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Explainable artificial intelligence (XAI) aims to help human decision-makers in understanding complex machine learning (ML) models. One of the hallmarks of XAI are measures of relative feature importance, which are theoretically justified…

Artificial Intelligence · Computer Science 2024-02-12 Joao Marques-Silva , Xuanxiang Huang

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, which were originally designed to assign attributions to individual players in coalition games, have become a commonly used approach in explainable machine learning to provide attributions to input features for black-box…

Machine Learning · Computer Science 2023-03-24 Che-Ping Tsai , Chih-Kuan Yeh , Pradeep Ravikumar

The Shapley value is widely used for data valuation in data markets. However, explaining the Shapley value of an owner in a data coalition is an unexplored and challenging task. To tackle this, we formulate the problem of finding the…

Computer Science and Game Theory · Computer Science 2025-07-03 Michelle Si , Jian Pei

There is much interest lately in explainability in statistics and machine learning. One aspect of explainability is to quantify the importance of various features (or covariates). Two popular methods for defining variable importance are…

Methodology · Statistics 2023-03-13 Isabella Verdinelli , Larry Wasserman

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…

Statistics Theory · Mathematics 2017-03-22 Art B. Owen , Clémentine Prieur

Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sensitivity indices, so-called Shapley effects have recently…

Computation · Statistics 2021-04-27 Takashi Goda

Dimensionality reduction (DR) techniques have been consistently supporting high-dimensional data analysis in various applications. Besides the patterns uncovered by these techniques, the interpretation of DR results based on each feature's…

Machine Learning · Computer Science 2021-03-11 Wilson Estécio Marcílio Júnior , Danilo Medeiros Eler

Deep neural networks have demonstrated remarkable performance across various domains, yet their decision-making processes remain opaque. Although many explanation methods are dedicated to bringing the obscurity of DNNs to light, they…

Computer Vision and Pattern Recognition · Computer Science 2025-12-17 Kanglong Fan , Yunqiao Yang , Chen Ma

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

In healthcare, making the best possible predictions with complex models (e.g., neural networks, ensembles/stacks of different models) can impact patient welfare. In order to make these complex models explainable, we present DeepSHAP for…

Machine Learning · Computer Science 2019-11-28 Hugh Chen , Scott Lundberg , Su-In Lee

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

Originally rooted in game theory, the Shapley Value (SV) has recently become an important tool in machine learning research. Perhaps most notably, it is used for feature attribution and data valuation in explainable artificial intelligence.…

Shapley values are a cornerstone of explainable AI, yet their proliferation into competing formulations has created a fragmented landscape with little consensus on practical deployment. While theoretical differences are well-documented,…

Machine Learning · Computer Science 2026-04-27 Inês Oliveira e Silva , Sérgio Jesus , Iker Perez , Rita P. Ribeiro , Carlos Soares , Hugo Ferreira , Pedro Bizarro

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

Even though Shapley value provides an effective explanation for a DNN model prediction, the computation relies on the enumeration of all possible input feature coalitions, which leads to the exponentially growing complexity. To address this…

Machine Learning · Computer Science 2023-03-07 Guanchu Wang , Yu-Neng Chuang , Mengnan Du , Fan Yang , Quan Zhou , Pushkar Tripathi , Xuanting Cai , Xia Hu

We discuss promising recent contributions on quantifying feature relevance using Shapley values, where we observed some confusion on which probability distribution is the right one for dropped features. We argue that the confusion is based…

Machine Learning · Statistics 2019-11-28 Dominik Janzing , Lenon Minorics , Patrick Blöbaum

Interpretability is central for scientific machine learning, as understanding \emph{why} models make predictions enables hypothesis generation and validation. While tabular foundation models show strong performance, existing explanation…

Machine Learning · Computer Science 2026-04-01 Luan Borges Teodoro Reis Sena , Francisco Galuppo Azevedo

The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method…

Computer Science and Game Theory · Computer Science 2020-02-11 Kedar Dhamdhere , Ashish Agarwal , Mukund Sundararajan

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…

Machine Learning · Statistics 2025-06-18 Marouane Il Idrissi , Agathe Fernandes Machado , Arthur Charpentier