A1689
Title: Deep kernel learning based Gaussian processes for Bayesian image regression analysis
Authors: Jian Kang - University of Michigan (United States) [presenting]
Abstract: Regression models are widely used in neuroimaging studies to learn associations between clinical variables and image data. Gaussian process (GP) priors are common Bayesian nonparametric approaches to model unknown regression functions with complex spatial correlations in high-dimensional data. Existing GP methods depend on pre-specified parametric covariance kernel functions, which often have insufficient flexibility to capture data complexity, limited generalizability across study populations, and computational bottlenecks in large-scale datasets. We propose a scalable fully Bayesian kernel learning framework for GP priors with applications in various image regression models. Under kernel series expansion, we utilize the estimation power of deep neural networks (DNNs) to adaptively learn basis functions from data. We establish theoretical properties of posterior concentration rates in estimating regression and kernel functions. Through simulation studies, we show improved estimation and signal detection accuracy across different regression model settings. We illustrate the proposed method by analyzing multiple neuroimaging datasets in different medical studies.
