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Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…

Computer Science and Game Theory · Computer Science 2026-05-21 Piotr Kępczyński , Oskar Skibski

Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely…

Machine Learning · Computer Science 2025-08-21 Majid Mohammadi , Krikamol Muandet , Ilaria Tiddi , Annette Ten Teije , Siu Lun Chau

We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney…

Computer Science and Game Theory · Computer Science 2026-04-02 Mikołaj Czarnecki , Michał Korniak , Oskar Skibski , Piotr Skowron

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

This paper explores the application of Shapley Value Regression in dissecting marketing performance at channel-partner level, complementing channel-level Marketing Mix Modeling (MMM). Utilizing real-world data from the financial services…

Machine Learning · Computer Science 2024-03-12 Sean Tang , Sriya Musunuru , Baoshi Zong , Brooks Thornton

Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has…

Artificial Intelligence · Computer Science 2026-05-14 Fabian Fumagalli , R. Teal Witter , Christopher Musco

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

A popular explainable AI (XAI) approach to quantify feature importance of a given model is via Shapley values. These Shapley values arose in cooperative games, and hence a critical ingredient to compute these in an XAI context is a…

Machine Learning · Computer Science 2022-02-25 Chih-Kuan Yeh , Kuan-Yun Lee , Frederick Liu , Pradeep Ravikumar

Open multi-agent systems are increasingly important in modeling real-world applications, such as smart grids, swarm robotics, etc. In this paper, we aim to investigate a recently proposed problem for open multi-agent systems, referred to as…

Multiagent Systems · Computer Science 2025-06-16 Jianhong Wang , Yang Li , Samuel Kaski , Jonathan Lawry

As Artificial Intelligence (AI) is having more influence on our everyday lives, it becomes important that AI-based decisions are transparent and explainable. As a consequence, the field of eXplainable AI (or XAI) has become popular in…

Artificial Intelligence · Computer Science 2024-04-18 Nils Ole Breuer , Andreas Sauter , Majid Mohammadi , Erman Acar

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

Explainability in yield prediction helps us fully explore the potential of machine learning models that are already able to achieve high accuracy for a variety of yield prediction scenarios. The data included for the prediction of yields…

Machine Learning · Computer Science 2023-04-17 Florian Huber , Hannes Engler , Anna Kicherer , Katja Herzog , Reinhard Töpfer , Volker Steinhage

The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and…

Machine Learning · Statistics 2022-02-11 Chris Harris , Richard Pymar , Colin Rowat

Data valuation has become an increasingly significant discipline in data science due to the economic value of data. In the context of machine learning (ML), data valuation methods aim to equitably measure the contribution of each data point…

Machine Learning · Computer Science 2023-06-13 Xiang Li , Haocheng Xia , Jinfei Liu

Shapley Values (SV) are widely used in explainable AI, but their estimation and interpretation can be challenging, leading to inaccurate inferences and explanations. As a starting point, we remind an invariance principle for SV and derive…

Machine Learning · Statistics 2023-06-01 Salim I. Amoukou , Nicolas J-B. Brunel , Tangi Salaün

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…

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

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's…

General Mathematics · Mathematics 2007-09-03 Vladislav Kargin

Suppose that $n$ computer devices are to be connected to a network via inhomogeneous Bernoulli trials. The Shapley value of a device quantifies how much the network's value increases due to the participation of that device. Characteristic…

Computer Science and Game Theory · Computer Science 2025-10-10 Jesse D Wei , Guo Wei

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational…

Computer Science and Game Theory · Computer Science 2017-11-28 Ayumi Igarashi , Rani Izsak , Edith Elkind
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