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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

We provide an inferential framework to assess variable importance for heterogeneous treatment effects. This assessment is especially useful in high-risk domains such as medicine, where decision makers hesitate to rely on black-box treatment…

Methodology · Statistics 2026-05-11 Pawel Morzywolek , Peter B. Gilbert , Alex Luedtke

Variable importance in regression analyses is of considerable interest in a variety of fields. There is no unique method for assessing variable importance. However, a substantial share of the available literature employs Shapley values,…

Methodology · Statistics 2026-01-05 Sinan Acemoglu , Christian Kleiber , Jörg Urban

We consider the problem of estimating an expected outcome from a stochastic simulation model. Our goal is to develop a theoretical framework on importance sampling for such estimation. By investigating the variance of an importance sampling…

Methodology · Statistics 2019-09-27 Yen-Chi Chen , Youngjun Choe

A principal curve serves as a powerful tool for uncovering underlying structures of data through 1-dimensional smooth and continuous representations. On the basis of optimal transport theories, this paper introduces a novel principal curve…

Methodology · Statistics 2025-01-15 Tongseok Lim , Kyeongsik Nam , Jinwon Sohn

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is…

Machine Learning · Computer Science 2024-01-31 Patrick Kolpaczki , Viktor Bengs , Maximilian Muschalik , Eyke Hüllermeier

In this paper, we address the estimation of the sensitivity indices called "Shapley eects". These sensitivity indices enable to handle dependent input variables. The Shapley eects are generally dicult to estimate, but they are easily…

Statistics Theory · Mathematics 2020-06-04 Baptiste Broto , François Bachoc , Marine Depecker , Jean-Marc Martinez

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

Interpretability of learning algorithms is crucial for applications involving critical decisions, and variable importance is one of the main interpretation tools. Shapley effects are now widely used to interpret both tree ensembles and…

Machine Learning · Statistics 2022-02-03 Clément Bénard , Gérard Biau , Sébastien da Veiga , Erwan Scornet

Shapley values are extensively used in explainable artificial intelligence (XAI) as a framework to explain predictions made by complex machine learning (ML) models. In this work, we focus on conditional Shapley values for predictive models…

Machine Learning · Statistics 2023-12-07 Lars Henry Berge Olsen

The Shapley value (SV) has emerged as a promising method for data valuation. However, computing or estimating the SV is often computationally expensive. To overcome this challenge, Jia et al. (2019) propose an advanced SV estimation…

Machine Learning · Statistics 2023-02-23 Jiachen T. Wang , Ruoxi Jia

Shapley values has established itself as one of the most appropriate and theoretically sound frameworks for explaining predictions from complex machine learning models. The popularity of Shapley values in the explanation setting is probably…

Machine Learning · Statistics 2021-06-24 Martin Jullum , Annabelle Redelmeier , Kjersti Aas

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

An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables,…

Machine Learning · Statistics 2020-03-16 Xingwei Hu

The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations (SPDEs). We find that if a spectral gap…

Probability · Mathematics 2017-05-05 Michael Salins , Konstantinos Spiliopoulos

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

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

Machine Learning · Statistics 2021-02-19 Yongchan Kwon , Manuel A. Rivas , 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

Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…

Machine Learning · Computer Science 2021-12-21 Thomas W. Campbell , Heinrich Roder , Robert W. Georgantas , Joanna Roder

Shapley value-based data valuation methods, originating from cooperative game theory, quantify the usefulness of each individual sample by considering its contribution to all possible training subsets. Despite their extensive applications,…

Machine Learning · Computer Science 2024-05-29 Ziao Yang , Han Yue , Jian Chen , Hongfu Liu
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