# Robust penalized least squares of depth trimmed residuals regression for high-dimensional data

arXiv: https://arxiv.org/abs/2309.01666 · HTML: https://mlsanity.com/paper/2309.01666/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 66 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [Adaptive Huber Regression](https://mlsanity.com/paper/1706.06991/) (2017)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [A critical review of LASSO and its derivatives for variable selection under dependence among covariates](https://mlsanity.com/paper/2012.11470/) (2020)
- [Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies](https://mlsanity.com/paper/2112.08471/) (2021)
- [The shooting S-estimator for robust regression](https://mlsanity.com/paper/1506.01223/) (2015)
- [Robust and sparse estimation methods for high dimensional linear and logistic regression](https://mlsanity.com/paper/1703.04951/) (2017)
- [Non-asymptotic analysis and inference for an outlyingness induced winsorized mean](https://mlsanity.com/paper/2105.02337/) (2021)
- [Least sum of squares of trimmed residuals regression](https://mlsanity.com/paper/2202.10329/) (2022)

## Abstract (arXiv)

Challenges with data in the big-data era include (i) the dimension p is often larger than the sample size n (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional methods inapplicable. Thus, it attracts tremendous attention from statistics, computer science, and bio-medical communities. Numerous penalized regression methods have been introduced as modern methods for analyzing high-dimensional data. Disproportionate attention has been paid to the challenge (ii) though. Penalized regression methods can do their job very well and are expected to handle the challenge (ii) simultaneously. Most of them, however, can break down by a single outlier (or single adversary contaminated point) as revealed in this article. The latter systematically examines leading penalized regression methods in the literature in terms of their robustness, provides quantitative assessment, and reveals that most of them can break down by a single outlier. Consequently, a novel robust penalized regression method based on the least sum of squares of depth trimmed residuals is proposed and studied carefully. Experiments with simulated and real data reveal that the newly proposed method can outperform some leading competitors in estimation and prediction accuracy in the cases considered.