SQUAREM: An R package for off-the-shelf acceleration of EM, MM and other EM-like monotone algorithms

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We discuss the R package SQUAREM for accelerating iterative algorithms which exhibit slow, monotone convergence. These include the well-known expectation-maximization algorithm, majorize-minimize (MM), and other EM-like algorithms such as expectation conditional maximization, and generalized EM algorithms. We demonstrate the simplicity, generality, and power of SQUAREM through a wide array of applications of EM/MM problems, including binary Poisson mixture, factor analysis, interval censoring, genetics admixture, and logistic regression maximum likelihood estimation (an MM problem). We show that SQUAREM is easy to apply, and can accelerate any fixed-point, smooth, contraction mapping with linear convergence rate. The squared iterative scheme (SQUAREM) algorithm provides significant speed-up of EM-like algorithms. The margin of the advantage for SQUAREM is especially huge for high-dimensional problems or when the EM step is relatively time-consuming to evaluate. SQUAREM can be used off-the-shelf since there is no need for the user to tweak any control parameters to optimize performance. Given its remarkable ease of use, SQUAREM may be considered as a default accelerator for slowly converging EM-like algorithms. All the comparisons of CPU computing time in the paper are made on a quad-core 2.3 GHz Intel Core i7 Mac computer. R package SQUAREM is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=SQUAREM/.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalJournal of Statistical Software
StatePublished - 2020


  • Convergence acceleration
  • EM algorithm
  • Extrapolation methods
  • Fixed-point iteration
  • High dimensional models
  • Monotone convergence
  • Optimization

ASJC Scopus subject areas

  • Software
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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