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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

Recent studies have examined the computational complexity of computing Shapley additive explanations (also known as SHAP) across various models and distributions, revealing their tractability or intractability in different settings.…

Machine Learning · Computer Science 2025-02-19 Reda Marzouk , Shahaf Bassan , Guy Katz , Colin de la Higuera

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

Deep Neural Networks are widely used in academy as well as corporate and public applications, including safety critical applications such as health care and autonomous driving. The ability to explain their output is critical for safety…

Machine Learning · Computer Science 2024-03-14 Florian Eilers , Xiaoyi Jiang

Banzhaf values provide a popular, interpretable alternative to the widely-used Shapley values for quantifying the importance of features in machine learning models. Like Shapley values, computing Banzhaf values exactly requires time…

Machine Learning · Computer Science 2025-02-19 Yurong Liu , R. Teal Witter , Flip Korn , Tarfah Alrashed , Dimitris Paparas , Christopher Musco , Juliana Freire

SHAP (SHapley Additive exPlanation) values are one of the leading tools for interpreting machine learning models, with strong theoretical guarantees (consistency, local accuracy) and a wide availability of implementations and use cases.…

Machine Learning · Computer Science 2022-07-28 Jilei Yang

In Machine Learning, the $\mathsf{SHAP}$-score is a version of the Shapley value that is used to explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is…

Artificial Intelligence · Computer Science 2023-03-31 Marcelo Arenas , Pablo Barceló , Leopoldo Bertossi , Mikaël Monet

The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient…

Machine Learning · Computer Science 2026-02-03 Fabian Fumagalli , Landon Butler , Justin Singh Kang , Kannan Ramchandran , R. Teal Witter

As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been…

Machine Learning · Statistics 2019-06-11 Amirata Ghorbani , James Zou

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

The reliability of machine learning models can be compromised when trained on low quality data. Many large-scale medical imaging datasets contain low quality labels extracted from sources such as medical reports. Moreover, images within a…

Machine Learning · Computer Science 2021-04-20 Siyi Tang , Amirata Ghorbani , Rikiya Yamashita , Sameer Rehman , Jared A. Dunnmon , James Zou , Daniel L. Rubin

Shapley values are one of the main tools used to explain predictions of tree ensemble models. The main alternative to Shapley values are Banzhaf values that have not been understood equally well. In this paper we make a step towards filling…

Machine Learning · Computer Science 2021-08-10 Adam Karczmarz , Anish Mukherjee , Piotr Sankowski , Piotr Wygocki

How can we explain the predictions of a machine learning model? When the data is structured as a multivariate time series, this question induces additional difficulties such as the necessity for the explanation to embody the time dependency…

Machine Learning · Computer Science 2021-06-11 Jonathan Crabbé , Mihaela van der Schaar

With water quality management processes, identifying and interpreting relationships between features, such as location and weather variable tuples, and water quality variables, such as levels of bacteria, is key to gaining insights and…

Artificial Intelligence · Computer Science 2022-12-12 Conor Muldoon , Levent Görgü , John J. O'Sullivan , Wim G. Meijer , Gregory M. P. O'Hare

The application of Shapley values to high-dimensional, time-series-like data is computationally challenging - and sometimes impossible. For $N$ inputs the problem is $2^N$ hard. In image processing, clusters of pixels, referred to as…

Quantitative Methods · Quantitative Biology 2024-09-30 Lauren Elborough , Duncan Taylor , Melissa Humphries

Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable degree of…

Machine Learning · Statistics 2024-04-11 Jeremy Goldwasser , Giles Hooker

For feature selection and related problems, we introduce the notion of classification game, a cooperative game, with features as players and hinge loss based characteristic function and relate a feature's contribution to Shapley value based…

Machine Learning · Statistics 2021-04-27 Sandhya Tripathi , N. Hemachandra , Prashant Trivedi

The value and copyright of training data are crucial in the artificial intelligence industry. Service platforms should protect data providers' legitimate rights and fairly reward them for their contributions. Shapley value, a potent tool…

Machine Learning · Computer Science 2025-11-21 Haifeng Sun , Yu Xiong , Runze Wu , Xinyu Cai , Changjie Fan , Lan Zhang , Xiang-Yang Li

Feature importance aims at measuring how crucial each input feature is for model prediction. It is widely used in feature engineering, model selection and explainable artificial intelligence (XAI). In this paper, we propose a new tree-model…

Machine Learning · Statistics 2020-09-17 Fan Fang , Carmine Ventre , Lingbo Li , Leslie Kanthan , Fan Wu , Michail Basios

The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid…

Methodology · Statistics 2025-10-23 Brian D. Williamson , Jean Feng