Related papers: Uncertainty of the Shapley Value
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…
We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney…
An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables,…
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…
We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…
We elicit incomplete preferences over monetary gambles with subjective uncertainty. Subjects rank gambles, and these rankings are used to estimate preferences; payments are based on estimated preferences. About 40\% of subjects express…
The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The…
Multimodal learning combines information from multiple data modalities to improve predictive performance. However, modalities often contribute unequally and in a data dependent way, making it unclear which data modalities are genuinely…
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…
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…
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…
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…
This is a working paper summarizing results of an ongoing research project whose aim is to uniquely characterize the uncertainty measure for the Dempster-Shafer Theory. A set of intuitive axiomatic requirements is presented, some of their…
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…
Recent publications have suggested using the Shapley value for anomaly localization for sensor data systems. Using a reasonable mathematical anomaly model for full control, experiments indicate that using a single fixed term in the Shapley…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
The idea of approximating the Shapley value of an n-person game by Monte Carlo simulation was first suggested by Mann and Shapley (1960) and they also introduced four different heuristical methods to reduce the estimation error. Since 1960,…
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…
Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under…
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…