  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.
