Nonparametric quantile scalar-on-image regression

Abstract

A quantile scalar-on-image regression model is developed to comprehensively study the relationship between cognitive decline and various clinical covariates and imaging factors. As a motivating example, the high-dimensional brain imaging data from the research on Alzheimer's disease are considered predictors of patients' cognitive decline. A Bayesian nonparametric model is proposed to handle the complex spatially distributed imaging data, where the coefficient function is assumed to be a latent Gaussian process. A soft-thresholding operator is introduced to capture the sparse structure of the regression coefficients. Utilizing kernel basis functions to approximate the latent Gaussian process facilitates easy-to-implement computation and consistent estimation. Inference is performed within the Bayesian framework, using an efficient Markov chain Monte Carlo algorithm. The proposed method is compared with the functional principal component analysis method in simulations and applied to a study of Alzheimer's disease.