Robust High-Dimensional Regression with Coefficient Thresholding and its Application to Imaging Data Analysis.

Area of Science:

• Statistics
• Machine Learning
• Neuroimaging Analysis

Background:

• High-dimensional data analysis is crucial for real-world applications like neuroimaging.
• Existing methods struggle with complex dependencies, heavy tails, and outliers in data.
• Robust statistical techniques are needed for reliable analysis of such datasets.

Purpose of the Study:

• To propose a novel robust high-dimensional regression method.
• To address challenges posed by complex predictor dependencies and outcome outliers.
• To enhance the analysis of neuroimaging data in psychiatric research.

Main Methods:

• Introduced a robust high-dimensional regression with coefficient thresholding.
• Utilized a nonconvex estimation procedure with a thresholding function and Huber loss.
• Developed theoretical analysis of risk functions for statistical consistency and convergence.
• Extended the method to incorporate spatial information.

Main Results:

• The proposed method demonstrates robustness against heavy tails and outliers.
• Theoretical analysis confirms statistical consistency and computational convergence.
• Simulation studies validate the finite-sample performance of the method.
• Successfully applied to a scalar-on-image regression for psychiatric disorder analysis using ABCD study data.

Conclusions:

• The novel robust regression method offers a powerful tool for high-dimensional data analysis.
• It effectively handles complex dependencies and data anomalies, improving reliability.
• The method shows promise for neuroimaging and psychiatric research, particularly with functional MRI data.