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Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…

Machine Learning · Computer Science 2022-05-27 Benedek Rozemberczki , Lauren Watson , Péter Bayer , Hao-Tsung Yang , Olivér Kiss , Sebastian Nilsson , 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

We consider the dataset valuation problem, that is, the problem of quantifying the incremental gain, to some relevant pre-defined utility of a machine learning task, of aggregating an individual dataset to others. The Shapley value is a…

Artificial Intelligence · Computer Science 2025-02-25 Felipe Garrido-Lucero , Benjamin Heymann , Maxime Vono , Patrick Loiseau , Vianney Perchet

Data valuation has found various applications in machine learning, such as data filtering, efficient learning and incentives for data sharing. The most popular current approach to data valuation is the Shapley value. While popular for its…

Machine Learning · Computer Science 2023-11-10 Lauren Watson , Zeno Kujawa , Rayna Andreeva , Hao-Tsung Yang , Tariq Elahi , Rik Sarkar

Besides accuracy, recent studies on machine learning models have been addressing the question on how the obtained results can be interpreted. Indeed, while complex machine learning models are able to provide very good results in terms of…

Machine Learning · Computer Science 2022-11-07 Guilherme Dean Pelegrina , Leonardo Tomazeli Duarte , Michel Grabisch

The Shapley value was originally introduced in cooperative game theory as a wealth distribution mechanism. It has since found use in knowledge representation and databases for the purpose of assigning scores to formulas and database tuples…

Artificial Intelligence · Computer Science 2026-02-26 Meghyn Bienvenu , Diego Figueira , Pierre Lafourcade

Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward…

Artificial Intelligence · Computer Science 2019-04-18 Julian Stier , Gabriele Gianini , Michael Granitzer , Konstantin Ziegler

Shapley value is a concept in cooperative game theory for measuring the contribution of each participant, which was named in honor of Lloyd Shapley. Shapley value has been recently applied in data marketplaces for compensation allocation…

Machine Learning · Computer Science 2020-03-24 Jinfei Liu

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

Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different…

Artificial Intelligence · Computer Science 2020-11-04 Tom Heskes , Evi Sijben , Ioan Gabriel Bucur , Tom Claassen

The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…

Computational Geometry · Computer Science 2020-02-14 Shuhao Tan

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

Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…

Machine Learning · Computer Science 2020-10-26 Ramin Okhrati , Aldo Lipani

The Shapley value provides a natural means of quantifying the contributions of facts to database query answers. In this work, we seek to broaden our understanding of Shapley value computation (SVC) in the database setting by revealing how…

Databases · Computer Science 2024-03-26 Meghyn Bienvenu , Diego Figueira , Pierre Lafourcade

Shapley additive explanations (SHAP) are widely recognised as computationally intractable for neural networks, since they induce an exponential search space over the input features. In this work, we take a first step towards scaling exact…

Machine Learning · Computer Science 2026-05-26 David Boetius , Shahaf Bassan , Guy Katz , Stefan Leue , Tobias Sutter

A searcher is tasked with exploring a graph with edge lengths and vertex weights, starting from a designated vertex. Initially, only the starting vertex is considered explored. At each step, the searcher adds an edge to the solution,…

Data Structures and Algorithms · Computer Science 2025-05-13 Svenja M. Griesbach , Felix Hommelsheim , Max Klimm , Kevin Schewior

The Shapley value is arguably the most central normative solution concept in cooperative game theory. It specifies a unique way in which the reward from cooperation can be "fairly" divided among players. While it has a wide range of real…

Computer Science and Game Theory · Computer Science 2014-02-14 Sasan Maleki , Long Tran-Thanh , Greg Hines , Talal Rahwan , Alex Rogers

We introduce the class CXRPQ of conjunctive xregex path queries, which are obtained from conjunctive regular path queries (CRPQs) by adding string variables (also called backreferences) as found in practical implementations of regular…

Formal Languages and Automata Theory · Computer Science 2019-12-20 Markus L. Schmid

In spite of increased attention on explainable machine learning models, explaining multi-output predictions has not yet been extensively addressed. Methods that use Shapley values to attribute feature contributions to the decision making…

Machine Learning · Computer Science 2023-03-31 Célia Wafa Ayad , Thomas Bonnier , Benjamin Bosch , Jesse Read

We study the complexity of computing the Shapley value in games with externalities. We focus on two representations based on marginal contribution nets (embedded MC-nets and weighted MC-nets). Our results show that while weighted MC-nets…

Computer Science and Game Theory · Computer Science 2022-12-01 Oskar Skibski