Bayesian image-on-image regression via deep kernel learning based Gaussian processes

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 extensive simulations where we synthesize data based on MNIST, Fashion MNIST and fMRI data from HCP. For HCP data analysis using BIRD-GP, we combine the voxelwise fALFF maps and regionwise 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. Additionally, we identify features from the resting-state fMRI data that are important for task fMRI prediction.