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In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money…

Computer Science and Game Theory · Computer Science 2017-09-14 Francesco Lupia , Angelo Mendicelli , Andrea Ribichini , Francesco Scarcello , Marco Schaerf

Feature attribution methods are a popular approach to explain the behavior of machine learning models. They assign importance scores to each input feature, quantifying their influence on the model's prediction. However, evaluating these…

Machine Learning · Computer Science 2025-06-02 Magamed Taimeskhanov , Damien Garreau

The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The…

Machine Learning · Computer Science 2021-02-23 Daniel Fryer , Inga Strümke , Hien Nguyen

Interpretable machine learning offers insights into what factors drive a certain prediction of a black-box system. A large number of interpreting methods focus on identifying explanatory input features, which generally fall into two main…

Machine Learning · Computer Science 2023-06-02 Vy Vo , Van Nguyen , Trung Le , Quan Hung Tran , Gholamreza Haffari , Seyit Camtepe , Dinh Phung

In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the…

Attribution scores can be applied in data management to quantify the contribution of individual items to conclusions from the data, as part of the explanation of what led to these conclusions. In Artificial Intelligence, Machine Learning,…

Databases · Computer Science 2024-01-15 Leopoldo Bertossi , Benny Kimelfeld , Ester Livshits , Mikaël Monet

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy

We propose probabilistic Shapley inference (PSI), a novel probabilistic framework to model and infer sufficient statistics of feature attributions in flexible predictive models, via latent random variables whose mean recovers Shapley…

Machine Learning · Computer Science 2025-09-09 Mert Ketenci , Iñigo Urteaga , Victor Alfonso Rodriguez , Noémie Elhadad , Adler Perotte

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 consider the problem of optimally sharing a financial position among agents with potentially different reference risk measures. The problem is equivalent to computing the infimal convolution of the risk metrics and finding the so-called…

Risk Management · Quantitative Finance 2023-06-21 Matteo Burzoni , Alessandro Doldi , Enea Monzio Compagnoni

We emphasize the importance of asking the right question when interpreting the decisions of a learning model. We discuss a natural extension of the theoretical machinery from Janzing et. al. 2020, which answers the question "Why did my…

Machine Learning · Statistics 2020-12-11 Debraj Basu

Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work…

Computer Science and Game Theory · Computer Science 2025-10-16 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

Despite their ubiquitous use, Shapley value feature attributions can be misleading due to feature interaction in both model and data. We propose an alternative attribution approach, Shapley Sets, which awards value to sets of features.…

Machine Learning · Computer Science 2023-07-06 Torty Sivill , Peter Flach

The study takes the social media industry as its research subject and examines the impact of scientific innovation capabilities on profit distribution within the value chain of the social media industry. It proposes a specific solution to…

Theoretical Economics · Economics 2024-12-25 Jianfei Xu , Rui Zhang , Junhui Fan

Explainable machine learning methods have been accompanied by substantial development. Despite their success, the existing approaches focus more on the general framework with no prior domain expertise. High-stakes financial sectors have…

Computational Finance · Quantitative Finance 2024-08-13 Dangxing Chen , Jingfeng Chen , Weicheng Ye

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

The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method…

Computer Science and Game Theory · Computer Science 2020-02-11 Kedar Dhamdhere , Ashish Agarwal , Mukund Sundararajan

Feature attributions based on the Shapley value are popular for explaining machine learning models; however, their estimation is complex from both a theoretical and computational standpoint. We disentangle this complexity into two factors:…

Machine Learning · Computer Science 2022-07-18 Hugh Chen , Ian C. Covert , Scott M. Lundberg , Su-In Lee

We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a…

Computer Science and Game Theory · Computer Science 2016-07-13 Yi Sun , Mukund Sundararajan

Machine learning and deep learning have become increasingly prevalent in financial prediction and forecasting tasks, offering advantages such as enhanced customer experience, democratising financial services, improving consumer protection,…

General Finance · Quantitative Finance 2023-11-14 Branka Hadji Misheva , Joerg Osterrieder