In many applications, we need to study a linear regression model that consists of a response variable and a large number of potential explanatory variables, and determine which variables are truly associated with the response. In Foygel Barber & Candès (2015, Ann. Statist., 43, 2055–2085), the authors introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and proved that this method achieves exact FDR control. In this paper, we propose a prototype knockoff filter for group selection by extending the Reid–Tibshirani (2016, Biostatistics, 17, 364–376) prototype method. Our prototype knockoff filter improves the computational efficiency and statistical power of the Reid–Tibshirani prototype method when it is applied for group selection. In some cases when the group features are spanned by one or a few hidden factors, we demonstrate that the Principal Component Analysis (PCA) prototype knockoff filter outperforms the Dai–Foygel Barber (2016, 33rd International Conference on Machine Learning (ICML 2016)) group knockoff filter. We present several numerical experiments to compare our prototype knockoff filter with the Reid–Tibshirani prototype method and the group knockoff filter. We have also conducted some analysis of the knockoff filter. Our analysis reveals that some knockoff path method statistics, including the Lasso path statistic, may lead to loss of power for certain design matrices and a specially designed response even if their signal strengths are still relatively strong.
A critical task in microbiome data analysis is to explore the association between a scalar response of interest and a large number of microbial taxa that are summarized as compositional data at different taxonomic levels. Motivated by fine‐mapping of the microbiome, we propose a two‐step compositional knockoff filter to provide the effective finite‐sample false discovery rate (FDR) control in high‐dimensional linear log‐contrast regression analysis of microbiome compositional data. In the first step, we propose a new compositional screening procedure to remove insignificant microbial taxa while retaining the essential sum‐to‐zero constraint. In the second step, we extend the knockoff filter to identify the significant microbial taxa in the sparse regression model for compositional data. Thereby, a subset of the microbes is selected from the high‐dimensional microbial taxa as related to the response under a prespecified FDR threshold. We study the theoretical properties of the proposed two‐step procedure, including both sure screening and effective false discovery control. We demonstrate these properties in numerical simulation studies to compare our methods to some existing ones and show power gain of the new method while controlling the nominal FDR. The potential usefulness of the proposed method is also illustrated with application to an inflammatory bowel disease data set to identify microbial taxa that influence host gene expressions.
more » « less- NSF-PAR ID:
- 10449292
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 77
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 984-995
- Size(s):
- ["p. 984-995"]
- Sponsoring Org:
- National Science Foundation
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Abstract Model-X knockoffs is a flexible wrapper method for high-dimensional regression algorithms, which provides guaranteed control of the false discovery rate (FDR). Due to the randomness inherent to the method, different runs of model-X knockoffs on the same dataset often result in different sets of selected variables, which is undesirable in practice. In this article, we introduce a methodology for derandomising model-X knockoffs with provable FDR control. The key insight of our proposed method lies in the discovery that the knockoffs procedure is in essence an e-BH procedure. We make use of this connection and derandomise model-X knockoffs by aggregating the e-values resulting from multiple knockoff realisations. We prove that the derandomised procedure controls the FDR at the desired level, without any additional conditions (in contrast, previously proposed methods for derandomisation are not able to guarantee FDR control). The proposed method is evaluated with numerical experiments, where we find that the derandomised procedure achieves comparable power and dramatically decreased selection variability when compared with model-X knockoffs.
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Summary 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.
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