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Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of…
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…
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…
Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf…
In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation…
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…
Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely…
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,…
This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the…
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…
Shapley value is a concept in cooperative game theory for measuring the contribution of each participant, which was named in honor of Lloyd Shapley. Shapley value has been recently applied in data marketplaces for compensation allocation…
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…
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…
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…
In Network games under cooperative framework, the position value is a link based allocation rule. It is obtained from the Shapley value of an associated cooperative game where the links of the network are considered players. The Shapley…
In this research, we discuss a problem of calculating the Shapley value in bankruptcy games. We show that the decision problem of computing the Shapley value in bankruptcy games is NP-complete. We also investigate the relationship between…
For feature selection and related problems, we introduce the notion of classification game, a cooperative game, with features as players and hinge loss based characteristic function and relate a feature's contribution to Shapley value based…
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…
We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…