Vine copula based knockoff generation for high-dimensional controlled variable selection

Abstract

Vine copulas are a flexible tool for high-dimensional dependence modeling. In this article, we discuss the generation of approximate model-X knockoffs with vine copulas. It is shown how Gaussian knockoffs can be generalized to Gaussian copula knockoffs. A convenient way to parametrize Gaussian copulas are partial correlation vines. We discuss how completion problems for partial correlation vines are related to Gaussian knockoffs. A natural generalization of partial correlation vines are vine copulas which are well suited for the generation of approximate model-X knockoffs. We discuss a specific D-vine structure which is advantageous to obtain vine copula knockoff models. In a simulation study, we demonstrate that vine copula knockoff models are effective and powerful for high-dimensional controlled variable selection.