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1. Compositional knockoff filter for high‐dimensional regression analysis of microbiome data

   https://doi.org/10.1111/biom.13336  

   Srinivasan, Arun; Xue, Lingzhou; Zhan, Xiang (September 2021, Biometrics)

   Abstract 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. 

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2. DeepLINK: Deep learning inference using knockoffs with applications to genomics

   https://doi.org/10.1073/pnas.2104683118  

   Zhu, Zifan; Fan, Yingying; Kong, Yinfei; Lv, Jinchi; Sun, Fengzhu (September 2021, Proceedings of the National Academy of Sciences)

   We propose a deep learning–based knockoffs inference framework, DeepLINK, that guarantees the false discovery rate (FDR) control in high-dimensional settings. DeepLINK is applicable to a broad class of covariate distributions described by the possibly nonlinear latent factor models. It consists of two major parts: an autoencoder network for the knockoff variable construction and a multilayer perceptron network for feature selection with the FDR control. The empirical performance of DeepLINK is investigated through extensive simulation studies, where it is shown to achieve FDR control in feature selection with both high selection power and high prediction accuracy. We also apply DeepLINK to three real data applications to demonstrate its practical utility. 

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3. ARK: Robust knockoffs inference with coupling

   https://doi.org/10.1214/24-AOS2480  

   Fan, Yingying; Gao, Lan; Lv, Jinchi (April 2025, The Annals of Statistics)

   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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4. A generalized knockoff procedure for FDR control in structural change detection

   https://doi.org/10.1016/j.jeconom.2022.07.008  

   Liu, Jingyuan; Sun, Ao; Ke, Yuan (February 2024, Journal of Econometrics)

   Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of FDR control strategies when selecting individual features, but the relevant works for structural change detection, such as profile analysis for piecewise constant coefficients and integration analysis with multiple data sources, are limited. In this paper, we propose a generalized knockoff procedure (GKnockoff) for FDR control under such problem settings. We prove that the GKnockoff possesses pairwise exchangeability, and is capable of controlling the exact FDR under finite sample sizes. We further explore GKnockoff under high dimensionality, by first introducing a new screening method to filter the high-dimensional potential structural changes. We adopt a data splitting technique to first reduce the dimensionality via screening and then conduct GKnockoff on the refined selection set. Furthermore, the powers of proposed methods are systematically studied. Numerical comparisons with other methods show the superior performance of GKnockoff, in terms of both FDR control and power. We also implement the proposed methods to analyze a macroeconomic dataset for detecting changes of driven effects of economic development on the secondary industry. 

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5. Detection of Local Differences in Spatial Characteristics Between Two Spatiotemporal Random Fields

   Harris, T. (October 2020, Journal of the American Statistical Association)

   null (Ed.)

   omparing the spatial characteristics of spatiotemporal random fields is often at demand. However, the comparison can be challenging due to the high-dimensional feature and dependency in the data. We develop a new multiple testing approach to detect local differences in the spatial characteristics of two spatiotemporal random fields by taking the spatial information into account. Our method adopts a twocomponent mixture model for location wise p-values and then derives a new false discovery rate (FDR) control, called mirror procedure, to determine the optimal rejection region. This procedure is robust to model misspecification and allows for weak dependency among hypotheses. To integrate the spatial heterogeneity, we model the mixture probability as well as study the benefit if any of allowing the alternative distribution to be spatially varying. AnEM-algorithm is developed to estimate the mixture model and implement the FDR procedure. We study the FDR control and the power of our new approach both theoretically and numerically, and apply the approach to compare the mean and teleconnection pattern between two synthetic climate fields. Supplementary materials for this article are available online. 

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