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We propose a variant of the Shapley value, the group Shapley value, to interpret counterfactual simulations in structural economic models by quantifying the importance of different components. Our framework compares two sets of parameters,…

Econometrics · Economics 2024-10-10 Yongchan Kwon , Sokbae Lee , Guillaume A. Pouliot

In this paper we propose an approximation method for high-dimensional $1$-periodic functions based on the multivariate ANOVA decomposition. We provide an analysis on the classical ANOVA decomposition on the torus and prove some important…

Numerical Analysis · Mathematics 2022-01-31 Daniel Potts , Michael Schmischke

Shapley values have become a cornerstone of explainable AI, but they are computationally expensive to use, especially when features are dependent. Evaluating them requires approximating a large number of conditional expectations, either via…

Artificial Intelligence · Computer Science 2026-02-11 Lars Henry Berge Olsen , Dennis Christensen

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

Understanding why a model makes a certain prediction can be as crucial as the prediction's accuracy in many applications. However, the highest accuracy for large modern datasets is often achieved by complex models that even experts struggle…

Artificial Intelligence · Computer Science 2017-11-28 Scott Lundberg , Su-In Lee

As opaque black-box predictive models become more prevalent, the need to develop interpretations for these models is of great interest. The concept of variable importance and Shapley values are interpretability measures that applies to any…

Machine Learning · Statistics 2025-03-10 Zexuan Sun , Garvesh Raskutti

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

The Shapley value, and its broader family of semi-values, has received much attention in various attribution problems. A fundamental and long-standing challenge is their efficient approximation, since exact computation generally requires an…

Machine Learning · Computer Science 2026-04-10 Weida Li , Yaoliang Yu , Bryan Kian Hsiang Low

In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…

Numerical Analysis · Mathematics 2022-01-31 Daniel Potts , Michael Schmischke

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

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

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

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

Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…

Machine Learning · Computer Science 2023-06-21 Joran Michiels , Maarten De Vos , Johan Suykens

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning…

Machine Learning · Computer Science 2022-09-28 Yongchan Kwon , James Zou

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

This work focuses on developing efficient post-hoc explanations for quantum AI algorithms. In classical contexts, the cooperative game theory concept of the Shapley value adapts naturally to post-hoc explanations, where it can be used to…

Quantum Physics · Physics 2025-04-18 Iain Burge , Michel Barbeau , Joaquin Garcia-Alfaro

Given a data set $\mathcal{D}$ containing millions of data points and a data consumer who is willing to pay for \$$X$ to train a machine learning (ML) model over $\mathcal{D}$, how should we distribute this \$$X$ to each data point to…

Machine Learning · Computer Science 2020-03-31 Ruoxi Jia , David Dao , Boxin Wang , Frances Ann Hubis , Nezihe Merve Gurel , Bo Li , Ce Zhang , Costas J. Spanos , Dawn Song

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

Machine Learning · Computer Science 2020-02-28 Amirata Ghorbani , Michael P. Kim , James Zou

Predictive black-box models can exhibit high accuracy but their opaque nature hinders their uptake in safety-critical deployment environments. Explanation methods (XAI) can provide confidence for decision-making through increased…

Machine Learning · Statistics 2023-06-27 Lucile Ter-Minassian , Oscar Clivio , Karla Diaz-Ordaz , Robin J. Evans , Chris Holmes
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