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arXiv · 2104.07752

New perspectives on knockoffs construction

Patrizia Berti·Emanuela Dreassi·Fabrizio Leisen·Luca Pratelli·Pietro Rigo
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Abstract

Let $Λ$ be the collection of all probability distributions for $(X,\widetilde{X})$, where $X$ is a fixed random vector and $\widetilde{X}$ ranges over all possible knockoff copies of $X$ (in the sense of \cite{CFJL18}). 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 $\widetilde{x}$ for $\widetilde{X}$ conditionally on $X=x$.

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Patrizia Berti, Emanuela Dreassi, Fabrizio Leisen, Luca Pratelli, Pietro Rigo. 2022-07-29. New perspectives on knockoffs construction. https://arxiv.org/abs/2104.07752

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