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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

Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…

Computer Science and Game Theory · Computer Science 2026-05-21 Piotr Kępczyński , Oskar Skibski

This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as `labels' and to exploit available data on the variables of interest to provide features…

Machine Learning · Statistics 2019-10-17 Steven M. Hill , Chris. J. Oates , Duncan A. Blythe , Sach Mukherjee

The presence of artificial intelligence (AI) in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images,…

Machine Learning · Statistics 2025-06-06 Pedro Delicado , Cristian Pachón-García

We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score…

Machine Learning · Computer Science 2018-08-09 Jianbo Chen , Le Song , Martin J. Wainwright , Michael I. Jordan

Perception occurs when individuals interpret the same information differently. It is a known cognitive phenomenon with implications for bias in human decision-making. Perception, however, remains understudied in machine learning (ML). This…

Artificial Intelligence · Computer Science 2025-10-21 Jose M. Alvarez , Salvatore Ruggieri

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

Machine Learning · Computer Science 2026-01-14 R. Teal Witter , Yurong Liu , Christopher Musco

Interpretable machine learning has been focusing on explaining final models that optimize performance. The current state-of-the-art is the Shapley additive explanations (SHAP) that locally explains variable impact on individual predictions,…

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

We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…

Methodology · Statistics 2025-04-28 Fredrik Lohne Aanes

Reward modelling from preference data is a crucial step in aligning large language models (LLMs) with human values, requiring robust generalisation to novel prompt-response pairs. In this work, we propose to frame this problem in a causal…

Artificial Intelligence · Computer Science 2026-05-12 Katarzyna Kobalczyk , Mihaela van der Schaar

Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…

Machine Learning · Statistics 2022-02-28 Matthew J. Vowels

One of the most popular methods of the machine learning prediction explanation is the SHapley Additive exPlanations method (SHAP). An imprecise SHAP as a modification of the original SHAP is proposed for cases when the class probability…

Machine Learning · Computer Science 2021-06-18 Lev V. Utkin , Andrei V. Konstantinov , Kirill A. Vishniakov

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

A predictive model makes outcome predictions based on some given features, i.e., it estimates the conditional probability of the outcome given a feature vector. In general, a predictive model cannot estimate the causal effect of a feature…

Machine Learning · Computer Science 2023-04-11 Jiuyong Li , Lin Liu , Ziqi Xu , Ha Xuan Tran , Thuc Duy Le , Jixue Liu

In recent years, there has been increasing interest in causal reasoning for designing fair decision-making systems due to its compatibility with legal frameworks, interpretability for human stakeholders, and robustness to spurious…

Machine Learning · Computer Science 2022-10-27 Aida Rahmattalabi , Alice Xiang

Predictive Process Analytics is becoming an essential aid for organizations, providing online operational support of their processes. However, process stakeholders need to be provided with an explanation of the reasons why a given process…

This paper discusses an application of Shapley values in the causal inference field, specifically on how to select the top confounder variables for coarsened exact matching method in a scalable way. We use a dataset from an observational…

Machine Learning · Statistics 2022-06-08 Jilei Yang , Wentao Su

Missing data is a prevalent issue that can significantly impair model performance and explainability. This paper briefly summarizes the development of the field of missing data with respect to Explainable Artificial Intelligence and…

Machine Learning · Computer Science 2025-01-23 Tuan L. Vo , Thu Nguyen , Luis M. Lopez-Ramos , Hugo L. Hammer , Michael A. Riegler , Pal Halvorsen

Explaining machine learning (ML) predictions has become crucial as ML models are increasingly deployed in high-stakes domains such as healthcare. While SHapley Additive exPlanations (SHAP) is widely used for model interpretability, it fails…

Machine Learning · Computer Science 2025-09-03 Woon Yee Ng , Li Rong Wang , Siyuan Liu , Xiuyi Fan