Related papers: High-dimensional copula-based Wasserstein dependen…

We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…

We propose a score test for dependence predictability in conditional copulas that is robust to temporal instabilities. Our semiparametric procedure accommodates flexible dynamics in the marginal processes and remains agnostic about the…

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…

For a bivariate probability distribution, local dependence around a single point on the support is often formulated as the second derivative of the logarithm of the probability density function. However, this definition lacks the invariance…

Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value…

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…

We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or…

To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…

We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…

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…

Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor…

Working with so-called linkages allows to define a copula-based, $[0,1]$-valued multivariate dependence measure $\zeta^1(\boldsymbol{X},Y)$ quantifying the scale-invariant extent of dependence of a random variable $Y$ on a $d$-dimensional…

Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…

We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…

Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional independence between…

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…

Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…