Related papers: Measuring the interactions among variables of func…
The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown…
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified…
By considering a least squares approximation of a given square integrable function f:[0,1]^n --> R by a shifted L-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence…
In this paper we address the problem of fuzzy measures index calculation. On the basis of fuzzy sets, Murofushi and Soneda proposed an interaction index to deal with the relations between two individuals. This index was later extended in a…
Feature attribution methods have become essential for explaining machine learning models. Many popular approaches, such as SHAP and Banzhaf values, are grounded in power indices from cooperative game theory, which measure the contribution…
This paper deals with a new measure of the influence of each feature on the response variable in classification problems, accounting for potential dependencies among certain feature subsets. Within this framework, we consider a sample of…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
The Choquet integral and the Owen extension (or multilinear extension) are the most popular tools in multicriteria decision making to take into account the interaction between criteria. It is known that the interaction transform and the…
An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates…
In social network analysis, there is a common perception that influence is relevant to determine the global behavior of the society and thus it can be used to enforce cooperation by targeting an adequate initial set of individuals or to…
Stochastic large scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article, we introduced the concept of uniform functions, which are suitable class of…
Models in Multicriteria Decision Analysis (MCDA) can be analyzed by means of an importance index and an interaction index for every group of criteria. We consider first discrete models in MCDA, without further restriction, which amounts to…
Suppose an experiment is conducted on pairs of objects with outcome responses a continuous variable measuring the interactions among the pairs. Furthermore, assume the response variable is hard to measure numerically but easy to be coded…
The Lovasz extension of a pseudo-Boolean function $f : \{0,1\}^n \to R$ is defined on each simplex of the standard triangulation of $[0,1]^n$ as the unique affine function $\hat f : [0,1]^n \to R$ that interpolates $f$ at the $n+1$ vertices…
This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
This paper introduces the Myerson interaction index (MII), an extension of the Shapley interaction index to cooperative games with communication structures restricted by graphs. We establish a formal framework for interaction indices on…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…