A0726
Title: Bayesian scalar-on-image regression with the spatially varying neural network 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 Bayesian non-linear scalar-on-image regression framework is proposed with a spatially varying neural network (SV-NN) prior. The SV-NN is constructed using a single hidden layer neural network with weights generated by the soft-thresholded Gaussian process. The framework is able to select interpretable image regions and to achieve high prediction accuracy with limited training samples. The SV-NN provides large prior support for the imaging effect function, enabling efficient posterior inference on image region selection and automatically determining the network structures. The posterior consistency of model parameters and selection consistency of image regions is established when the number of voxels/pixels grows much faster than the sample size. An efficient posterior computation algorithm is developed based on stochastic gradient Langevin dynamics (SGLD). The methods are compared with state-of-the-art deep learning methods via analyses of multiple real data sets, including task fMRI data from the Adolescent Brain Cognitive Development (ABCD) study.
