A Bayesian Robust Regression Method for Corrupted Data Reconstruction

TL;DR

This paper introduces two novel robust regression algorithms, TRIP and BRHT, that incorporate prior knowledge and Bayesian reweighting to effectively resist adaptive adversarial attacks and improve data reconstruction accuracy.

Contribution

The paper develops the TRIP and BRHT algorithms, which enhance robustness against adaptive attacks by integrating prior information and Bayesian reweighting, with proven convergence and superior experimental performance.

Findings

Algorithms outperform benchmarks under various dataset attacks.

Proven convergence under mild conditions.

Effective in real-world space solar array data recovery.

Abstract

Because of the widespread existence of noise and data corruption, recovering the true regression parameters with a certain proportion of corrupted response variables is an essential task. Methods to overcome this problem often involve robust least-squares regression, but few methods perform well when confronted with severe adaptive adversarial attacks. In many applications, prior knowledge is often available from historical data or engineering experience, and by incorporating prior information into a robust regression method, we develop an effective robust regression method that can resist adaptive adversarial attacks. First, we propose the novel TRIP (hard Thresholding approach to Robust regression with sImple Prior) algorithm, which improves the breakdown point when facing adaptive adversarial attacks. Then, to improve the robustness and reduce the estimation error caused by the inclusion of priors, we use the idea of Bayesian reweighting to construct the more robust BRHT (robust Bayesian Reweighting regression via Hard Thresholding) algorithm. We prove the theoretical convergence of the proposed algorithms under mild conditions, and extensive experiments show that under different types of dataset attacks, our algorithms outperform other benchmark ones. Finally, we apply our methods to a data-recovery problem in a real-world application involving a space solar array, demonstrating their good applicability.