Representing sparse Gaussian DAGs as sparse R-vines allowing for non-Gaussian dependence

TL;DR

This paper introduces a novel method that links sparse Gaussian DAGs with vine copula models, enabling scalable high-dimensional dependence modeling with non-Gaussian features, and demonstrates improved performance over standard methods.

Contribution

It establishes a connection between sparse DAGs and vine copulas, allowing for efficient non-Gaussian dependence modeling in high dimensions.

Findings

Outperforms standard vine structure estimation methods in simulations

Enables scalable modeling of non-Gaussian dependence

Shows effectiveness in high-dimensional data applications

Abstract

Modeling dependence in high dimensional systems has become an increasingly important topic. Most approaches rely on the assumption of a multivariate Gaussian distribution such as statistical models on directed acyclic graphs (DAGs). They are based on modeling conditional independencies and are scalable to high dimensions. In contrast, vine copula models accommodate more elaborate features like tail dependence and asymmetry, as well as independent modeling of the marginals. This flexibility comes however at the cost of exponentially increasing complexity for model selection and estimation. We show a novel connection between DAGs with limited number of parents and truncated vine copulas under sufficient conditions. This motivates a more general procedure exploiting the fast model selection and estimation of sparse DAGs while allowing for non-Gaussian dependence using vine copulas. We demonstrate in a simulation study and using a high dimensional data application that our approach outperforms standard methods for vine structure estimation.