Related papers: Hypergraphs in the characterization of regular vin…
What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs? What can be underlying local dynamics on individuals, which ultimately lead to the observed patterns, beyond apparently random evolution?…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
This is an overview of double categories of "open systems": systems that can interact with their environment. We focus on the variable sharing paradigm, where we compose open systems by identifying variables. This paradigm is often…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
We propose a generalisation of the logistic regression model, that aims to account for non-linear main effects and complex interactions, while keeping the model inherently explainable. This is obtained by starting with log-odds that are…
Composites, or linear combinations of variables, play an important role in multivariate behavioral research. They appear in the form of indices, inventories, formative constructs, parcels, and emergent variables. Although structural…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
Conditional copulas models allow the dependence structure between multiple response variables to be modelled as a function of covariates. LocalCop (Acar & Lysy, 2024) is an R/C++ package for computationally efficient semiparametric…
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a…
Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and check constraints on high-dimensional distributions. So far, corresponding tests have been limited to…
We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
We construct the COpula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork…
Factor copula models for item response data are more interpretable and fit better than (truncated) vine copula models when dependence can be explained through latent variables, but are not robust to violations of conditional independence.…
Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single…
This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take…
Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two…