mlsanityData to 7 Oct 2026

Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequality

arXiv 2407.17949 ↗First posted 25 Jul 2024stat.ML cs.LG math.OCcited by 1

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Abstract (arXiv)

We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in Euclidean spaces to the EM algorithm, via its representation as coordinate-wise minimization of the free energy. In so doing, we obtain finite sample error bounds and exponential convergence of the EM algorithm under a natural generalisation of the log-Sobolev inequality. We further show that this framework naturally extends to several variants of EM, offering a unified approach for studying such algorithms.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 21 of its 66 references that are in the map. First posted on arXiv 25 Jul 2024.

Builds on

21 of 66 references.

References · 21

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  2. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  3. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  4. 2014Statistical guarantees for the EM algorithm: From population to sample-based analysiscited by 131
  5. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  6. 2019On the geometry of Stein variational gradient descentcited by 82
  7. 2018Singularity, Misspecification, and the Convergence Rate of EMcited by 38
  8. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 33
  9. 2016Global analysis of Expectation Maximization for mixtures of two Gaussianscited by 31
  10. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  11. 2020Homeomorphic-Invariance of EM: Non-Asymptotic Convergence in KL Divergence for Exponential Families via Mirror Descentcited by 18
  12. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
9 more
  1. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  2. 2019On the Global Convergence of (Fast) Incremental Expectation Maximization Methodscited by 12
  3. 2023Momentum Particle Maximum Likelihoodcited by 12
  4. 2016Simultaneous Clustering and Estimation of Heterogeneous Graphical Modelscited by 10
  5. 2024Proximal Interacting Particle Langevin Algorithmscited by 8
  6. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
  7. 2014High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normalitycited by 6
  8. 2021Comparison of Markov chains via weak Poincar'e inequalities with application to pseudo-marginal MCMCcited by 5
  9. 2019On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spacescited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Wasserstein Contraction of Coordinate Ascent Variational Inferencecited by 1