# An integrated perspective of robustness in regression through the lens of the bias-variance trade-off

arXiv: https://arxiv.org/abs/2407.10418 · HTML: https://mlsanity.com/paper/2407.10418/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 16 of 16)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [DORO: Distributional and Outlier Robust Optimization](https://mlsanity.com/paper/2106.06142/) (2021)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Overparameterized Linear Regression under Adversarial Attacks](https://mlsanity.com/paper/2204.06274/) (2022)
- [Regularization properties of adversarially-trained linear regression](https://mlsanity.com/paper/2310.10807/) (2023)
- [Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation](https://mlsanity.com/paper/1910.10583/) (2019)
- [The Trimmed Lasso: Sparsity and Robustness](https://mlsanity.com/paper/1708.04527/) (2017)
- [Calibration of Distributionally Robust Empirical Optimization Models](https://mlsanity.com/paper/1711.06565/) (2017)
- [Sup-Norm Convergence of Deep Neural Network Estimator for Nonparametric Regression by Adversarial Training](https://mlsanity.com/paper/2307.04042/) (2023)
- [Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties](https://mlsanity.com/paper/1505.05257/) (2015)
- [A Greedy and Optimistic Approach to Clustering with a Specified Uncertainty of Covariates](https://mlsanity.com/paper/2204.08205/) (2022)

## Abstract (arXiv)

This paper presents an integrated perspective on robustness in regression. Specifically, we examine the relationship between traditional outlier-resistant robust estimation and robust optimization, which focuses on parameter estimation resistant to imaginary dataset-perturbations. While both are commonly regarded as robust methods, these concepts demonstrate a bias-variance trade-off, indicating that they follow roughly converse strategies.