mlsanityData to 7 Oct 2026

Global analysis of Expectation Maximization for mixtures of two Gaussians

arXiv 1608.07630 ↗First posted 26 Aug 2016math.ST cs.LG stat.COcited by 31

Not on the map. Why?

Abstract (arXiv)

Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from any maximizer. This article addresses this disconnect between the statistical principles behind EM and its algorithmic properties. Specifically, it provides a global analysis of EM for specific models in which the observations comprise an i.i.d. sample from a mixture of two Gaussians. This is achieved by (i) studying the sequence of parameters from idealized execution of EM in the infinite sample limit, and fully characterizing the limit points of the sequence in terms of the initial parameters; and then (ii) based on this convergence analysis, establishing statistical consistency (or lack thereof) for the actual sequence of parameters produced by EM.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Aug 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2018: 1; 2019: 0; 2020: 1; 2021: 5; 2022: 7; 2023: 8; 2024: 5; 2025: 2; 2026: 2.

31 papers.

Sort:

By area:

  1. 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 56
  2. 2021Clustering Mixtures with Almost Optimal Separation in Polynomial Timecited by 28
  3. 2024A theoretical perspective on mode collapse in variational inferencecited by 14
  4. 2018Breaking the gridlock in Mixture-of-Experts: Consistent and Efficient Algorithmscited by 13
  5. 2021Improved Convergence Guarantees for Learning Gaussian Mixture Models by EM and Gradient EMcited by 11
  6. 2020Provable Hierarchical Imitation Learning via EMcited by 10
  7. 2023Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithmscited by 7
  8. 2021The EM Algorithm is Adaptively-Optimal for Unbalanced Symmetric Gaussian Mixturescited by 6
  9. 2022Optimal Estimation and Computational Limit of Low-rank Gaussian Mixturescited by 6
  10. 2024Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Modelscited by 6
  11. 2021A sampling-based approach for efficient clustering in large datasetscited by 4
  12. 2021High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guaranteescited by 2
19 more
  1. 2022A Geometric Approach to k-meanscited by 2
  2. 2022Beyond EM Algorithm on Over-specified Two-Component Location-Scale Gaussian Mixturescited by 2
  3. 2022On the Semi-supervised Expectation Maximizationcited by 2
  4. 2022EM's Convergence in Gaussian Latent Tree Modelscited by 2
  5. 2023Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learningcited by 2
  6. 2023Learning Mixtures of Gaussians with Censored Datacited by 2
  7. 2023Big Learning Expectation Maximizationcited by 2
  8. 2025Convergence Dynamics of Over-Parameterized Score Matching for a Single Gaussiancited by 2
  9. 2022An Exponentially Increasing Step-size for Parameter Estimation in Statistical Modelscited by 1
  10. 2023Sharp analysis of EM for learning mixtures of pairwise differencescited by 1
  11. 2023EM for Mixture of Linear Regression with Clustered Datacited by 1
  12. 2023Joint Problems in Learning Multiple Dynamical Systemscited by 1
  13. 2024Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequalitycited by 1
  14. 2024Partial Distribution Matching via Partial Wasserstein Adversarial Networkscited by 1
  15. 2024In-context Learning for Mixture of Linear Regressions: Existence, Generalization and Training Dynamicscited by 1
  16. 2022Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Modelscited by 0
  17. 2025Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transportcited by 0
  18. 2026Individual-heterogeneous sub-Gaussian Mixture Modelscited by 0
  19. 2026Local linear convergence of gradient methods for overparameterized Gaussian mixturescited by 0