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New perspectives on knockoffs construction

Abstract

Let Λ\Lambda be the collection of all probability distributions for (X,X~)(X,\widetilde{X}), where XX is a fixed random vector and X~\widetilde{X} ranges over all possible knockoff copies of XX (in the sense of \cite{CFJL18}). Three topics are developed in this paper: (i) A new characterization of Λ\Lambda is proved; (ii) A certain subclass of Λ\Lambda, defined in terms of copulas, is introduced; (iii) The (meaningful) special case where the components of XX are conditionally independent is treated in depth. In real problems, after observing X=xX=x, each of points (i)-(ii)-(iii) may be useful to generate a value x~\widetilde{x} for X~\widetilde{X} conditionally on X=xX=x.

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