Functional knockoffs selection with applications to functional data analysis in high dimensions

TL;DR

This paper introduces a novel functional model-X knockoffs framework designed for high-dimensional functional data, providing effective FDR control and demonstrating superior performance through simulations and brain imaging data analysis.

Contribution

It develops a new functional knockoffs method tailored for high-dimensional data, with theoretical guarantees and practical algorithms for FDR control.

Findings

Effective FDR control achieved in high-dimensional functional models

Superior performance over existing methods in simulations

Successful application to brain imaging datasets

Abstract

The knockoffs is a recently proposed powerful framework that effectively controls the false discovery rate (FDR) for variable selection. However, none of the existing knockoff solutions are directly suited to handle multivariate or high-dimensional functional data, which has become increasingly prevalent in various scientific applications. In this paper, we propose a novel functional model-X knockoffs selection framework tailored to sparse high-dimensional functional models, and show that our proposal can achieve the effective FDR control for any sample size. Furthermore, we illustrate the proposed functional model-X knockoffs selection procedure along with the associated theoretical guarantees for both FDR control and asymptotic power using examples of commonly adopted functional linear additive regression models and the functional graphical model. In the construction of functional knockoffs, we integrate essential components including the correlation operator matrix, the Karhunen-Lo\`eve expansion, and semidefinite programming, and develop executable algorithms. We demonstrate the superiority of our proposed methods over the competitors through both extensive simulations and the analysis of two brain imaging datasets.