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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

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

There is much interest lately in explainability in statistics and machine learning. One aspect of explainability is to quantify the importance of various features (or covariates). Two popular methods for defining variable importance are…

Methodology · Statistics 2023-03-13 Isabella Verdinelli , Larry Wasserman

Causal Structure Learning (CSL), also referred to as causal discovery, amounts to extracting causal relations among variables in data. CSL enables the estimation of causal effects from observational data alone, avoiding the need to perform…

Machine Learning · Computer Science 2025-02-12 Fabrizio Russo , Francesca Toni

Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…

Machine Learning · Computer Science 2022-05-27 Benedek Rozemberczki , Lauren Watson , Péter Bayer , Hao-Tsung Yang , Olivér Kiss , Sebastian Nilsson , Rik Sarkar

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

As Artificial Intelligence (AI) is having more influence on our everyday lives, it becomes important that AI-based decisions are transparent and explainable. As a consequence, the field of eXplainable AI (or XAI) has become popular in…

Artificial Intelligence · Computer Science 2024-04-18 Nils Ole Breuer , Andreas Sauter , Majid Mohammadi , Erman Acar

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning…

Machine Learning · Computer Science 2022-09-28 Yongchan Kwon , James Zou

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional…

Machine Learning · Computer Science 2020-06-30 Hugh Chen , Joseph D. Janizek , Scott Lundberg , Su-In Lee

Shapley values have become increasingly popular in the machine learning literature thanks to their attractive axiomatisation, flexibility, and uniqueness in satisfying certain notions of `fairness'. The flexibility arises from the myriad…

Machine Learning · Statistics 2021-03-09 Daniel Vidali Fryer , Inga Strümke , Hien Nguyen

Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature…

Machine Learning · Computer Science 2021-03-01 Jiaxuan Wang , Jenna Wiens , Scott Lundberg

Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be…

Machine Learning · Computer Science 2026-04-14 Tom Bewley , Salim I. Amoukou , Emanuele Albini , Saumitra Mishra , Manuela Veloso

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central…

Computer Science and Game Theory · Computer Science 2013-08-29 Oskar Skibski , Tomasz P. Michalak , Michael Wooldridge

Shapley values have become a cornerstone of explainable AI, but they are computationally expensive to use, especially when features are dependent. Evaluating them requires approximating a large number of conditional expectations, either via…

Artificial Intelligence · Computer Science 2026-02-11 Lars Henry Berge Olsen , Dennis Christensen

The Shapley value is one of the most important solution concepts in cooperative game theory. In coalitional games without externalities, it allows to compute a unique payoff division that meets certain desirable fairness axioms. However, in…

Computer Science and Game Theory · Computer Science 2015-03-19 Oskar Skibski

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

Shapley-related techniques have gained attention as both global and local interpretation tools because of their desirable properties. However, their computation using conditional expectations is computationally expensive. Approximation…

Machine Learning · Statistics 2022-07-13 Zhipu Zhou , Jie Chen , Linwei Hu

The analysis of causation is a challenging task that can be approached in various ways. With the increasing use of machine learning based models in computational socioeconomics, explaining these models while taking causal connections into…

Machine Learning · Computer Science 2022-01-19 Tannista Banerjee , Ayan Paul , Vishak Srikanth , Inga Strümke

For neural models to garner widespread public trust and ensure fairness, we must have human-intelligible explanations for their predictions. Recently, an increasing number of works focus on explaining the predictions of neural models in…

Computation and Language · Computer Science 2020-12-15 Oana-Maria Camburu , Eleonora Giunchiglia , Jakob Foerster , Thomas Lukasiewicz , Phil Blunsom

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