  In neuroimaging studies, it becomes increasingly important to study
associations between different imaging modalities using image-on-image
regression (IIR), which faces challenges in interpretation, statistical
inference, and prediction. Our motivating problem is how to predict task-evoked
fMRI activity using resting-state fMRI data in the Human Connectome Project
(HCP). The main difficulty lies in effectively combining different types of
imaging predictors with varying resolutions and spatial domains in IIR. To
address these issues, we develop Bayesian Image-on-image Regression via Deep
Kernel Learning Gaussian Processes (BIRD-GP) and develop efficient posterior
computation methods through Stein variational gradient descent. We demonstrate
the advantages of BIRD-GP over state-of-the-art IIR methods using simulations.
For HCP data analysis using BIRD-GP, we combine the voxel-wise fALFF maps and
region-wise connectivity matrices to predict fMRI contrast maps for language
and social recognition tasks. We show that fALFF is less predictive than the
connectivity matrix for both tasks, but combining both yields improved results.
Angular Gyrus Right emerges as the most predictable region for the language
task (75.9% predictable voxels), while Superior Parietal Gyrus Right tops for
the social recognition task (48.9% predictable voxels). Additionally, we
identify features from the resting-state fMRI data that are important for task
fMRI prediction.
