Image response regression via deep neural networks

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 85; no. 5; pp. 1589 - 1614
• Main Authors: Zhang, Daiwei, Li, Lexin, Sripada, Chandra, Kang, Jian
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.11.2023
• Subjects: Artificial neural networks; Asymptotic methods; Functional magnetic resonance imaging; Heterogeneity; Magnetic resonance imaging; Neural networks; Original; Smoothness; non-parametric regression; varying coefficient models; high-dimensional inference; deep neural networks; functional magnetic resonance imaging; tensor regression
• ISSN: 1369-7412; 1467-9868; 1467-9868
• DOI: 10.1093/jrsssb/qkad073

Delineating associations between images and covariates is a central aim of imaging studies. To tackle this problem, we propose a novel non-parametric approach in the framework of spatially varying coefficient models, where the spatially varying functions are estimated through deep neural networks. Our method incorporates spatial smoothness, handles subject heterogeneity, and provides straightforward interpretations. It is also highly flexible and accurate, making it ideal for capturing complex association patterns. We establish estimation and selection consistency and derive asymptotic error bounds. We demonstrate the method’s advantages through intensive simulations and analyses of two functional magnetic resonance imaging data sets.