B1514
Title: Bayesian spatially varying weight neural networks with the soft-thresholded Gaussian process prior
Authors: Ben Wu - Renmin University of China (China) [presenting]
Keru Wu - Duke University (United States)
Jian Kang - University of Michigan (United States)
Abstract: Deep neural networks (DNN) have been adopted in the scalar-on-image regression, which predicts the outcome variable using image predictors. However, training DNN often requires a large sample size to achieve good prediction accuracy, and the model-fitting results can be difficult to interpret. A novel single-layer Bayesian neural network (BNN) is constructed with spatially varying weights for the scalar-on-image regression. The goal is to select interpretable image regions and to achieve high prediction accuracy with limited training samples. The soft-thresholded Gaussian process (STGP) prior is assigned to the spatially varying weights and an efficient posterior computation algorithm is developed based on stochastic gradient Langevin dynamics (SGLD). The BNN-STGP provides large prior support for sparse, piecewise-smooth, and continuous spatially varying weight functions, enabling efficient posterior inference on image region selection and automatically determining the network structures. The posterior consistency of model parameters is established and the selection consistency of image regions when the number of voxels/pixels grows much faster than the sample size. The methods are compared with state-of-the-art deep learning methods via analyses of multiple real data sets, including the task fMRI data in the adolescent brain cognitive development (ABCD) study.
