# A Bayesian Robust Regression Method for Corrupted Data Reconstruction

arXiv: https://arxiv.org/abs/2212.12787 · HTML: https://mlsanity.com/paper/2212.12787/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 46 references that are in the map.
- First posted on arXiv 24 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [Robust Estimation via Robust Gradient Estimation](https://mlsanity.com/paper/1802.06485/) (2018)
- [Efficient Algorithms and Lower Bounds for Robust Linear Regression](https://mlsanity.com/paper/1806.00040/) (2018)
- [Robust regression with covariate filtering: Heavy tails and adversarial contamination](https://mlsanity.com/paper/2009.12976/) (2020)
- [Robust Regression via Hard Thresholding](https://mlsanity.com/paper/1506.02428/) (2015)
- [Optimal Robust Linear Regression in Nearly Linear Time](https://mlsanity.com/paper/2007.08137/) (2020)
- [Adaptive Hard Thresholding for Near-optimal Consistent Robust Regression](https://mlsanity.com/paper/1903.08192/) (2019)
- [Online Robust Regression via SGD on the l1 loss](https://mlsanity.com/paper/2007.00399/) (2020)
- [Knowledge Matters: Importance of Prior Information for Optimization](https://mlsanity.com/paper/1301.4083/) (2013)
- [Robust Regression Revisited: Acceleration and Improved Estimation Rates](https://mlsanity.com/paper/2106.11938/) (2021)
- [Fast and Robust Least Squares Estimation in Corrupted Linear Models](https://mlsanity.com/paper/1406.3175/) (2014)
- [A General Method for Robust Bayesian Modeling](https://mlsanity.com/paper/1510.05078/) (2015)
- [Compressed Sensing with Adversarial Sparse Noise via L1 Regression](https://mlsanity.com/paper/1809.08055/) (2018)
- [Robust Gaussian Process Regression for Real-Time High Precision GPS Signal Enhancement](https://mlsanity.com/paper/1906.01095/) (2019)
- [Bayesian Robustness: A Nonasymptotic Viewpoint](https://mlsanity.com/paper/1907.11826/) (2019)

## Abstract (arXiv)

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.