Panning for gold: ‘model‐X’ knockoffs for high dimensional controlled variable selection

By E.J. Candes, Yingying Fan, Lucas Janson, Jinchi Lv. 2016

553 citations recorded by the source corpus.

Many contemporary large‐scale applications involve building interpretable models linking a large set of potential covariates to a response in a non‐linear fashion, such as when the response is binary. Although this modelling problem has been extensively studied, it remains unclear how to control the fraction of false discoveries effectively even in high dimensional logistic regression, not to mention general high dimensional non‐linear models. To address such a practical problem, we propose a new framework of ‘model‐X’ knockoffs, which reads from a different perspective the knockoff procedure that was originally designed for controlling the false discovery rate in linear models. Whereas the knockoffs procedure is constrained to homoscedastic linear models with n⩾p, the key innovation here is that model‐X knockoffs provide valid inference from finite samples in settings in which the conditional distribution of the response is arbitrary and completely unknown. Furthermore, this holds no matter the number of covariates. Correct inference in such a broad setting is achieved by constructing knockoff variables probabilistically instead of geometrically. To do this, our approach requires that the covariates are random (independent and identically distributed rows) with a distribution that is known, although we provide preliminary experimental evidence that our procedure is robust to unknown or estimated distributions. To our knowledge, no other procedure solves the controlled variable selection problem in such generality but, in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case–control study of Crohn's disease in the UK, making twice as many discoveries as the original analysis of the same data.

Subfields: Statistics and Probability

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Citations in the corpus

Forward stability and model path selection (2021, neutral): “…lines, our goal is not necessarily to identify the subset of signals as is the primary objective with tools like knockoffs (Barber and Candes 2015; Candes et al. 2018; Barber et al. 2018; Janson et al. 2016), pseudovariables (Wu et al. 2007; Hu et al. 2018), or stability selection (SS)…”
A modern maximum-likelihood theory for high-dimensional logistic regression (2018, methodology): “A parallel literature develops methodologies for discovering variables in high-dimensional models with guaranteed control of the false discovery rate (FDR) and in some cases the family-wise error rate (FWER) (see for instance, [22,58] and the references cited therein).”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, methodology): “To implement a test, we employ the conditional randomization test (CRT) framework developed in Candès et al. (2018a); see Berrett et al. (2020) for a related proposal.”