Bayesian Scalar-on-Image Regression with the Spatially Varying Neural Network Prior

Music City Center 

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 a good prediction accuracy and the model fitting results can be difficult to interpret. In this work, we propose a noval Bayesian non-linear scalar-on-image regression framework with a spatially varying neural network (SV-NN) prior. The SV-NN is constructed using a single hidden layer neural network with its weights generated by the soft-thresholded Gaussian process. Our 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. We establish the posterior consistency of model parameters and selection consistency of image regions when the number of voxels/pixels grows much faster than the sample size. We develop an efficient posterior computation algorithm based on stochastic gradient Langevin dynamics (SGLD). We compared our methods 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.

Scalar-on-Image Regression