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Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work…

Computer Science and Game Theory · Computer Science 2025-10-16 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

The Shapley value, a solution concept from cooperative game theory, has recently been considered for both unrooted and rooted phylogenetic trees. Here, we focus on the Shapley value of unrooted trees and first revisit the so-called split…

Populations and Evolution · Quantitative Biology 2018-02-07 Kristina Wicke , Mareike Fischer

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

Shapley values have seen widespread use in machine learning as a way to explain model predictions and estimate the importance of covariates. Accurately explaining models is critical in real-world models to both aid in decision making and to…

Machine Learning · Statistics 2024-08-19 Daniel de Marchi , Michael Kosorok , Scott de Marchi

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…

Probability · Mathematics 2017-04-04 Riccardo Colini-Baldeschi , Marco Scarsini , Stefano Vaccari

This paper introduces GeoShapley, a game theory approach to measuring spatial effects in machine learning models. GeoShapley extends the Nobel Prize-winning Shapley value framework in game theory by conceptualizing location as a player in a…

Machine Learning · Computer Science 2025-02-21 Ziqi Li

The Shapley value is a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that…

Databases · Computer Science 2022-01-04 Daniel Deutch , Nave Frost , Benny Kimelfeld , Mikaël Monet

While preference modelling is becoming one of the pillars of machine learning, the problem of preference explanation remains challenging and underexplored. In this paper, we propose \textsc{Pref-SHAP}, a Shapley value-based model…

Machine Learning · Statistics 2022-11-09 Robert Hu , Siu Lun Chau , Jaime Ferrando Huertas , Dino Sejdinovic

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

With the widespread use of sophisticated machine learning models in sensitive applications, understanding their decision-making has become an essential task. Models trained on tabular data have witnessed significant progress in explanations…

Machine Learning · Computer Science 2022-06-16 Aditya Lahiri , Kamran Alipour , Ehsan Adeli , Babak Salimi

In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML).…

Emerging Technologies · Computer Science 2024-11-05 Iain Burge , Michel Barbeau , Joaquin Garcia-Alfaro

In this manuscript, we define and study probabilistic values for cooperative games on simplicial complexes. Inspired by the work of Weber "Probabilistic values for games", we establish the new theory step by step, following the classical…

Combinatorics · Mathematics 2020-01-17 Ivan Martino

Shapley values are model-agnostic methods for explaining model predictions. Many commonly used methods of computing Shapley values, known as off-manifold methods, rely on model evaluations on out-of-distribution input samples. Consequently,…

Machine Learning · Statistics 2023-02-28 Muhammad Faaiz Taufiq , Patrick Blöbaum , Lenon Minorics

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

Existing methods of explainable AI and interpretable ML cannot explain change in the values of an output variable for a statistical unit in terms of the change in the input values and the change in the "mechanism" (the function transforming…

Machine Learning · Computer Science 2022-06-28 Kailash Budhathoki , George Michailidis , Dominik Janzing

The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…

Computer Science and Game Theory · Computer Science 2026-01-22 Zhuofan Jia , Jian Pei

Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature…

Machine Learning · Computer Science 2021-03-01 Jiaxuan Wang , Jenna Wiens , Scott Lundberg

Feature selection is one of the most relevant processes in any methodology for creating a statistical learning model. Usually, existing algorithms establish some criterion to select the most influential variables, discarding those that do…

Machine Learning · Statistics 2024-05-10 Carlos Sebastián , Carlos E. González-Guillén

Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under…

Machine Learning · Computer Science 2026-03-31 Fadoua Amri-Jouidel , Emmanuel Kemel , Stéphane Mussard

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