High-Dimensional Robust Scalar-On-Image Regression via Thresholding Function and Nonconvex Learning

• Activity Number: 603 - New Development on Statistics in Imaging
• Type: Topic Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Imaging
• Author(s): Bingyuan Liu* and Qi Zhang and Lingzhou Xue and Jian Kang and Peter X.K. Song
• Companies: Pennsylvania State University and Nankai University and Pennsylvania State University and University of Michigan and School of Public Health, University of Michigan
• Keywords: Scalar-on-Image regression; Robust estimation; Thresholding function; Nonconvex optimization; Group penalty; fMRI data

Abstract

In neuroimaging studies, regression models are widely used to study the relationship between the imaging features and clinical outcome. It is a very challenging problem since scale-on-image regression models are usually high-dimensional, having group structure, and with many outliers.

To tackle with these challenges, proper regularized sparse regression estimator is desired. L0-regularization has appealing asymptotic properties but are unrealistic to implement. In this paper, motivated by the hard thresholding property of L0-penalized solution, we propose a novel estimator via adding thresholding function in loss. And we also incorporate robust huber loss and group lasso penalty into the estimator. By analyzing the landscape of this nonconvex loss, we establish the consistency of estimator and uniqueness of the minimizer, when the dimensionality grow exponentially with the sample size. Then we adopt composite gradient descent algorithm to solve the problem, and prove the convergence of the algorithm in our setting. Further we illustrate that our estimator performs well in simulation and analysis of fMRI data in the Autism Brain Imaging Data Exchange study.