Image-on-Scalar Regression via Deep Neural Networks

In medical imaging studies, a topic of central interest is the association analysis of massive imaging data with covariates of interest. The difficulty arises from the ultrahigh imaging dimensions, heterogeneous noises, and limited number of training images. To address these challenges, we propose a novel and conceptually straightforward neural network-based image-on-scalar regression model, in which the spatially varying functions of the main effects, individual deviations, and noise variances are all constructed through neural networks. Compared with existing methods, our method can identify a wider variety of spatial patterns, better captures the individual-wise heterogeneity, and is less affected by a small number of individuals. We provide estimation and selection algorithms with theoretically guaranteed asymptotic properties when the number of voxels grows faster than the number of individuals. We demonstrate the efficacy of our method through extensive simulation studies and the analysis of the fMRI data in the Autism Brain Imaging Data Exchange study and the Adolescent Brain Cognitive Development study.