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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

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…

Machine Learning · Computer Science 2020-06-29 Luke Merrick , Ankur Taly

The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation…

Machine Learning · Computer Science 2023-12-29 Jacopo Teneggi , Beepul Bharti , Yaniv Romano , Jeremias Sulam

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…

Probability · Mathematics 2017-04-04 Riccardo Colini-Baldeschi , Marco Scarsini , Stefano Vaccari

The presence of artificial intelligence (AI) in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images,…

Machine Learning · Statistics 2025-06-06 Pedro Delicado , Cristian Pachón-García

We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for…

Databases · Computer Science 2023-06-22 Ester Livshits , Leopoldo Bertossi , Benny Kimelfeld , Moshe Sebag

Shapley value is a concept from game theory. Recently, it has been used for explaining complex models produced by machine learning techniques. Although the mathematical definition of Shapley value is straight-forward, the implication of…

Machine Learning · Computer Science 2020-08-13 Sisi Ma , Roshan Tourani

Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…

Machine Learning · Statistics 2023-09-19 Liuqing Yang , Yongdao Zhou , Haoda Fu , Min-Qian Liu , Wei Zheng

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…

Machine Learning · Statistics 2025-06-18 Marouane Il Idrissi , Agathe Fernandes Machado , Arthur Charpentier

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…

Computer Science and Game Theory · Computer Science 2013-07-02 Haris Aziz , Bart de Keijzer

Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…

Machine Learning · Computer Science 2023-06-21 Joran Michiels , Maarten De Vos , Johan Suykens

Shapley Values (SV) are widely used in explainable AI, but their estimation and interpretation can be challenging, leading to inaccurate inferences and explanations. As a starting point, we remind an invariance principle for SV and derive…

Machine Learning · Statistics 2023-06-01 Salim I. Amoukou , Nicolas J-B. Brunel , Tangi Salaün

The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing [16] showing that it is the \emph{unique} method…

Artificial Intelligence · Computer Science 2020-02-10 Mukund Sundararajan , Amir Najmi

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…

Statistics Theory · Mathematics 2017-03-22 Art B. Owen , Clémentine Prieur

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

Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different…

Artificial Intelligence · Computer Science 2020-11-04 Tom Heskes , Evi Sijben , Ioan Gabriel Bucur , Tom Claassen

Reinforcement learning has achieved remarkable success in complex decision-making environments, yet its lack of transparency limits its deployment in practice, especially in safety-critical settings. Shapley values from cooperative game…

Machine Learning · Computer Science 2025-11-11 Daniel Beechey , Özgür Şimşek

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

Machine Learning · Statistics 2021-02-19 Yongchan Kwon , Manuel A. Rivas , James Zou

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. The Shapley framework for explainability has strength in its general applicability combined with its…

Machine Learning · Statistics 2021-12-21 Christopher Frye , Colin Rowat , Ilya Feige

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…

Machine Learning · Computer Science 2020-10-05 Masayoshi Mase , Art B. Owen , Benjamin Seiler