Multi-Task Learning with High-Dimensional Noisy Images

• 成果类型: Article
• 署名作者: Ma, Xin; Kundu, Suprateek
• 署名单位: Emory University; University of Texas System; UTMD Anderson Cancer Center
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2140052
• 发表日期: 2024
• 页码: 650-663
• 关键词: functional regression; measurement error; model selection; sparse recovery; estimators; inference; variables

摘要

Recent medical imaging studies have given rise to distinct but inter-related datasets corresponding to multiple experimental tasks or longitudinal visits. Standard scalar-on-image regression models that fit each dataset separately are not equipped to leverage information across inter-related images, and existing multi-task learning approaches are compromised by the inability to account for the noise that is often observed in images. We propose a novel joint scalar-on-image regression framework involving wavelet-based image representations with grouped penalties that are designed to pool information across inter-related images for joint learning, and which explicitly accounts for noise in high-dimensional images via a projection-based approach. In the presence of nonconvexity arising due to noisy images, we derive nonasymptotic error bounds under nonconvex as well as convex grouped penalties, even when the number of voxels increases exponentially with sample size. A projected gradient descent algorithm is used for computation, which is shown to approximate the optimal solution via well-defined nonasymptotic optimization error bounds under noisy images. Extensive simulations and application to a motivating longitudinal Alzheimer's disease study illustrate significantly improved predictive ability and greater power to detect true signals, that are simply missed by existing methods without noise correction due to the attenuation to null phenomenon. for this article are available online.