Related papers: The Shapley Axiomatization for Values in Partition…
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,…
Lloyd Shapley's cooperative value allocation theory stands as a central concept in game theory, extensively utilized across various domains to distribute resources, evaluate individual contributions, and ensure fairness. The Shapley value…
This paper establishes a complete theoretical foundation for the Hodge-theoretic extension of the Shapley value introduced by Stern and Tettenhorst (2019). We show that a set of five axioms--efficiency, linearity, symmetry, a modified…
We show that a cooperative game may be decomposed into a sum of component games, one for each player, using the combinatorial Hodge decomposition on a graph. This decomposition is shown to satisfy certain efficiency, null-player, symmetry,…
Shapley values, which were originally designed to assign attributions to individual players in coalition games, have become a commonly used approach in explainable machine learning to provide attributions to input features for black-box…
The computation of a solution concept of a cooperative game usually depends on values of all coalitions. However, in some applications, values of some of the coalitions might be unknown due to various reasons. We introduce a method to…
Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…
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…
Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation…
This paper focuses on the fundamental challenge of partitioning input variables in attribution methods for Explainable AI, particularly in Shapley value-based approaches. Previous methods always compute attributions given a predefined…
We study the cost sharing problem for cooperative games in situations where the cost function $C$ is not available via oracle queries, but must instead be derived from data, represented as tuples $(S, C(S))$, for different subsets $S$ of…
In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the…
The information decomposition problem requires an additive decomposition of the mutual information between the input and target variables into nonnegative terms. The recently introduced solution to this problem, Information Attribution,…
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…
In this manuscript, we define and study probabilistic values for cooperative games on simplicial complexes. Inspired by the work of Weber "Probabilistic values for games", we establish the new theory step by step, following the classical…
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…
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…
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…
Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…
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…