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

arXiv: https://arxiv.org/abs/2109.14856 · HTML: https://mlsanity.com/paper/2109.14856/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 69 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 15 of 15)

- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [The Landscape of Empirical Risk for Non-convex Losses](https://mlsanity.com/paper/1607.06534/) (2016)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [On Iterative Hard Thresholding Methods for High-dimensional M-Estimation](https://mlsanity.com/paper/1410.5137/) (2014)
- [Statistical consistency and asymptotic normality for high-dimensional robust M-estimators](https://mlsanity.com/paper/1501.00312/) (2015)
- [Support recovery without incoherence: A case for nonconvex regularization](https://mlsanity.com/paper/1412.5632/) (2014)
- [Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow](https://mlsanity.com/paper/1506.03382/) (2015)
- [Can parametric statistical methods be trusted for fMRI based group studies?](https://mlsanity.com/paper/1511.01863/) (2015)
- [Optimal computational and statistical rates of convergence for sparse nonconvex learning problems](https://mlsanity.com/paper/1306.4960/) (2013)
- [Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process](https://mlsanity.com/paper/1604.03192/) (2016)
- [Scale calibration for high-dimensional robust regression](https://mlsanity.com/paper/1811.02096/) (2018)
- [Bayesian network marker selection via the thresholded graph Laplacian Gaussian prior](https://mlsanity.com/paper/1810.00274/) (2018)
- [Thresholded Multiscale Gaussian Processes with Application to Bayesian Feature Selection for Massive Neuroimaging Data](https://mlsanity.com/paper/1504.06074/) (2015)
- [Asymptotic equivalence of regularization methods in thresholded parameter space](https://mlsanity.com/paper/1605.03310/) (2016)

## Built on by (most cited first, 1 of 1)

- [Statistical Opportunities in Neuroimaging](https://mlsanity.com/paper/2602.12974/) (2026)

## Abstract (arXiv)

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust high-dimensional regression with coefficient thresholding, in which an efficient nonconvex estimation procedure is proposed through a thresholding function and the robust Huber loss. The proposed regularization method accounts for complex dependence structures in predictors and is robust against outliers in outcomes. Theoretically, we analyze rigorously the landscape of the population and empirical risk functions for the proposed method. The fine landscape enables us to establish both {statistical consistency and computational convergence} under the high-dimensional setting. The finite-sample properties of the proposed method are examined by extensive simulation studies. An illustration of real-world application concerns a scalar-on-image regression analysis for an association of psychiatric disorder measured by the general factor of psychopathology with features extracted from the task functional magnetic resonance imaging data in the Adolescent Brain Cognitive Development study.