Deep kernel learning based Gaussian processes for Bayesian image regression analysis

Oregon Convention Center 

Regression models are widely used in neuroimaging studies to learn complex associations between clinical variables and image data. Gaussian process (GP) is one of the most popular Bayesian nonparametric methods and has been widely used as prior models for the unknown functions in those models. However, many existing GP methods need to pre-specify the functional form of the kernels, which often suffer less flexibility in model fitting and computational bottlenecks in large-scale datasets. To address these challenges, we develop a scalable Bayesian kernel learning framework for GP priors in various image regression models. Our approach leverages deep neural networks (DNNs) to perform low-rank approximations of GP kernel functions via spectral decomposition. With Bayesian kernel learning techniques, we achieve improved accuracy in parameter estimation and variable selection in image regression models. We establish large prior support and posterior consistency of the kernel estimations. Through extensive simulations, we demonstrate our model outperforms other competitive methods. We illustrate the proposed method by analyzing multiple neuroimaging datasets in different medical studies.