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Consider a case–control study in which we have a random sample, constructed in such a way that the proportion of cases in our sample is different from that in the general population—for instance, the sample is constructed to achieve a fixed ratio of cases to controls. Imagine that we wish to determine which of the potentially many covariates under study truly influence the response by applying the new model‐X knockoffs approach. This paper demonstrates that it suffices to design knockoff variables using data that may have a different ratio of cases to controls. For example, the knockoff variables can be constructed using the distribution of the original variables under any of the following scenarios: (a) a population of controls only; (b) a population of cases only; and (c) a population of cases and controls mixed in an arbitrary proportion (irrespective of the fraction of cases in the sample at hand). The consequence is that knockoff variables may be constructed using unlabelled data, which are often available more easily than labelled data, while maintaining Type‐I error guarantees.
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This content will become publicly available on April 1, 2026
ARK: Robust knockoffs inference with coupling
We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and k-familywise error rate (k-FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or k-FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework. Additionally, we formally connect our concept of knockoff variable coupling to a type of Wasserstein distance.
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- Award ID(s):
- 2125142
- PAR ID:
- 10654634
- Publisher / Repository:
- Institute of Mathematical Statistics
- Date Published:
- Journal Name:
- The Annals of Statistics
- Volume:
- 53
- Issue:
- 2
- ISSN:
- 0090-5364
- Page Range / eLocation ID:
- 749–773
- Subject(s) / Keyword(s):
- Statistics/Knockoffs inference, Wasserstein distance, false discovery rate control, familywise error rate control, coupling, robustness, high dimensionality
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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