Year: 2025
Type: article
Abstract: 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.
Source: The Annals of Statistics
DOI: 10.1214/24-aos2480
Authors: Yingying Fan, Lan Gao, Jinchi Lv
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: MIM: Machine Learning, Systems Modeling, and Experimental Approaches to Understand the Universal Rules of Life of Microbiota Using Marine Time Series Data, Adaptive Reproducible High-Dimensional Nonlinear Inference for Big Biological Data, Collaborative Research: New Theory and Methods for High-Dimensional Multi-Task and Transfer Learning Inference, High-Dimensional Random Forests Learning, Inference, and Beyond
OpenAlex ID: W4409975319