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We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between…

Computation · Statistics 2024-09-11 Logan Bell , Nikhil Devanathan , Stephen Boyd

Large language models (LLMs) excel on new tasks without additional training, simply by providing natural language prompts that demonstrate how the task should be performed. Prompt ensemble methods comprehensively harness the knowledge of…

Computation and Language · Computer Science 2024-12-17 Hanxi Liu , Xiaokai Mao , Haocheng Xia , Jian Lou , Jinfei Liu , Kui Ren

Value-decomposition methods, which reduce the difficulty of a multi-agent system by decomposing the joint state-action space into local observation-action spaces, have become popular in cooperative multi-agent reinforcement learning (MARL).…

Artificial Intelligence · Computer Science 2023-03-17 Shuhan Qi , Shuhao Zhang , Qiang Wang , Jiajia Zhang , Jing Xiao , Xuan Wang

In collaborative machine learning (CML), data valuation, i.e., evaluating the contribution of each client's data to the machine learning model, has become a critical task for incentivizing and selecting positive data contributions. However,…

Cryptography and Security · Computer Science 2025-05-27 Shuyuan Zheng , Sudong Cai , Chuan Xiao , Yang Cao , Jianbin Qin , Masatoshi Yoshikawa , Makoto Onizuka

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

The Shapley value provides a principled foundation for data valuation, but exact computation is #P-hard due to the exponential coalition space. Existing accelerations remain global and ignore a structural property of modern predictors: for…

Machine Learning · Computer Science 2026-03-05 Xuan Yang , Hsi-Wen Chen , Ming-Syan Chen , Jian Pei

The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…

Computer Science and Game Theory · Computer Science 2025-08-20 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

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

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

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

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…

Optimization and Control · Mathematics 2014-12-18 Ramón Flores , Elisenda Molina , Juan Tejada

Federated Learning (FL) bridges the gap between collaborative machine learning and preserving data privacy. To sustain the long-term operation of an FL ecosystem, it is important to attract high quality data owners with appropriate…

Artificial Intelligence · Computer Science 2021-09-07 Zelei Liu , Yuanyuan Chen , Han Yu , Yang Liu , Lizhen Cui

Federated learning (FL) has emerged as a pivotal approach in machine learning, enabling multiple participants to collaboratively train a global model without sharing raw data. While FL finds applications in various domains such as…

Machine Learning · Computer Science 2024-06-04 Nurbek Tastan , Samar Fares , Toluwani Aremu , Samuel Horvath , Karthik Nandakumar

The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…

Computer Science and Game Theory · Computer Science 2021-07-19 Vijay V. Vazirani

The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…

Computer Science and Game Theory · Computer Science 2023-03-31 Martin Cerny , Michel Grabisch

An energy community is modeled as a cooperative game, where a veto player is needed beyond the prosumers to manage the community, and the worth of a coalition is its benefit compared to the selfish behaviour of the prosumers. Properties of…

Optimization and Control · Mathematics 2026-02-27 Giancarlo Bigi , Davide Fioriti , Antonio Frangioni , Mauro Passacantando , Davide Poli

Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important…

Machine Learning · Computer Science 2022-10-14 Jianhong Wang , Yuan Zhang , Tae-Kyun Kim , Yunjie Gu

Cooperative games are those in which both agents share the same payoff structure. Value-based reinforcement-learning algorithms, such as variants of Q-learning, have been applied to learning cooperative games, but they only apply when the…

Machine Learning · Computer Science 2017-05-25 Leonid Peshkin , Kee-Eung Kim , Nicolas Meuleau , Leslie Pack Kaelbling

Cooperative games are those in which both agents share the same payoff structure. Value-based reinforcement-learning algorithms, such as variants of Q-learning, have been applied to learning cooperative games, but they only apply when the…

Artificial Intelligence · Computer Science 2014-08-08 Leonid Peshkin , Kee-Eung Kim , Nicolas Meuleau , Leslie Pack Kaelbling

We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score…

Machine Learning · Computer Science 2018-08-09 Jianbo Chen , Le Song , Martin J. Wainwright , Michael I. Jordan