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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

The SHAP (short for Shapley additive explanation) framework has become an essential tool for attributing importance to variables in predictive tasks. In model-agnostic settings, SHAP uses the concept of Shapley values from cooperative game…

Machine Learning · Statistics 2026-02-12 Justin Whitehouse , Ayush Sawarni , Vasilis Syrgkanis

The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This…

Theoretical Economics · Economics 2024-07-23 André Casajus , Yukihiko Funaki , Frank Huettner

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…

Every weighted tree corresponds naturally to a cooperative game that we call a "tree game"; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the…

Quantitative Methods · Quantitative Biology 2009-09-02 Claus-Jochen Haake , Akemi Kashiwada , Francis Edward Su

Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study…

Computer Science and Game Theory · Computer Science 2018-11-12 Jan Bok

Shapley values have become increasingly popular in the machine learning literature thanks to their attractive axiomatisation, flexibility, and uniqueness in satisfying certain notions of `fairness'. The flexibility arises from the myriad…

Machine Learning · Statistics 2021-03-09 Daniel Vidali Fryer , Inga Strümke , Hien Nguyen

Measuring individual productivity (or equivalently distributing the overall productivity) in a network structure of workers displaying peer effects has been a subject of ongoing interest in many areas ranging from academia to industry. In…

Computer Science and Game Theory · Computer Science 2024-02-07 N. Allouch , Luis A. Guardiola , A. Meca

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

Data valuation is an essential task in a data marketplace. It aims at fairly compensating data owners for their contribution. There is increasing recognition in the machine learning community that the Shapley value -- a foundational…

Cryptography and Security · Computer Science 2023-02-20 Zhihua Tian , Jian Liu , Jingyu Li , Xinle Cao , Ruoxi Jia , Jun Kong , Mengdi Liu , Kui Ren

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

With wide application of Artificial Intelligence (AI), it has become particularly important to make decisions of AI systems explainable and transparent. In this paper, we proposed a new Explainable Artificial Intelligence (XAI) method…

Artificial Intelligence · Computer Science 2025-04-01 Chi Zhao , Jing Liu , Elena Parilina

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

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

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

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

What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles,…

Machine Learning · Computer Science 2021-06-14 Benedek Rozemberczki , Rik Sarkar

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 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

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