcello , Marco Schaerf

Explainable artificial intelligence (XAI) is essential for trustworthy machine learning (ML), particularly in high-stakes domains such as healthcare and finance. Shapley value (SV) methods provide a principled framework for feature…

Machine Learning · Statistics 2025-10-03 Wangxuan Fan , Siqi Li , Doudou Zhou , Yohei Okada , Chuan Hong , Molei Liu , Nan Liu