# A concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise

arXiv: https://arxiv.org/abs/1702.05063 · HTML: https://mlsanity.com/paper/1702.05063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2017.

## Built on by (most cited first, 1 of 1)

- [On the Nonasymptotic Scaling Guarantee of Hyperparameter Estimation in Inhomogeneous, Weakly-Dependent Complex Network Dynamical Systems](https://mlsanity.com/paper/2601.15603/) (2026)

## Abstract (arXiv)

We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function that controls the local suprema of the empirical process. So far, only the case of linear contrast estimation was tackled in the literature with this level of generality on the model. We solve here the case of a quadratic contrast, by separating the behavior of a linearized empirical process and the empirical process driven by the squares of functions of models.