# Robust Learning of Mixtures of Gaussians

arXiv: https://arxiv.org/abs/2007.05912 · HTML: https://mlsanity.com/paper/2007.05912/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2020.

## Built on by (most cited first, 15 of 15)

- [Learning Mixtures of Gaussians Using the DDPM Objective](https://mlsanity.com/paper/2307.01178/) (2023)
- [Clustering Mixtures with Almost Optimal Separation in Polynomial Time](https://mlsanity.com/paper/2112.00706/) (2021)
- [Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation](https://mlsanity.com/paper/2106.08537/) (2021)
- [Learning GMMs with Nearly Optimal Robustness Guarantees](https://mlsanity.com/paper/2104.09665/) (2021)
- [Tensor Moments of Gaussian Mixture Models: Theory and Applications](https://mlsanity.com/paper/2202.06930/) (2022)
- [Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Models](https://mlsanity.com/paper/2411.15669/) (2024)
- [Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians](https://mlsanity.com/paper/2109.01064/) (2021)
- [Robust Model Selection and Nearly-Proper Learning for GMMs](https://mlsanity.com/paper/2106.02774/) (2021)
- [Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separation](https://mlsanity.com/paper/2312.11769/) (2023)
- [Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behavior](https://mlsanity.com/paper/2503.20193/) (2025)
- [Big Learning Expectation Maximization](https://mlsanity.com/paper/2312.11926/) (2023)
- [Learning High-dimensional Gaussians from Censored Data](https://mlsanity.com/paper/2504.19446/) (2025)
- [Robust Voting Rules from Algorithmic Robust Statistics](https://mlsanity.com/paper/2112.06380/) (2021)
- [A Spectral Algorithm for List-Decodable Covariance Estimation in Relative Frobenius Norm](https://mlsanity.com/paper/2305.00966/) (2023)
- [Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms](https://mlsanity.com/paper/2601.05157/) (2026)

## Abstract (arXiv)

We resolve one of the major outstanding problems in robust statistics. In particular, if X is an evenly weighted mixture of two arbitrary d-dimensional Gaussians, we devise a polynomial time algorithm that given access to samples from X an eps-fraction of which have been adversarially corrupted, learns X to error poly(eps) in total variation distance.