New perspectives on knockoffs construction.

Let Λ be the collection of all probability distributions for (X , X ˜) , where X is a fixed random vector and X ˜ ranges over all possible knockoff copies of X (in the sense of Candes et al. (2018)). Three topics are developed in this paper: (i) A new characterization of Λ is proved; (ii) A certain subclass of Λ , defined in terms of copulas, is introduced; (iii) The (meaningful) special case where the components of X are conditionally independent is treated in depth. In real problems, after observing X = x , each of points (i)–(ii)–(iii) may be useful to generate a value x ˜ for X ˜ conditionally on X = x. • The paper provides some new theoretical insights on the knockoffs procedure introduced by Barber and Candes (2015). Let Λ be the set of all possible knockofffs. In Section 2, a new characterization of Λ is proved. • In Section 3, a certain (proper) subclass Λ 0 ⊂ Λ is introduced. The elements of Λ 0 admit a simple and explicit representation in terms of copulas. • In Section 4, we focus on the case where the variables X 1 , ... , X p are conditionally independent. Under this assumption, we show how to build a knockoff X ˜. [ABSTRACT FROM AUTHOR]