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This study introduces the \emph{edge-based Shapley value}, a novel allocation rule within cooperative game theory, specifically tailored for networked systems, where value is generated through interactions represented by edges. Traditional…

Computer Science and Game Theory · Computer Science 2025-07-17 Taiki Yamada , Taisuke Matsubae , Tomoya Akamatsu

In a variety of business situations, the introduction or improvement of machine learning approaches is impaired as these cannot draw on existing analytical models. However, in many cases similar problems may have already been solved…

Machine Learning · Computer Science 2020-05-22 Robin Hirt , Niklas Kühl , Yusuf Peker , Gerhard Satzger

A task of interest in machine learning (ML) is that of ascribing explanations to the predictions made by ML models. Furthermore, in domains deemed high risk, the rigor of explanations is paramount. Indeed, incorrect explanations can and…

Artificial Intelligence · Computer Science 2025-07-11 Mohamed Siala , Jordi Planes , Joao Marques-Silva

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…

Artificial Intelligence · Computer Science 2020-07-01 I. Elizabeth Kumar , Suresh Venkatasubramanian , Carlos Scheidegger , Sorelle Friedler

An emerging problem in trustworthy machine learning is to train models that produce robust interpretations for their predictions. We take a step towards solving this problem through the lens of axiomatic attribution of neural networks. Our…

Machine Learning · Computer Science 2019-10-29 Jiefeng Chen , Xi Wu , Vaibhav Rastogi , Yingyu Liang , Somesh Jha

Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several…

Machine Learning · Statistics 2024-04-15 Lars Henry Berge Olsen , Ingrid Kristine Glad , Martin Jullum , Kjersti Aas

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…

Attribution methods compute importance scores for input features to explain model predictions. However, assessing the faithfulness of these methods remains challenging due to the absence of attribution ground truth to model predictions. In…

Cryptography and Security · Computer Science 2025-10-02 Peiyu Yang , Naveed Akhtar , Jiantong Jiang , Ajmal Mian

Feature attribution explains neural network outputs by identifying relevant input features. The attribution has to be faithful, meaning that the attributed features must mirror the input features that influence the output. One recent trend…

Machine Learning · Computer Science 2024-02-15 Yang Zhang , Yawei Li , Hannah Brown , Mina Rezaei , Bernd Bischl , Philip Torr , Ashkan Khakzar , Kenji Kawaguchi

Many tasks in explainable machine learning, such as data valuation and feature attribution, perform expensive computation for each data point and are intractable for large datasets. These methods require efficient approximations, and…

Machine Learning · Computer Science 2024-10-31 Ian Covert , Chanwoo Kim , Su-In Lee , James Zou , Tatsunori Hashimoto

The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…

Risk Management · Quantitative Finance 2015-03-17 Hirbod Assa

Large language models (LLMs) demonstrate strong capabilities in in-context learning, but verifying the correctness of their generated responses remains a challenge. Prior work has explored attribution at the sentence level, but these…

Computation and Language · Computer Science 2025-07-10 Yingtai Xiao , Yuqing Zhu , Sirat Samyoun , Wanrong Zhang , Jiachen T. Wang , Jian Du

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

This paper firstly addresses the problem of risk assessment under false data injection attacks on uncertain control systems. We consider an adversary with complete system knowledge, injecting stealthy false data into an uncertain control…

Systems and Control · Electrical Eng. & Systems 2022-12-12 Sribalaji C. Anand , André M. H. Teixeira , Anders Ahlén

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

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

Feature attribution is widely used in interpretable machine learning to explain how influential each measured input feature value is for an output inference. However, measurements can be uncertain, and it is unclear how the awareness of…

Machine Learning · Computer Science 2021-01-26 Danding Wang , Wencan Zhang , Brian Y. Lim

Shapley value has recently become a popular way to explain the predictions of complex and simple machine learning models. This paper is discusses the factors that influence Shapley value. In particular, we explore the relationship between…

Machine Learning · Statistics 2021-11-24 Harsh Kumar , Jithu Chandran

In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be…

Risk Management · Quantitative Finance 2024-10-28 Yuyu Chen , Ruodu Wang

In healthcare, making the best possible predictions with complex models (e.g., neural networks, ensembles/stacks of different models) can impact patient welfare. In order to make these complex models explainable, we present DeepSHAP for…

Machine Learning · Computer Science 2019-11-28 Hugh Chen , Scott Lundberg , Su-In Lee