# On the robust learning mixtures of linear regressions

arXiv: https://arxiv.org/abs/2305.15317 · HTML: https://mlsanity.com/paper/2305.15317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 9 of 9)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Mixture Models, Robustness, and Sum of Squares Proofs](https://mlsanity.com/paper/1711.07454/) (2017)
- [List-Decodable Robust Mean Estimation and Learning Mixtures of Spherical Gaussians](https://mlsanity.com/paper/1711.07211/) (2017)
- [Learning Mixtures of Linear Regressions with Nearly Optimal Complexity](https://mlsanity.com/paper/1802.07895/) (2018)
- [Small Covers for Near-Zero Sets of Polynomials and Learning Latent Variable Models](https://mlsanity.com/paper/2012.07774/) (2020)
- [EM Converges for a Mixture of Many Linear Regressions](https://mlsanity.com/paper/1905.12106/) (2019)
- [Learning Mixtures of Linear Regressions in Subexponential Time via Fourier Moments](https://mlsanity.com/paper/1912.07629/) (2019)
- [Spectral Experts for Estimating Mixtures of Linear Regressions](https://mlsanity.com/paper/1306.3729/) (2013)
- [Estimating the Coefficients of a Mixture of Two Linear Regressions by Expectation Maximization](https://mlsanity.com/paper/1704.08231/) (2017)

## Abstract (arXiv)

In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be obtained under some mild separation condition. This algorithm has significantly better robustness than the previous result.