Related papers: A note on the Sobol' indices and interactive crite…
Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying…
We prove a representation theorem for the Choquet integral model. The preference relation is defined on a two-dimensional heterogeneous product set $X = X_1 \times X_2$ where elements of $X_1$ and $X_2$ are not necessarily comparable with…
Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule…
We introduce an Indian-buffet-type model for multi-factorial innovation in which each arriving agent may exhibit both previously observed and new features. The number of new features follows a power-law behavior, while the probability of…
Several non-linear functions and machine learning methods have been developed for flexible specification of the systematic utility in discrete choice models. However, they lack interpretability, do not ensure monotonicity conditions, and…
Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…
Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…
The Choquet integral is a powerful aggregation operator which lists many well-known models as its special cases. We look at these special cases and provide their axiomatic analysis. In cases where an axiomatization has been previously given…
In multicriteria decision aiding (MCDA), the Choquet integral has been used as an aggregation operator to deal with the case of interacting decision criteria. While the application of the Choquet integral for ranking problems have been…
The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
Explaining the decision-making process of machine learning models is crucial for ensuring their reliability and transparency for end users. One popular explanation form highlights key input features, such as i) tokens (e.g., Shapley Values…
Incremental determinization is a recently proposed algorithm for solving quantified Boolean formulas with one quantifier alternation. In this paper, we formalize incremental determinization as a set of inference rules to help understand the…
In light of the tremendous amount of data produced by social media, a large body of research have revisited the relevance estimation of the users' generated content. Most of the studies have stressed the multidimensional nature of relevance…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
By using the method of Loewner chains, we establish some sufficient conditions for the analyticity and univalency of functions defined by an integral operator. Also, we refine the result to a quasiconformal extension criterion with the help…
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…
This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation,…
In this paper, we propose a new generalization of the classical discrete Choquet integral to the multivalued framework in terms of an admissible order that refines the natural partial order on the considered value set. The new Choquet-like…
Feature interaction is a core ingredient in ranking models for large-scale recommender systems, yet making it both expressive and efficiently scalable remains challenging. Exhaustive pairwise interaction is powerful but incurs quadratic…