  We discuss 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. 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 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 can be
downloaded at https://cran.r-project.org/web/packages/SQUAREM/index.html.
