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Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…

Machine Learning · Computer Science 2020-10-26 Ramin Okhrati , Aldo Lipani

In multi-criteria decision analysis workshops, participants often appraise the options individually before discussing the scoring as a group. The individual appraisals lead to score ranges within which the group then seeks the necessary…

General Economics · Economics 2020-12-29 Tom Pape

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

This work considers two-player zero-sum semi-Markov games with incomplete information on one side and perfect observation. At the beginning, the system selects a game type according to a given probability distribution and informs to Player…

Optimization and Control · Mathematics 2021-07-16 Fang Chen , Xianping Guo , Zhong-Wei Liao

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

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

Boolean functions and their representation through logics, circuits, machine learning classifiers, or binary decision diagrams (BDDs) play a central role in the design and analysis of computing systems. Quantifying the relative impact of…

Computer Science and Game Theory · Computer Science 2023-05-16 Hans Harder , Simon Jantsch , Christel Baier , Clemens Dubslaff

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 conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…

Information Theory · Computer Science 2017-10-16 Arman Rahimzamani , Sreeram Kannan

Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the…

Information Theory · Computer Science 2009-11-05 Paul Cuff

We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…

Optimization and Control · Mathematics 2017-01-04 Fabien Gensbittel , Catherine Rainer

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…

Machine Learning · Statistics 2025-08-19 Michael Mayer , Mario V. Wüthrich

We present information value, a measure which quantifies the predictability of an utterance relative to a set of plausible alternatives. We introduce a method to obtain interpretable estimates of information value using neural text…

Computation and Language · Computer Science 2023-10-23 Mario Giulianelli , Sarenne Wallbridge , Raquel Fernández

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

This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such…

Optimization and Control · Mathematics 2007-05-23 Denis V. Juriev

Imperfect-recall games, in which players may forget previously acquired information, have found many practical applications, ranging from game abstractions to team games and testing AI agents. In this paper, we quantify the utility gain by…

Computer Science and Game Theory · Computer Science 2024-12-30 Ratip Emin Berker , Emanuel Tewolde , Ioannis Anagnostides , Tuomas Sandholm , Vincent Conitzer

This paper deals with a new measure of the influence of each feature on the response variable in classification problems, accounting for potential dependencies among certain feature subsets. Within this framework, we consider a sample of…

Optimization and Control · Mathematics 2024-08-06 Laura Davila-Pena , Alejandro Saavedra-Nieves , Balbina Casas-Méndez

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is…

Machine Learning · Computer Science 2024-01-31 Patrick Kolpaczki , Viktor Bengs , Maximilian Muschalik , Eyke Hüllermeier

We introduce Value Coalition Logic, a typed assignment-based reconstruction of classical coalition logic. The strategic semantics is unchanged: coalitional ability is still interpreted by the standard one-step game-form clause. The change…

Logic in Computer Science · Computer Science 2026-05-26 Shanxia Wang

Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley…

Artificial Intelligence · Computer Science 2024-08-14 Santiago Cifuentes , Leopoldo Bertossi , Nina Pardal , Sergio Abriola , Maria Vanina Martinez , Miguel Romero
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