mlsanityData to 7 Oct 2026

Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression

arXiv 1810.05752 ↗First posted 12 Oct 2018stat.ML cs.LG math.STcited by 25

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Abstract (arXiv)

The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that EM enjoys global convergence for Gaussian Mixture Models. For Mixed Linear Regression, however, only local convergence results have been established, and those only for the high SNR regime. We show here that EM converges for mixed linear regression with two components (it is known that it may fail to converge for three or more), and moreover that this convergence holds for random initialization. Our analysis reveals that EM exhibits very different behavior in Mixed Linear Regression from its behavior in Gaussian Mixture Models, and hence our proofs require the development of several new ideas.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Oct 2018.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 8; 2024: 6; 2025: 0; 2026: 1.

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  1. 2023Demystifying Softmax Gating Function in Gaussian Mixture of Expertscited by 33
  2. 2023Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Expertscited by 28
  3. 2023A General Theory for Softmax Gating Multinomial Logistic Mixture of Expertscited by 23
  4. 2022Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Modelscited by 22
  5. 2023Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Expertscited by 17
  6. 2022On Learning Mixture of Linear Regressions in the Non-Realizable Settingcited by 10
  7. 2022Prediction Sets for High-Dimensional Mixture of Experts Modelscited by 8
  8. 2021A Wasserstein Minimax Framework for Mixed Linear Regressioncited by 7
  9. 2021The EM Algorithm is Adaptively-Optimal for Unbalanced Symmetric Gaussian Mixturescited by 6
  10. 2024Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Modelscited by 6
  11. 2023Imbalanced Mixed Linear Regressioncited by 3
  12. 2021High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guaranteescited by 2
13 more
  1. 2022Support Recovery in Mixture Models with Sparse Parameterscited by 2
  2. 2022Beyond EM Algorithm on Over-specified Two-Component Location-Scale Gaussian Mixturescited by 2
  3. 2022EM's Convergence in Gaussian Latent Tree Modelscited by 2
  4. 2024Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffscited by 2
  5. 2024Learning Mixtures of Experts with EM: A Mirror Descent Perspectivecited by 2
  6. 2021Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Modelscited by 1
  7. 2023Sharp analysis of EM for learning mixtures of pairwise differencescited by 1
  8. 2023EM for Mixture of Linear Regression with Clustered Datacited by 1
  9. 2023Global Convergence of Online Identification for Mixed Linear Regressioncited by 1
  10. 2024Agnostic Learning of Mixed Linear Regressions with EM and AM Algorithmscited by 1
  11. 2024In-context Learning for Mixture of Linear Regressions: Existence, Generalization and Training Dynamicscited by 1
  12. 2024Fast convergence of a Federated Expectation-Maximization Algorithmcited by 0
  13. 2026Expectation Maximization (EM) Converges for General Agnostic Mixturescited by 0