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Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley…

Artificial Intelligence · Computer Science 2024-08-14 Santiago Cifuentes , Leopoldo Bertossi , Nina Pardal , Sergio Abriola , Maria Vanina Martinez , Miguel Romero

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…

Machine Learning · Statistics 2025-08-19 Michael Mayer , Mario V. Wüthrich

Feature selection is a classical problem in statistics and machine learning, and it continues to remain an extremely challenging problem especially in the context of unknown non-linear relationships with dependent features. On the other…

Machine Learning · Statistics 2026-04-17 Chenghui Zheng , Garvesh Raskutti

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

The study takes the social media industry as its research subject and examines the impact of scientific innovation capabilities on profit distribution within the value chain of the social media industry. It proposes a specific solution to…

Theoretical Economics · Economics 2024-12-25 Jianfei Xu , Rui Zhang , Junhui Fan

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

Measuring the value of individual samples is critical for many data-driven tasks, e.g., the training of a deep learning model. Recent literature witnesses the substantial efforts in developing data valuation methods. The primary data…

Machine Learning · Computer Science 2024-06-06 Ou Wu , Weiyao Zhu , Mengyang Li

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…

Computer Science and Game Theory · Computer Science 2026-05-13 Guilherme Dean Pelegrina , Patrick Kolpaczki , Eyke Hüllermeier

Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…

Machine Learning · Statistics 2020-02-07 Kjersti Aas , Martin Jullum , Anders Løland

Interpreting predictions from tree ensemble methods such as gradient boosting machines and random forests is important, yet feature attribution for trees is often heuristic and not individualized for each prediction. Here we show that…

Machine Learning · Computer Science 2019-03-08 Scott M. Lundberg , Gabriel G. Erion , Su-In Lee

When using machine learning techniques in decision-making processes, the interpretability of the models is important. In the present paper, we adopted the Shapley additive explanation (SHAP), which is based on fair profit allocation among…

Machine Learning · Computer Science 2022-03-03 Yasunobu Nohara , Koutarou Matsumoto , Hidehisa Soejima , Naoki Nakashima

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 value has recently become a popular way to explain the predictions of complex and simple machine learning models. This paper is discusses the factors that influence Shapley value. In particular, we explore the relationship between…

Machine Learning · Statistics 2021-11-24 Harsh Kumar , Jithu Chandran

Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives,…

Machine Learning · Computer Science 2020-10-27 Rachael Hwee Ling Sim , Yehong Zhang , Mun Choon Chan , Bryan Kian Hsiang Low

Note that a newer expanded version of this paper is now available at: arXiv:1802.03888 It is critical in many applications to understand what features are important for a model, and why individual predictions were made. For tree ensemble…

Artificial Intelligence · Computer Science 2018-02-20 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

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…

Machine Learning · Computer Science 2020-06-29 Luke Merrick , Ankur Taly

Shapley values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley…

Computer Science and Game Theory · Computer Science 2024-09-11 Ilya Rozenfeld

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 coefficient of determination, the $R^2$, is often used to measure the variance explained by an affine combination of multiple explanatory covariates. An attribution of this explanatory contribution to each of the individual covariates…

Methodology · Statistics 2020-08-11 Daniel Fryer , Inga Strumke , Hien Nguyen