Title: Sparse learning and structure identification for ultra-high-dimensional image-on-scalar regression
Authors: Xinyi Li - Clemson University (United States) [presenting]
Lily Wang - Iowa State University (United States)
Huixia Judy Wang - George Washington University (United States)
Abstract: High-dimensional image-on-scalar regression is proposed, where the spatial heterogeneity of covariate effects on imaging responses is investigated via a flexible partially linear spatially varying coefficient model. To tackle the challenges of spatial smoothing over the imaging response's complex domain consisting of regions of interest, the proposed method approximates the spatially varying coefficient functions via bivariate spline functions over triangulation. The aim is to first study estimation when the active constant coefficients and varying coefficient functions are known in advance, then a unified approach is developed for simultaneous sparse learning (i.e., variable selection) and model structure identification (i.e., determination of spatially varying vs. constant coefficients) in the presence of ultra-high-dimensional covariates. The proposed method can identify zero, nonzero constant and spatially varying components correctly and efficiently. The estimators of constant coefficients and varying coefficient functions are consistent and asymptotically normal. The method is evaluated by Monte Carlo simulation studies and applied to a dataset provided by the Alzheimer's Disease Neuroimaging Initiative (ADNI).