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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

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

Machine Learning · Computer Science 2020-02-28 Amirata Ghorbani , Michael P. Kim , James Zou

Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the…

Machine Learning · Statistics 2022-02-04 Rory Mitchell , Joshua Cooper , Eibe Frank , Geoffrey Holmes

We study combinatorial auctions for the secondary spectrum market. In this market, short-term licenses shall be given to wireless nodes for communication in their local neighborhood. In contrast to the primary market, channels can be…

Data Structures and Algorithms · Computer Science 2011-04-29 Martin Hoefer , Thomas Kesselheim , Berthold Vöcking

Shapley values are widely used for model-agnostic data valuation and feature attribution, yet they implicitly assume contributors are interchangeable. This can be problematic when contributors are dependent (e.g., reused/augmented data or…

Machine Learning · Computer Science 2026-02-11 Kiljae Lee , Ziqi Liu , Weijing Tang , Yuan Zhang

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

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…

Computer Science and Game Theory · Computer Science 2025-11-20 Xi Zheng , Xiangyu Chang , Ruoxi Jia , Yong Tan

"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…

Machine Learning · Computer Science 2023-03-07 Ruoxi Jia , David Dao , Boxin Wang , Frances Ann Hubis , Nick Hynes , Nezihe Merve Gurel , Bo Li , Ce Zhang , Dawn Song , Costas Spanos

Originally introduced in game theory, Shapley values have emerged as a central tool in explainable machine learning, where they are used to attribute model predictions to specific input features. However, computing Shapley values exactly is…

Machine Learning · Computer Science 2025-03-11 Christopher Musco , R. Teal Witter

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

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

Existing methods of explainable AI and interpretable ML cannot explain change in the values of an output variable for a statistical unit in terms of the change in the input values and the change in the "mechanism" (the function transforming…

Machine Learning · Computer Science 2022-06-28 Kailash Budhathoki , George Michailidis , Dominik Janzing

With spectrum auctions as our prime motivation, in this paper we analyze combinatorial auctions where agents' valuations exhibit complementarities. Assuming that the agents only value bundles of size at most $k$ and also assuming that we…

Computer Science and Game Theory · Computer Science 2016-06-07 Dengwang Tang , Vijay Subramanian

In recent years, network models have become more complex with the development of big data. Therefore, more advanced network analysis is required. In this paper, we introduce a new quantitative measure named combinatorial evaluation, which…

Computer Science and Game Theory · Computer Science 2025-06-06 Taiki Yamada

In lending, where prices are specific to both customers and products, having a well-functioning personalized pricing policy in place is essential to effective business making. Typically, such a policy must be derived from observational…

Machine Learning · Computer Science 2023-09-08 Christopher Bockel-Rickermann , Sam Verboven , Tim Verdonck , Wouter Verbeke

Shapley value and its priority-aware extensions are widely used for valuation in machine learning, but existing methods require pairwise priority to be binary and acyclic, a restriction spectacularly violated in real-data examples such as…

Machine Learning · Computer Science 2026-05-15 Kiljae Lee , Ziqi Liu , Weijing Tang , Yuan Zhang

We investigate approximately optimal mechanisms in settings where bidders' utility functions are non-linear; specifically, convex, with respect to payments (such settings arise, for instance, in procurement auctions for energy). We provide…

Computer Science and Game Theory · Computer Science 2017-02-23 Amy Greenwald , Takehiro Oyakawa , Vasilis Syrgkanis

The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the…

Machine Learning · Computer Science 2021-04-26 Ian Covert , Su-In Lee

We study the problem of designing revenue-maximizing auctions for allocating multiple goods to flexible consumers. In our model, each consumer is interested in a subset of goods known as its flexibility set and wants to consume one good…

Computer Science and Game Theory · Computer Science 2018-02-01 Shiva Navabi , Ashutosh Nayyar

This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level \textit{Shapley curves} to measure the true variable…

Machine Learning · Statistics 2024-04-04 Ratmir Miftachov , Georg Keilbar , Wolfgang Karl Härdle