# Statistical Robustness of Interval CVaR Based Regression Models under Perturbation and Contamination

arXiv: https://arxiv.org/abs/2601.11420 · HTML: https://mlsanity.com/paper/2601.11420/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 16 Jan 2026.

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

- [Learning by Minimizing the Sum of Ranked Range](https://mlsanity.com/paper/2010.01741/) (2020)
- [Distributionally Robust Optimization and Robust Statistics](https://mlsanity.com/paper/2401.14655/) (2024)
- [Sum of Ranked Range Loss for Supervised Learning](https://mlsanity.com/paper/2106.03300/) (2021)
- [Large-scale Optimization of Partial AUC in a Range of False Positive Rates](https://mlsanity.com/paper/2203.01505/) (2022)
- [Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation](https://mlsanity.com/paper/2201.00508/) (2022)
- [Breakdown Point of Robust Support Vector Machine](https://mlsanity.com/paper/1409.0934/) (2014)
- [Statistical Robustness of Empirical Risks in Machine Learning](https://mlsanity.com/paper/2005.08458/) (2020)
- [Statistical Robustness of Kernel Learning Estimator with Respect to Data Perturbation](https://mlsanity.com/paper/2406.10555/) (2024)

## Abstract (arXiv)

Robustness under perturbation and contamination is a prominent issue in statistical learning. We address the robust nonlinear regression based on the so-called interval conditional value-at-risk (In-CVaR), which is introduced to enhance robustness by trimming extreme losses. While recent literature shows that the In-CVaR based statistical learning exhibits superior robustness performance than classical robust regression models, its theoretical robustness analysis for nonlinear regression remains largely unexplored. We rigorously quantify robustness under contamination, with a unified study of distributional breakdown point for a broad class of regression models, including linear, piecewise affine and neural network models with ℓ1, ℓ2 and Huber losses. Moreover, we analyze the qualitative robustness of the In-CVaR based estimator under perturbation. We show that under several minor assumptions, the In-CVaR based estimator is qualitatively robust in terms of the Prokhorov metric if and only if the largest portion of losses is trimmed. Overall, this study analyzes robustness properties of In-CVaR based nonlinear regression models under both perturbation and contamination, which illustrates the advantages of In-CVaR risk measure over conditional value-at-risk and expectation for robust regression in both theory and numerical experiments.