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

Modeling dependence in high dimensional systems has become an increasingly important topic. Most approaches rely on the assumption of a joint 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 based models can accommodate more elaborate features like tail dependence and asymmetry. This exibility comes however at the cost of exponentially increasing complexity for model selection and estimation. We show a connection between these two model classes by giving a novel representation of DAG models in terms of sparse vine models. Therefore we can exploit the fast model selection and estimation of sparse DAGs while allowing for non-Gaussian dependence in the vine models. We demonstrate for a high dimensional data set that this approach outperforms standard methods for vine structure estimation.      «

Modeling dependence in high dimensional systems has become an increasingly important topic. Most approaches rely on the assumption of a joint 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 based models can accommodate more elaborate features like tail dependence and asymmetry. This exibility comes however at the cost of exponentially increasin...     »