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The increasing complexity of foundational models underscores the necessity for explainability, particularly for fine-tuning, the most widely used training method for adapting models to downstream tasks. Instance attribution, one type of…

Machine Learning · Computer Science 2024-06-10 Jingtan Wang , Xiaoqiang Lin , Rui Qiao , Chuan-Sheng Foo , Bryan Kian Hsiang Low

Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives,…

Machine Learning · Computer Science 2020-10-27 Rachael Hwee Ling Sim , Yehong Zhang , Mun Choon Chan , Bryan Kian Hsiang Low

In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…

Statistics Theory · Mathematics 2018-01-11 Nazih Benoumechiara , Kevin Elie-Dit-Cosaque

We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…

Computer Science and Game Theory · Computer Science 2016-01-26 Yuval Filmus , Joel Oren , Kannan Soundararajan

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

Influence functions approximate how removing a training example changes a quantity of interest, called the target function, such as a held-out loss. To estimate the influence of a group of examples, the standard practice is to sum the…

Machine Learning · Computer Science 2026-05-18 Jaeseung Heo , Kyeongheung Yun , Youngbin Choi , Sehyun Hwang , Jungseul Ok , Dongwoo Kim

Shapley values provide model agnostic feature attributions for model outcome at a particular instance by simulating feature absence under a global population distribution. The use of a global population can lead to potentially misleading…

Machine Learning · Computer Science 2021-06-29 Sahra Ghalebikesabi , Lucile Ter-Minassian , Karla Diaz-Ordaz , Chris Holmes

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

Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation…

Machine Learning · Computer Science 2023-01-10 Jianhong Wang , Yuan Zhang , Yunjie Gu , Tae-Kyun Kim

For reinforcement learning systems to be widely adopted, their users must understand and trust them. We present a theoretical analysis of explaining reinforcement learning using Shapley values, following a principled approach from game…

Machine Learning · Computer Science 2023-06-12 Daniel Beechey , Thomas M. S. Smith , Özgür Şimşek

Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so…

Machine Learning · Computer Science 2023-08-01 Vincent Lemaire , Fabrice Clérot , Marc Boullé

Feature attributions are post-training analysis methods that assess how various input features of a machine learning model contribute to an output prediction. Their interpretation is straightforward when features act independently, but it…

Machine Learning · Computer Science 2026-01-29 Kurt Butler , Guanchao Feng , Petar Djuric

Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf…

Databases · Computer Science 2024-04-17 Pratik Karmakar , Mikaël Monet , Pierre Senellart , Stéphane Bressan

Shapley value is a widely used tool in explainable artificial intelligence (XAI), as it provides a principled way to attribute contributions of input features to model outputs. However, estimation of Shapley value requires capturing…

Machine Learning · Computer Science 2025-11-05 Cheng Lu , Jiusun Zeng , Yu Xia , Jinhui Cai , Shihua Luo

In this paper we introduce a metric aimed at helping machine learning practitioners quickly summarize and communicate the overall importance of each feature in any black-box machine learning prediction model. Our proposed metric, based on a…

Methodology · Statistics 2019-08-27 Nickalus Redell

Machine learning models frequently experience performance drops under distribution shifts. The underlying cause of such shifts may be multiple simultaneous factors such as changes in data quality, differences in specific covariate…

Machine Learning · Computer Science 2023-06-07 Haoran Zhang , Harvineet Singh , Marzyeh Ghassemi , Shalmali Joshi

Additive feature explanations rely primarily on game-theoretic notions such as the Shapley value by viewing features as cooperating players. The Shapley value's popularity in and outside of explainable AI stems from its axiomatic…

Machine Learning · Computer Science 2025-07-23 Patrick Kolpaczki , Tim Nielen , Eyke Hüllermeier

We propose a variant of the Shapley value, the group Shapley value, to interpret counterfactual simulations in structural economic models by quantifying the importance of different components. Our framework compares two sets of parameters,…

Econometrics · Economics 2024-10-10 Yongchan Kwon , Sokbae Lee , Guillaume A. Pouliot

This paper introduces the Myerson interaction index (MII), an extension of the Shapley interaction index to cooperative games with communication structures restricted by graphs. We establish a formal framework for interaction indices on…

Optimization and Control · Mathematics 2026-05-28 Jorge González-Ortega , Elisenda Molina , Juan Tejada

We extend the coopetition index introduced by Aleandri and Dall'Aglio (2025) for simple games to the broader class of monotone transferable utility (TU) games and to all non-empty coalitions, including singletons. The new formulation allows…

Computer Science and Game Theory · Computer Science 2025-11-20 Michele Aleandri , Marco Dall'Aglio