VARIABLE SCREENING AND SPATIAL SMOOTHING IN FRÉCHET REGRESSION WITH APPLICATION TO DIFFUSION TENSOR IMAGING

• 成果类型: Article
• 署名作者: Yan, Lei; Zhang, Xin; Lan, Zhou; Bandyopadhyay, Dipankar; Wu, Yichao
• 署名单位: State University System of Florida; Florida State University; Harvard University; Harvard University Medical Affiliates; Brigham & Women's Hospital; Harvard University; Harvard Medical School; Virginia Commonwealth University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/24-AOAS1978
• 发表日期: 2025
• 页码: 655-679
• 关键词: alzheimers-disease; feature-selection; association; covariance; dependence; MODEL; RISK

摘要

Modern applications in medical imaging often include high-dimensional predictors and spatially dependent responses in the non-Euclidean space. For example, in imaging-genetics studies, our objective is to study the relationship between single-nucleotide polymorphisms (SNPs), a high-dimensional predictor vector, and diffusion tensor imaging (DTI) responses, which are thousands to millions of voxelwise 3 x 3 symmetric positive definite (SPD) matrices. In this paper we develop a fast and pragmatic method of regressing spatially associated random responses on a high-dimensional predictor set. Specifically, we focus on two related problems: fast variable screening of high-dimensional predictors and smoothing techniques for nonEuclidean spatially associated responses. Under a Fr & eacute;chet regression framework (which handles regression of SPD matrix-variate responses on covariates in Euclidean space), we propose a two-stage approach, where a screening method (using distance covariances in metric spaces) is employed to mitigate high-dimensionality (Stage 1), followed by deriving a closed-form solution that powers elegant smoothing of the spatially associated SPD responses (Stage 2). We investigate the finite-sample properties of our method using synthetic data generated under various settings and present illustration via analysis of an imaging-genetics (DTI responses with genetic and demographic predictors) dataset, derived from the Alzheimer's Disease Neuroimaging Initiative 2. Code for implementing our proposed method is available in the GitHub link: https://github.com/leiyan-ly/Frechet-regression.