# Robust polynomial regression up to the information theoretic limit

arXiv: https://arxiv.org/abs/1708.03257 · HTML: https://mlsanity.com/paper/1708.03257/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [Improved Active Learning via Dependent Leverage Score Sampling](https://mlsanity.com/paper/2310.04966/) (2023)
- [Distribution-Independent Regression for Generalized Linear Models with Oblivious Corruptions](https://mlsanity.com/paper/2309.11657/) (2023)
- [Outlier Robust Multivariate Polynomial Regression](https://mlsanity.com/paper/2403.09465/) (2024)

## Abstract (arXiv)

We consider the problem of robust polynomial regression, where one receives samples (xi, yi) that are usually within σ of a polynomial y = p(x), but have a ρ chance of being arbitrary adversarial outliers. Previously, it was known how to efficiently estimate p only when ρ < frac1log d. We give an algorithm that works for the entire feasible range of ρ < 1/2, while simultaneously improving other parameters of the problem. We complement our algorithm, which gives a factor 2 approximation, with impossibility results that show, for example, that a 1.09 approximation is impossible even with infinitely many samples.