Related papers: Probabilistic values for simplicial complexes

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

In many cases the Nash equilibria are not predictive of the experimental players' behaviour. For some games of Game Theory it is proposed here a method to estimate the probabilities with which the different options will be actually chosen…

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,…

Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…

We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…

In cooperative game theory, associated games allow for providing meaningful characterizations of solution concepts. Moreover, generalized values allow computing an influence or power index of each coalition in a game. In this paper, we view…

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…

We consider MultiCriteria Decision Analysis models which are defined over discrete attributes, taking a finite number of values. We do not assume that the model is monotonically increasing with respect to the attributes values. Our aim is…

Feature attribution methods help make machine learning-based inference explainable by determining how much one or several features have contributed to a model's output. A particularly popular attribution method is based on the Shapley value…

We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games. We show that the following tasks are polynomial time equivalent: - Solving simple…

With the widespread use of sophisticated machine learning models in sensitive applications, understanding their decision-making has become an essential task. Models trained on tabular data have witnessed significant progress in explanations…

Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these…

Cooperative games are an important class of problems in game theory, where the goal is to distribute a value among a set of players who are allowed to cooperate by forming coalitions. An outcome of the game is given by an allocation vector…

In recent years, network models have become more complex with the development of big data. Therefore, more advanced network analysis is required. In this paper, we introduce a new quantitative measure named combinatorial evaluation, which…

A weighted simplicial complex is a simplicial complex with values (called weights) on the vertices. In this paper, we consider weighted simplicial complexes with $\mathbb{R}^2$-valued weights. We study the weighted homology and the weighted…

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

This paper introduces the shapr R package, a versatile tool for generating Shapley value-based prediction explanations for machine learning and statistical regression models. Moreover, the shaprpy Python library brings the core capabilities…

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…

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking…