Robust Learning of Mixtures of Gaussians
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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.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jul 2020.
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Citing papers per year: 2021: 6; 2022: 1; 2023: 4; 2024: 1; 2025: 2; 2026: 1.
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- 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 56
- 2021Clustering Mixtures with Almost Optimal Separation in Polynomial Timecited by 28
- 2021Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimationcited by 21
- 2021Learning GMMs with Nearly Optimal Robustness Guaranteescited by 12
- 2022Tensor Moments of Gaussian Mixture Models: Theory and Applicationscited by 7
- 2024Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Modelscited by 5
- 2021Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussianscited by 4
- 2021Robust Model Selection and Nearly-Proper Learning for GMMscited by 3
- 2023Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separationcited by 3
- 2025Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behaviorcited by 3
- 2023Big Learning Expectation Maximizationcited by 2
- 2021Robust Voting Rules from Algorithmic Robust Statisticscited by 1
- 2026Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms8 Jan 2026
- 2025Learning High-dimensional Gaussians from Censored Data28 Apr 2025
- 2025Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behavior26 Mar 2025
- 2024Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Models23 Nov 2024
- 2023Big Learning Expectation Maximization19 Dec 2023
- 2023Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separation19 Dec 2023
- 2023Learning Mixtures of Gaussians Using the DDPM Objective3 Jul 2023
- 2023A Spectral Algorithm for List-Decodable Covariance Estimation in Relative Frobenius Norm1 May 2023
- 2022Tensor Moments of Gaussian Mixture Models: Theory and Applications14 Feb 2022
- 2021Robust Voting Rules from Algorithmic Robust Statistics13 Dec 2021
- 2021Clustering Mixtures with Almost Optimal Separation in Polynomial Time1 Dec 2021
- 2021Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians2 Sep 2021
3 more
- 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 56
- 2023Learning Mixtures of Gaussians Using the DDPM Objective3 Jul 2023
- 2021Clustering Mixtures with Almost Optimal Separation in Polynomial Timecited by 28
- 2021Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimationcited by 21
- 2021Learning GMMs with Nearly Optimal Robustness Guaranteescited by 12
- 2022Tensor Moments of Gaussian Mixture Models: Theory and Applicationscited by 7
- 2024Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Modelscited by 5
- 2021Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussianscited by 4
- 2021Robust Model Selection and Nearly-Proper Learning for GMMscited by 3
- 2023Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separationcited by 3
- 2025Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behaviorcited by 3
- 2023Big Learning Expectation Maximizationcited by 2
- 2021Robust Voting Rules from Algorithmic Robust Statisticscited by 1
- 2023A Spectral Algorithm for List-Decodable Covariance Estimation in Relative Frobenius Normcited by 1
12 most cited of 14 All 14 (JSON)
- 2026Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms8 Jan 2026
- 2025Learning High-dimensional Gaussians from Censored Data28 Apr 2025
- 2025Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behavior26 Mar 2025
- 2024Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Models23 Nov 2024
- 2023Big Learning Expectation Maximization19 Dec 2023
- 2023Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separation19 Dec 2023
- 2023A Spectral Algorithm for List-Decodable Covariance Estimation in Relative Frobenius Norm1 May 2023
- 2022Tensor Moments of Gaussian Mixture Models: Theory and Applications14 Feb 2022
- 2021Robust Voting Rules from Algorithmic Robust Statistics13 Dec 2021
- 2021Clustering Mixtures with Almost Optimal Separation in Polynomial Time1 Dec 2021
- 2021Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians2 Sep 2021
- 2021Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation16 Jun 2021
12 newest of 14 All 14 (JSON)