Representing Sparse Gaussian DAGs as Sparse R-Vines Allowing for Non-Gaussian Dependence

Dominik Müller, Claudia Czado

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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. By numerical examples in hundreds of dimensions, we demonstrate that our approach outperforms the standard method for vine structure selection. Supplementary material for this article is available online.

Original languageEnglish
Pages (from-to)334-344
Number of pages11
JournalJournal of Computational and Graphical Statistics
Volume27
Issue number2
DOIs
StatePublished - 3 Apr 2018

Keywords

  • Dependence modeling
  • Directed acyclic graph
  • Graphical model
  • Vine copula

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